This chapter introduces the t-test, a statistical tool used to test for significant differences between the means of two groups. It discusses the independent t-test for comparing means of two independent samples, and the dependent or paired t-test for comparing means of the same sample tested twice. The chapter covers the assumptions of the t-test, how to formulate hypotheses, compute t-values, and interpret results based on critical values. Key aspects include the formula for computing the t-statistic and standard error, conducting significance tests using t-distribution tables, and checking assumptions such as normality and homogeneity of variance.
DATA ANALYSIS in research methodology (1)-1.pptxSuyogpatil86
This document discusses various methods for collecting data in research, including telephone interviews, questionnaires, and secondary data. It provides details on the merits and limitations of telephone interviews, which allow flexible and fast collection of information but restrict responses to those with phone access. Questionnaires are popular due to low cost, but have low response rates and risk ambiguous answers. Secondary data can be published or unpublished, and must be carefully evaluated for reliability, suitability, and adequacy for the research purpose. The document also covers factors to consider when selecting appropriate data collection methods, such as the research scope and objectives, available funds and time, and required precision. It describes data processing steps like editing raw data to detect and correct errors.
This document discusses different types of t-tests used to compare means: one sample t-tests, independent samples t-tests, and paired samples t-tests. It provides examples and steps for conducting each type of t-test in SPSS. Key points include that one sample t-tests compare a sample mean to a known value, independent samples t-tests compare means between two unrelated groups, and paired samples t-tests compare means within the same group across two time points or conditions. The document also outlines assumptions, how to interpret output and p-values, and how to report results for each t-test. Three cases are presented to demonstrate application of each t-test type.
Section 1 Data File DescriptionThe fictional data represents a te.docxbagotjesusa
This document describes using dummy predictor variables in multiple regression analysis. It provides an example using hypothetical data on faculty salaries. Key points:
- Dummy variables allow inclusion of categorical predictors like gender or political party in regression by coding them numerically.
- For k categories, k-1 dummy variables are needed. This example uses gender (coded 0,1) and college (coded 1,2,3) as predictors.
- Regression and ANOVA provide equivalent information about differences in mean salaries for gender and across colleges. Dummy variable regression tests are equivalent to ANOVA comparisons.
- The document screens the salary data for violations of regression assumptions like normality before running analyses.
This document provides an overview of a presentation on statistical hypothesis testing using the t-test. It discusses what a t-test is, how to perform a t-test, and provides an example of a t-test comparing spelling test scores of two groups that received different teaching strategies. The document outlines the six steps for conducting statistical hypothesis testing using a t-test: 1) stating the hypotheses, 2) choosing the significance level, 3) determining the critical values, 4) calculating the test statistic, 5) comparing the test statistic to the critical values, and 6) writing a conclusion.
The slides discuss comparing two means to ascertain which mean is of greater statistical significance. In these slides we will learn about three research questions in which the t-test can be used to analyze the data and compare the means from two independent groups, two paired samples, and a sample and a population.
Chi-square tests are great to show if distributions differ or i.docxMARRY7
Chi-square tests are great to show if distributions differ or if two variables interact in producing outcomes. What are some examples of variables that you might want to check using the chi-square tests? What would these results tell you?
DataSee comments at the right of the data set.IDSalaryCompaMidpointAgePerformance RatingServiceGenderRaiseDegreeGender1Grade8231.000233290915.80FAThe ongoing question that the weekly assignments will focus on is: Are males and females paid the same for equal work (under the Equal Pay Act)? 10220.956233080714.70FANote: to simplfy the analysis, we will assume that jobs within each grade comprise equal work.11231.00023411001914.80FA14241.04323329012160FAThe column labels in the table mean:15241.043233280814.90FAID – Employee sample number Salary – Salary in thousands 23231.000233665613.31FAAge – Age in yearsPerformance Rating – Appraisal rating (Employee evaluation score)26241.043232295216.21FAService – Years of service (rounded)Gender: 0 = male, 1 = female 31241.043232960413.90FAMidpoint – salary grade midpoint Raise – percent of last raise35241.043232390415.31FAGrade – job/pay gradeDegree (0= BS\BA 1 = MS)36231.000232775314.31FAGender1 (Male or Female)Compa - salary divided by midpoint37220.956232295216.21FA42241.0432332100815.70FA3341.096313075513.60FB18361.1613131801115.61FB20341.0963144701614.81FB39351.129312790615.51FB7411.0254032100815.70FC13421.0504030100214.71FC22571.187484865613.80FD24501.041483075913.81FD45551.145483695815.20FD17691.2105727553130FE48651.1405734901115.31FE28751.119674495914.41FF43771.1496742952015.51FF19241.043233285104.61MA25241.0432341704040MA40251.086232490206.30MA2270.870315280703.90MB32280.903312595405.60MB34280.903312680204.91MB16471.175404490405.70MC27401.000403580703.91MC41431.075402580504.30MC5470.9794836901605.71MD30491.0204845901804.30MD1581.017573485805.70ME4661.15757421001605.51ME12601.0525752952204.50ME33641.122573590905.51ME38560.9825745951104.50ME44601.0525745901605.21ME46651.1405739752003.91ME47621.087573795505.51ME49601.0525741952106.60ME50661.1575738801204.60ME6761.1346736701204.51MF9771.149674910010041MF21761.1346743951306.31MF29721.074675295505.40MF
Week 1Week 1.Measurement and Description - chapters 1 and 21Measurement issues. Data, even numerically coded variables, can be one of 4 levels - nominal, ordinal, interval, or ratio. It is important to identify which level a variable is, asthis impact the kind of analysis we can do with the data. For example, descriptive statistics such as means can only be done on interval or ratio level data.Please list under each label, the variables in our data set that belong in each group.NominalOrdinalIntervalRatiob.For each variable that you did not call ratio, why did you make that decision?2The first step in analyzing data sets is to find some summary descriptive statistics for key variables.For salary, compa, age, performance rating, and service; find the mean, standard deviation, and range for 3 groups: ...
Here are my responses to the guide questions:
1. I decided to teach in SHS because I wanted to help guide students in their transition to college and career. I find it rewarding to support students' personal and academic growth during this important stage of their lives.
2. Two of the most significant experiences I've had teaching Research involve seeing students get excited about their topics and taking ownership of their work. It's amazing to see their eyes light up when they discover something interesting during the research process. I also appreciate witnessing students' confidence grow as they learn to independently plan and conduct research. These experiences are meaningful because they show the positive impact of research skills on student learning and development.
3. One of my most
WEEK 6 – EXERCISES Enter your answers in the spaces pr.docxwendolynhalbert
WEEK 6 – EXERCISES
Enter your answers in the spaces provided. Save the file using your last name as the beginning of the file name (e.g., ruf_week6_exercises) and submit via “Assignments.” When appropriate,
show your work
. You can do the work by hand, scan/take a digital picture, and attach that file with your work.
1
.
A psychotherapist studied whether his clients self-disclosed more while sitting in an easy chair or lying down on a couch. All clients had previously agreed to allow the sessions to be videotaped for research purposes. The therapist randomly assigned 10 clients to each condition. The third session for each client was videotaped and an independent observer counted the clients’ disclosures. The therapist reported that “clients made more disclosures when sitting in easy chairs (
M
= 18.20) than when lying down on a couch (
M
= 14.31),
t
(18) = 2.84,
p
< .05, two-tailed.” Explain these results to a person who understands the
t
test for a single sample but knows nothing about the
t
test for independent means.
2.
A researcher compared the adjustment of adolescents who had been raised in homes that were either very structured or unstructured. Thirty adolescents from each type of family completed an adjustment inventory. The results are reported in the table below. Explain these results to a person who understands the
t
test for a single sample but knows nothing about the
t
test for independent means.
Means on Four Adjustment Scales for
Adolescents from Structured versus Unstructured Homes
Scale
Structured Homes
Unstructured Homes
t
Social Maturity
106.82
113.94
–1.07
School Adjustment
116.31
107.22
2.03*
Identity Development
89.48
94.32
1.93*
Intimacy Development
102.25
104.33
.32
______________________
*
p
< .05
3.
Do men with higher levels of a particular hormone show higher levels of assertiveness? Levels of this hormone were tested in 100 men. The top 10 and the bottom 10 were selected for the study. All participants took part in a laboratory simulation in which they were asked to role-play a person picking his car up from a mechanic’s shop. The simulation was videotaped and later judged by independent raters on each of four types of assertive statements made by the participant. The results are shown in the table below. Explain these results to a person who fully understands the
t
test for a single sample but knows nothing about the
t
test for independent means.
Mean Number of Assertive Statements
Type of Assertive Statement
Group
1
2
3
4
Men with High Levels
2.14
1.16
3.83
0.14
Men with Low Levels
1.21
1.32
2.33
0.38
t
3.81**
0.89
2.03*
0.58
______________________
*
p
< .05;
**
p
< 0.1
4.
A manager of a small store wanted to discourage shoplifters by putting signs around the store saying “Shoplifting is a crime!” However, he wanted to make sure this would not result in customers buying less. To test this, he displayed the signs every other W.
DATA ANALYSIS in research methodology (1)-1.pptxSuyogpatil86
This document discusses various methods for collecting data in research, including telephone interviews, questionnaires, and secondary data. It provides details on the merits and limitations of telephone interviews, which allow flexible and fast collection of information but restrict responses to those with phone access. Questionnaires are popular due to low cost, but have low response rates and risk ambiguous answers. Secondary data can be published or unpublished, and must be carefully evaluated for reliability, suitability, and adequacy for the research purpose. The document also covers factors to consider when selecting appropriate data collection methods, such as the research scope and objectives, available funds and time, and required precision. It describes data processing steps like editing raw data to detect and correct errors.
This document discusses different types of t-tests used to compare means: one sample t-tests, independent samples t-tests, and paired samples t-tests. It provides examples and steps for conducting each type of t-test in SPSS. Key points include that one sample t-tests compare a sample mean to a known value, independent samples t-tests compare means between two unrelated groups, and paired samples t-tests compare means within the same group across two time points or conditions. The document also outlines assumptions, how to interpret output and p-values, and how to report results for each t-test. Three cases are presented to demonstrate application of each t-test type.
Section 1 Data File DescriptionThe fictional data represents a te.docxbagotjesusa
This document describes using dummy predictor variables in multiple regression analysis. It provides an example using hypothetical data on faculty salaries. Key points:
- Dummy variables allow inclusion of categorical predictors like gender or political party in regression by coding them numerically.
- For k categories, k-1 dummy variables are needed. This example uses gender (coded 0,1) and college (coded 1,2,3) as predictors.
- Regression and ANOVA provide equivalent information about differences in mean salaries for gender and across colleges. Dummy variable regression tests are equivalent to ANOVA comparisons.
- The document screens the salary data for violations of regression assumptions like normality before running analyses.
This document provides an overview of a presentation on statistical hypothesis testing using the t-test. It discusses what a t-test is, how to perform a t-test, and provides an example of a t-test comparing spelling test scores of two groups that received different teaching strategies. The document outlines the six steps for conducting statistical hypothesis testing using a t-test: 1) stating the hypotheses, 2) choosing the significance level, 3) determining the critical values, 4) calculating the test statistic, 5) comparing the test statistic to the critical values, and 6) writing a conclusion.
The slides discuss comparing two means to ascertain which mean is of greater statistical significance. In these slides we will learn about three research questions in which the t-test can be used to analyze the data and compare the means from two independent groups, two paired samples, and a sample and a population.
Chi-square tests are great to show if distributions differ or i.docxMARRY7
Chi-square tests are great to show if distributions differ or if two variables interact in producing outcomes. What are some examples of variables that you might want to check using the chi-square tests? What would these results tell you?
DataSee comments at the right of the data set.IDSalaryCompaMidpointAgePerformance RatingServiceGenderRaiseDegreeGender1Grade8231.000233290915.80FAThe ongoing question that the weekly assignments will focus on is: Are males and females paid the same for equal work (under the Equal Pay Act)? 10220.956233080714.70FANote: to simplfy the analysis, we will assume that jobs within each grade comprise equal work.11231.00023411001914.80FA14241.04323329012160FAThe column labels in the table mean:15241.043233280814.90FAID – Employee sample number Salary – Salary in thousands 23231.000233665613.31FAAge – Age in yearsPerformance Rating – Appraisal rating (Employee evaluation score)26241.043232295216.21FAService – Years of service (rounded)Gender: 0 = male, 1 = female 31241.043232960413.90FAMidpoint – salary grade midpoint Raise – percent of last raise35241.043232390415.31FAGrade – job/pay gradeDegree (0= BS\BA 1 = MS)36231.000232775314.31FAGender1 (Male or Female)Compa - salary divided by midpoint37220.956232295216.21FA42241.0432332100815.70FA3341.096313075513.60FB18361.1613131801115.61FB20341.0963144701614.81FB39351.129312790615.51FB7411.0254032100815.70FC13421.0504030100214.71FC22571.187484865613.80FD24501.041483075913.81FD45551.145483695815.20FD17691.2105727553130FE48651.1405734901115.31FE28751.119674495914.41FF43771.1496742952015.51FF19241.043233285104.61MA25241.0432341704040MA40251.086232490206.30MA2270.870315280703.90MB32280.903312595405.60MB34280.903312680204.91MB16471.175404490405.70MC27401.000403580703.91MC41431.075402580504.30MC5470.9794836901605.71MD30491.0204845901804.30MD1581.017573485805.70ME4661.15757421001605.51ME12601.0525752952204.50ME33641.122573590905.51ME38560.9825745951104.50ME44601.0525745901605.21ME46651.1405739752003.91ME47621.087573795505.51ME49601.0525741952106.60ME50661.1575738801204.60ME6761.1346736701204.51MF9771.149674910010041MF21761.1346743951306.31MF29721.074675295505.40MF
Week 1Week 1.Measurement and Description - chapters 1 and 21Measurement issues. Data, even numerically coded variables, can be one of 4 levels - nominal, ordinal, interval, or ratio. It is important to identify which level a variable is, asthis impact the kind of analysis we can do with the data. For example, descriptive statistics such as means can only be done on interval or ratio level data.Please list under each label, the variables in our data set that belong in each group.NominalOrdinalIntervalRatiob.For each variable that you did not call ratio, why did you make that decision?2The first step in analyzing data sets is to find some summary descriptive statistics for key variables.For salary, compa, age, performance rating, and service; find the mean, standard deviation, and range for 3 groups: ...
Here are my responses to the guide questions:
1. I decided to teach in SHS because I wanted to help guide students in their transition to college and career. I find it rewarding to support students' personal and academic growth during this important stage of their lives.
2. Two of the most significant experiences I've had teaching Research involve seeing students get excited about their topics and taking ownership of their work. It's amazing to see their eyes light up when they discover something interesting during the research process. I also appreciate witnessing students' confidence grow as they learn to independently plan and conduct research. These experiences are meaningful because they show the positive impact of research skills on student learning and development.
3. One of my most
WEEK 6 – EXERCISES Enter your answers in the spaces pr.docxwendolynhalbert
WEEK 6 – EXERCISES
Enter your answers in the spaces provided. Save the file using your last name as the beginning of the file name (e.g., ruf_week6_exercises) and submit via “Assignments.” When appropriate,
show your work
. You can do the work by hand, scan/take a digital picture, and attach that file with your work.
1
.
A psychotherapist studied whether his clients self-disclosed more while sitting in an easy chair or lying down on a couch. All clients had previously agreed to allow the sessions to be videotaped for research purposes. The therapist randomly assigned 10 clients to each condition. The third session for each client was videotaped and an independent observer counted the clients’ disclosures. The therapist reported that “clients made more disclosures when sitting in easy chairs (
M
= 18.20) than when lying down on a couch (
M
= 14.31),
t
(18) = 2.84,
p
< .05, two-tailed.” Explain these results to a person who understands the
t
test for a single sample but knows nothing about the
t
test for independent means.
2.
A researcher compared the adjustment of adolescents who had been raised in homes that were either very structured or unstructured. Thirty adolescents from each type of family completed an adjustment inventory. The results are reported in the table below. Explain these results to a person who understands the
t
test for a single sample but knows nothing about the
t
test for independent means.
Means on Four Adjustment Scales for
Adolescents from Structured versus Unstructured Homes
Scale
Structured Homes
Unstructured Homes
t
Social Maturity
106.82
113.94
–1.07
School Adjustment
116.31
107.22
2.03*
Identity Development
89.48
94.32
1.93*
Intimacy Development
102.25
104.33
.32
______________________
*
p
< .05
3.
Do men with higher levels of a particular hormone show higher levels of assertiveness? Levels of this hormone were tested in 100 men. The top 10 and the bottom 10 were selected for the study. All participants took part in a laboratory simulation in which they were asked to role-play a person picking his car up from a mechanic’s shop. The simulation was videotaped and later judged by independent raters on each of four types of assertive statements made by the participant. The results are shown in the table below. Explain these results to a person who fully understands the
t
test for a single sample but knows nothing about the
t
test for independent means.
Mean Number of Assertive Statements
Type of Assertive Statement
Group
1
2
3
4
Men with High Levels
2.14
1.16
3.83
0.14
Men with Low Levels
1.21
1.32
2.33
0.38
t
3.81**
0.89
2.03*
0.58
______________________
*
p
< .05;
**
p
< 0.1
4.
A manager of a small store wanted to discourage shoplifters by putting signs around the store saying “Shoplifting is a crime!” However, he wanted to make sure this would not result in customers buying less. To test this, he displayed the signs every other W.
T test for two independent samples and inductionEmmanuel Buah
Recruitment and selection is important to find people who are a good fit for the organization to reduce costs from high turnover. A good recruitment system should be efficient, effective at finding suitable candidates, and fair by being non-discriminatory. Employers should do human resource planning to forecast needs and match available supply to demand to help with recruitment and development.
STATISTICS : Changing the way we do: Hypothesis testing, effect size, power, ...Musfera Nara Vadia
Researchers should take several steps to make statistical results meaningful:
1. Perform a power analysis to determine adequate sample size and ensure power is above .50, ideally .80. Power is the probability of detecting real effects.
2. Never set the alpha level lower than .05 and try to set it higher to .10 if acceptable.
3. Report effect sizes and confidence intervals to provide context around statistical significance. Effect sizes indicate the magnitude of differences between groups.
Assessment 3 – Hypothesis, Effect Size, Power, and t Tests.docxcargillfilberto
Assessment 3 – Hypothesis, Effect Size, Power, and
t
Tests
Complete the following problems within this Word document. Do not submit other files. Show your work for problem sets that require calculations. Ensure that your answer to each problem is clearly visible. You may want to highlight your answer or use a different type color to set it apart.
Hypothesis, Effect Size, and Power
Problem Set 3.1: Sampling Distribution of the Mean Exercise
Criterion:
Interpret population mean and variance.
Instructions:
Read the information below and answer the questions.
Suppose a researcher wants to learn more about the mean attention span of individuals in some hypothetical population. The researcher cites that the attention span (the time in minutes attending to some task) in this population is normally distributed with the following characteristics: 20
36
. Based on the parameters given in this example, answer the following questions:
1. What is the population mean (μ)? __________________________
2. What is the population variance
? __________________________
3. Sketch the distribution of this population. Make sure you draw the shape of the distribution and label the mean plus and minus three standard deviations.
Problem Set 3.2: Effect Size and Power
Criterion:
Explain effect size and power.
Instructions:
Read each of the following three scenarios and answer the questions.
Two researchers make a test concerning the effectiveness of a drug use treatment. Researcher A determines that the effect size in the population of males is
d
= 0.36; Researcher B determines that the effect size in the population of females is
d
= 0.20. All other things being equal, which researcher has more power to detect an effect? Explain. ______________________________________________________________________
Two researchers make a test concerning the levels of marital satisfaction among military families. Researcher A collects a sample of 22 married couples (
n
= 22); Researcher B collects a sample of 40 married couples (
n
= 40). All other things being equal, which researcher has more power to detect an effect? Explain. ______________________________________________________________________
Two researchers make a test concerning standardized exam performance among senior high school students in one of two local communities. Researcher A tests performance from the population in the northern community, where the standard deviation of test scores is 110 (
); Researcher B tests performance from the population in the southern community, where the standard deviation of test scores is 60 (
). All other things being equal, which researcher has more power to detect an effect? Explain. ______________________________________________________________________
Problem Set 3.3: Hypothesis, Direction, and Population Mean
Criterion:
Explain the relationship between hypothesis, tests, and population mean.
Instructions:
Read the following and answer the questions.
This document introduces parametric tests and provides information about the t-test. It defines parametric tests as those applied to normally distributed data measured on interval or ratio scales. Parametric tests make inferences about the parameters of the probability distribution from which the sample data were drawn. Examples of common parametric tests are provided, including the t-test. The t-test is used to compare two means from independent samples or correlated samples. Steps for conducting a t-test are outlined, including calculating the t-statistic and making decisions based on critical t-values. Two examples of using a t-test on experimental data are shown.
This part of the thesis describes the methodology section which provides details of the research activities, data collection strategies, and administration of questionnaires and interviews to achieve the study objectives and address the problem. It discusses preparing and testing questionnaires, identifying persons responsible for data collection, and approaches for administering questionnaires and conducting interviews.
The document provides an overview of student's t-test, a statistical technique used to determine if there are significant differences between the means of two groups. It discusses the different types of t-tests, including one-sample, independent samples, and paired/correlated samples t-tests. Key steps for conducting each type of t-test are outlined, including calculating t-values, degrees of freedom, and comparing results to significance levels. The t-test is a commonly used hypothesis testing tool that allows testing assumptions about population means.
Marketing Research Hypothesis Testing.pptxxababid981
This document provides an overview of parametric and non-parametric hypothesis tests. It defines parametric tests as those that assume an underlying normal distribution, and lists common parametric tests like the z-test, t-test, F-test, and ANOVA. Non-parametric tests make no distributional assumptions and common examples discussed include the Mann-Whitney U test, chi-square test, and Kruskal-Wallis test. The document provides details on assumptions and procedures for conducting each of these important statistical hypothesis tests.
11 T(EA) FOR TWO TESTS BETWEEN THE MEANS OF DIFFERENT GROUPS11 .docxnovabroom
11 T(EA) FOR TWO TESTS BETWEEN THE MEANS OF DIFFERENT GROUPS
11: MEDIA LIBRARY
Premium Videos
Core Concepts in Stats Video
· Testing the Difference Between Two Sample Means
Lightboard Lecture Video
· Independent t Tests
Time to Practice Video
· Chapter 11: Problem 5
Difficulty Scale
(A little longer than the previous chapter but basically the same kind of procedures and very similar questions. Not too hard, but you have to pay attention.)
WHAT YOU WILL LEARN IN THIS CHAPTER
· Using the t test for independent means when appropriate
· Computing the observed t value
· Interpreting the t value and understanding what it means
· Computing the effect size for a t test for independent means
INTRODUCTION TO THE T TEST FOR INDEPENDENT SAMPLES
Even though eating disorders are recognized for their seriousness, little research has been done that compares the prevalence and intensity of symptoms across different cultures. John P. Sjostedt, John F. Schumaker, and S. S. Nathawat undertook this comparison with groups of 297 Australian and 249 Indian university students. Each student was measured on the Eating Attitudes Test and the Goldfarb Fear of Fat Scale. High scores on both measures indicate the presence of an eating disorder. The groups’ scores were compared with one another. On a comparison of means between the Indian and the Australian participants, Indian students scored higher on both of the tests, and this was due mainly to the scores of women. The results for the Eating Attitudes Test were t(544) = −4.19, p < .0001, and the results for the Goldfarb Fear of Fat Scale were t(544) = −7.64, p < .0001.
Now just what does all this mean? Read on.
Why was the t test for independent means used? Sjostedt and his colleagues were interested in finding out whether there was a difference in the average scores of one (or more) variable(s) between the two groups. The t test is called independent because the two groups were not related in any way. Each participant in the study was tested only once. The researchers applied a t test for independent means, arriving at the conclusion that for each of the outcome variables, the differences between the two groups were significant at or beyond the .0001 level. Such a small chance of a Type I error means that there is very little probability that the difference in scores between the two groups was due to chance and not something like group membership, in this case representing nationality, culture, or ethnicity.
Want to know more? Go online or to the library and find …
Sjostedt, J. P., Schumaker, J. F., & Nathawat, S. S. (1998). Eating disorders among Indian and Australian university students. Journal of Social Psychology, 138(3), 351–357.
LIGHTBOARD LECTURE VIDEO
Independent t Tests
THE PATH TO WISDOM AND KNOWLEDGE
Here’s how you can use Figure 11.1, the flowchart introduced in Chapter 9, to select the appropriate test statistic, the t test for independent means. Follow along the highlighted sequence of steps in Figure 1.
11 T(EA) FOR TWO TESTS BETWEEN THE MEANS OF DIFFERENT GROUPS11 .docxhyacinthshackley2629
A study compared eating disorder symptoms between 297 Australian and 249 Indian university students using the Eating Attitudes Test and Goldfarb Fear of Fat Scale. Indian students scored higher on both tests, especially women. Statistical analysis found the differences were highly significant (p < .0001) between the groups. However, the small effect size (-0.14) suggests the actual magnitude of the difference between memory technique groups was likely small.
Assignment 4Chapter 1010.1. In a t test for a single samp.docxssuser562afc1
Assignment 4
Chapter 10
10.1. In a t test for a single sample, the sample's mean is compared to the population .
10.2. When we use a paired-samples t test to compare the pretest and posttest scores for a group of 45 people, the degrees of freedom (df) are _____.
10.3. If we conduct a t test for independent samples, and n1 = 32 and n2 = 35, the degrees of freedom (df) are _____.
10.4. A researcher wants to study the effect of college education on people's earning by comparing the annual salaries of a randomly-selected group of 100 college graduates to the annual salaries of 100 randomly-selected group of people whose highest level of education is high school. To compare the mean annual salaries of the two groups, the researcher should use a t test for ______.
10.5. A training coordinator wants to determine the effectiveness of a program that makes extensive use of educational technology when training new employees. She compares the scores of her new employees who completed the training on a nationally-normed test to the mean score of all those in the country who took the same test. The appropriate statistical test the training coordinator should use for her analysis is the t
test for ______.
10.6. As part of the process to develop two parallel forms of a questionnaire, the persons creating the questionnaire may administer both forms to a group of students, and then use a t test for ______ samples to compare
the mean scores on the two forms.
Circle the correct answer:
10.7. A difference of 4 points between two homogeneous groups is likely to be more/less statistically significant than the same difference (of 4 points) between two heterogeneous groups, when all four groups are taking completing the same survey and have approximately the same number of subjects.
a.
10.8. A difference of 3 points on a 100-item test taken by two groups is likely to be more/less statistically significant than a difference of 3 points on a 30-item test taken by the same two groups.
10.9 When a t test for paired samples is used to compare the pretest and the posttest means, the number of pretest scores is thesame as/different thanthe number of post-test scores.
10.10. When we want to compare whether females' scores on the GMAT are different from males' scores, we should use a t test for paired samples/independentsamples.
10.11 In studies where the alternative (research) hypothesis is directional, the critical values for a one tailedtest/two-tailed testshould be used to determine the level of significance (i.e., the p value).
10.12 When the alternative hypothesis is: HA: u1=u2, the critical values for onetailed test/two-tailedtest should be used to determine the level of statistical significance.
10.13. In a study conducted to compare the test scores of experimental and control groups, a 50-item test is administered to both groups at the end of the study. The mean of the experimental group on the test is 1 point h ...
Chapter NineShow all workProblem 1)A skeptical paranorma.docxneedhamserena
Chapter Nine
Show all work
Problem 1)
A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO is less than 1 in every one thousand.
State the null hypothesis and the alternative hypothesis for a test of significance.
Problem 2)
At one school, the average amount of time that tenth-graders spend watching television each week is 18.4 hours.
The principal introduces a campaign to encourage the students to watch less television.
One year later, the principal wants to perform a hypothesis test to determine whether the average amount of time spent watching television per week has decreased.
Formulate the null and alternative hypotheses for the study described.
Problem 3)
A two-tailed test is conducted at the 5% significance level.
What is the P-value required to reject the null hypothesis?
Problem 4)
A two-tailed test is conducted at the 5% significance level.
What is the
right tail percentile
required to reject the null hypothesis?
Problem 5)
What is the difference between an Type I and a Type II error?
Provide an example of both.
Chapter 10
Show all work
Problem 1)
Steven collected data from 20 college students on their emotional responses to classical music.
Students listened to two 30-second segments from “The Collection from the Best of Classical Music.”
After listening to a segment, the students rated it on a scale from 1 to 10, with 1 indicating that it “made them very sad” to 10 indicating that it “made them very happy.” Steve computes the total scores from each student and created a variable called “hapsad.”
Steve then conducts a one-sample t-test on the data, knowing that there is an established mean for the publication of others that have taken this test of 6.
The following is the scores:
5.0
5.0
10.0
3.0
13.0
13.0
7.0
5.0
5.0
15.0
14.0
18.0
8.0
12.0
10.0
7.0
3.0
15.0
4.0
3.0
a)
Conduct a one-sample t-test.
What is the t-test score?
What is the mean?
Was the test significant?
If it was significant at what P-value level was it significant?
b)
What is your null and alternative hypothesis? Given the results did you reject or fail to reject the null and why?
(Use instructions on page 349 of your textbook, under Hypothesis Tests with the t Distribution to conduct SPSS or Excel analysis).
Problem 2)
Billie wishes to test the hypothesis that overweight individuals tend to eat faster than normal-weight individuals.
To test this hypothesis, she has two assistants sit in a McDonald’s restaurant and identify individuals who order the Big Mac special for lunch.
The Big Mackers as they become known are then classified by the assistants as overweight, normal weight, or neither overweight nor normal weight.
The assistants identify 10 overweight and 10 normal weight Big Mackers.
The assistants record the amount of time it takes them to eight the Big Mac special.
1.0
585.0
1.0
540.0
1.0
660.0
1.0
571.0
1.0
584.0
1.0
653.0
1.0
574.0
1.0
569.0
1.0
619.
Student's t-test is used to determine if two population means are statistically different based on random samples from those populations. It calculates a ratio of the difference between sample means to the variability within each sample. If the t-value is large enough based on the sample sizes and pre-set significance level (often 0.05), then the population means are considered statistically different. The t-test is commonly used to compare outcomes before and after an intervention or between treated and control groups.
Student's t-test is used to determine if two population means are statistically different based on random samples from those populations. It calculates a ratio of the difference between two sample means over the variability within each sample. If the t-value is large enough based on the sample sizes and pre-set significance level (often 0.05), then the population means are considered statistically different. The t-test is commonly used to compare outcomes before and after an intervention or between treated and untreated groups.
PSY520 – Module 5Answer Sheet Submit your answers in the.docxwoodruffeloisa
PSY520 – Module 5
Answer Sheet
Submit your answers in the boxes provided. No credit will be given for responses not found in the correct answer area.
Chapter 13:
13.6It’s well established, we’ll assume, that lab rats require an average of 32 trials in a complex water maze before reaching a learning criterion of three consecutive errorless trials. To determine whether a mildly adverse stimulus has any effect on performance, a sample of seven lab rats were given a mild electrical shock just before each trial.
Question:
Steps:
Calculations or Logic:
Answer:
Given that X 5 34.89 and s 5 3.02, test the null hypothesis with t , using the .05 level of significance.
What is the research hypothesis?
What is the null hypothesis?
Is this a one-tailed or two-tailed test?
What are the degrees of freedom?
What is the t critical for .05 significance?
What is the calculated t?
Do you accept or reject the null hypothesis?
Construct a 95 percent confidence interval for the true number of trials required to learn the water maze.
Interpret this confidence interval.
13.8Assume that on average, healthy young adults dream 90 minutes each night, as inferred from a number of measures, including rapid eye movement (REM) sleep. An investigator wishes to determine whether drinking coffee just before going to sleep affects the amount of dream time. After drinking a standard amount of coffee, dream time is monitored for each of 28 healthy young adults in a random sample. Results show a sample mean, X, of 88 minutes and a sample standard deviation, s, of 9 minutes.
Question:
Steps:
Calculations or Logic:
Answer:
Use t to test the null hypothesis at the .05 level of significance.
What is the research hypothesis?
What is the null hypothesis?
Is this a one-tailed or two-tailed test?
What are the degrees of freedom?
What is the t critical for .05 significance?
What is the calculated t?
Do you accept or reject the null hypothesis?
If appropriate (because the null hypothesis has been rejected), construct a 95 percent confidence interval and interpret this interval.
13.9In the gas mileage test described in this chapter, would you prefer a smaller or a larger sample size if you were the car manufacturer? Why? a vigorous prosecutor for the federal regulatory agency? Why
Question:
Smaller or Larger?
Why?
In the gas mileage test described in this chapter, would you prefer a smaller or a larger sample size if you were the car manufacturer?
In the gas mileage test described in this chapter, would you prefer a smaller or a larger sample size if you were a vigorous prosecutor for the federal regulatory agency?
13.10Even though the population standard deviation is unknown, an investigator uses z rather than the more appropriate t to test a hypothesis at the .05 level of significance.
Question:
Larger or smaller?
Is the true level of significance larger or smaller than .05
Is the true critical value larger or smaller than that for the cr ...
Week 5 Lecture 14 The Chi Square TestQuite often, patterns of .docxcockekeshia
Week 5 Lecture 14
The Chi Square Test
Quite often, patterns of responses or measures give us a lot of information. Patterns are generally the result of counting how many things fit into a particular category. Whenever we make a histogram, bar, or pie chart we are looking at the pattern of the data. Frequently, changes in these visual patterns will be our first clues that things have changed, and the first clue that we need to initiate a research study (Lind, Marchel, & Wathen, 2008).
One of the most useful test in examining patterns and relationships in data involving counts (how many fit into this category, how many into that, etc.) is the chi-square. It is extremely easy to calculate and has many more uses than we will cover. Examining patterns involves two uses of the Chi-square - the goodness of fit and the contingency table. Both of these uses have a common trait: they involve counts per group. In fact, the chi-square is the only statistic we will look at that we use when we have counts per multiple groups (Tanner & Youssef-Morgan, 2013). Chi Square Goodness of Fit Test
The goodness of fit test checks to see if the data distribution (counts per group) matches some pattern we are interested in. Example: Are the employees in our example company distributed equal across the grades? Or, a more reasonable expectation for a company might be are the employees distributed in a pyramid fashion – most on the bottom and few at the top?
The Chi Square test compares the actual versus a proposed distribution of counts by generating a measure for each cell or count: (actual – expected)2/actual. Summing these for all of the cells or groups provides us with the Chi Square Statistic. As with our other tests, we determine the p-value of getting a result as large or larger to determine if we reject or not reject our null hypothesis. An example will show the approach using Excel.
Regardless of the Chi Square test, the chi square related functions are found in the fx Statistics window rather than the Data Analysis where we found the t and ANOVA test functions. The most important for us are:
· CHISQ.TEST (actual range, expected range) – returns the p-value for the test
· CHISQ.INV.RT(p-value, df) – returns the actual Chi Square value for the p-value or probability value used.
· CHISQ.DIST.RT(X, df) – returns the p-value for a given value.
When we have a table of actual and expected results, using the =CHISQ.TEST(actual range, expected range) will provide us with the p-value of the calculated chi square value (but does not give us the actual calculated chi square value for the test). We can compare this value against our alpha criteria (generally 0.05) to make our decision about rejecting or not rejecting the null hypothesis.
If, after finding the p-value for our chi square test, we want to determine the calculated value of the chi square statistic, we can use the =CHISQ.INV.RT(probability, df) function, the value for probability is .
Week 6 DQ1. What is your research questionIs there a differen.docxcockekeshia
Week 6 DQ
1. What is your research question?
Is there a difference between the math utility of a male and a female?
2. What is the null hypothesis for your question?
Hn There is no difference in the math utility between male and female.
Alternative hypotheses can also be created in the case the null hypothesis is proven incorrect. Two alternative hypotheses are:
Ha1 Feales have a higher math utility.
Ha2 Males have a higher math utility.
3. What research design would align with this question?
According to Frankfort-Nachmias and Leon-Guerrero (2015) a descriptive research design would be best for this type of study.
4. What comparison of means test was used to answer the question (be sure to defend the use of the test using the article you found in your search)?
The independent-samples T test was used to analyze the means for this data.
5. What dependent variable was used and how is it measured?
The dependent variable is the student’s math utility. It is measured from -3.51 to 1.31(University high school longitudinal study dataset. (2009).
6. What independent variable is used and how is it measured?
Either male (1) of female (2) (University high school longitudinal study dataset. (2009).
7. If you found significance, what is the strength of the effect?
The significance was 0.0000. This is much better than the standard of .05 significance as outlined by Frankfort-Nachmias and Leon-Guerrero (2015).
8. Identify your research question and explain your results for a lay audience, what is the answer to your research question?
My research question was “Is there a difference between the math utility of a male and a female?” Based on the analysis of the means (or average) through testing using the independent-samples T test there was no measurable difference between the math utility of male or females. This leads us to accept the null hypothesis of “There is no difference in the math utility between male and female” as true.
Group Statistics
T1 Student's sex
N
Mean
Std. Deviation
Std. Error Mean
T1 Scale of student's mathematics utility
Male
9453
.0140
1.01962
.01049
Female
9349
-.0481
.97291
.01006
Independent Samples Test
Levene's Test for Equality of Variances
t-test for Equality of Means
F
Sig.
t
df
Sig. (2-tailed)
Mean Difference
Std. Error Difference
95% Confidence Interval of the Difference
Lower
Upper
T1 Scale of student's mathematics utility
Equal variances assumed
17.400
.000
4.276
18800
.000
.06216
.01454
.03367
.09066
Equal variances not assumed
4.277
18775.932
.000
.06216
.01453
.03367
.09065
University high school longitudinal study dataset. (2009).
References
Frankfort-Nachmias, C., & Leon-Guerrero, A. (2015). Social statistics for a diverse society (7th ed.). Thousand Oaks, CA: Sage Publications.
University high school longitudinal study dataset. (2009). Retrieved from class.waldenu.edu
The t Test for Related Samples
The t Test for Related Samples
Program Transcript
MAT.
Happiness Data SetAuthor Jackson, S.L. (2017) Statistics plain ShainaBoling829
Happiness Data Set
Author: Jackson, S.L. (2017) Statistics plain and simple. (4th ed.). Boston, MA: Cengage Learning.
I attach the previous essay so you have idea on how to do this assignment. It is similar to the assignment last week.
Assignment Content
1.
Top of Form
As you get closer to the final project in Week 6, you should have a better idea of the role of statistics in research. This week, you will calculate a one-way ANOVA for the independent groups. Reading and interpreting the output correctly is highly important. Most people who read research articles never see the actual output or data; they read the results statements by the researcher, which is why your summary must be accurate.
Consider your hypothesis statements you created in Part 2.
Calculate a one-way ANOVA, including a Tukey's HSD for the data from the Happiness and Engagement Dataset.
Write a 125- to 175-word summary of your interpretation of the results of the ANOVA, and describe how using an ANOVA was more advantageous than using multiple t tests to compare your independent variable on the outcome. Copy and paste your Microsoft® Excel® output below the summary.
Format your summary according to APA format.
Submit your summary, including the Microsoft® Excel® output to the assignment.
Reference/Module:
Module 13: Comparing More Than Two Groups
Using Designs with Three or More Levels of an Independent Variable
Comparing More than Two Kinds of Treatment in One Study
Comparing Two or More Kinds of Treatment with a Control Group
Comparing a Placebo Group to the Control and Experimental Groups
Analyzing the Multiple-Group Design
One-Way Between-Subjects ANOVA: What It Is and What It Does
Review of Key Terms
Module Exercises
Critical Thinking Check AnswersModule 14: One-Way Between-Subjects Analysis of Variance (ANOVA)
Calculations for the One-Way Between-Subjects ANOVA
Interpreting the One-Way Between-Subjects ANOVA
Graphing the Means and Effect Size
Assumptions of the One-Way Between-Subjects ANOVA
Tukey's Post Hoc Test
Review of Key Terms
Module Exercises
Critical Thinking Check AnswersChapter 7 Summary and ReviewChapter 7 Statistical Software Resources
In this chapter, we discuss the common types of statistical analyses used with designs involving more than two groups. The inferential statistics discussed in this chapter differ from those presented in the previous two chapters. In Chapter 5, single samples were being compared to populations (z test and t test), and in Chapter 6, two independent or correlated samples were being compared. In this chapter, the statistics are designed to test differences between more than two equivalent groups of subjects.
Several factors influence which statistic should be used to analyze the data collected. For example, the type of data collected and the number of groups being compared must be considered. Moreover, the statistic used to analyze the data will vary depending on whether the study involves a between-subjects design (designs in ...
2016 Symposium Poster - statistics - FinalBrian Lin
This document discusses common pitfalls in statistical analysis and provides examples to illustrate typical mistakes. It notes that statistical significance does not always imply practical significance. Even with the same means and variances, different datasets can have very different distributions. Correlation does not necessarily indicate causation. Qualitative scales should not always be treated as quantitative variables. Choosing the appropriate statistical test is important to get the right results. Sample size calculations depend on study details and objectives. Involving statisticians early in the research process helps ensure proper experimental design and analysis.
Chapter NineShow all workProblem 1)A skept.docxneedhamserena
Chapter Nine
Show all work
Problem 1)
A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO is less than 1 in every one thousand.
State the null hypothesis and the alternative hypothesis for a test of significance.
Problem 2)
At one school, the average amount of time that tenth-graders spend watching television each week is 18.4 hours.
The principal introduces a campaign to encourage the students to watch less television.
One year later, the principal wants to perform a hypothesis test to determine whether the average amount of time spent watching television per week has decreased.
Formulate the null and alternative hypotheses for the study described.
Problem 3)
A two-tailed test is conducted at the 5% significance level.
What is the P-value required to reject the null hypothesis?
Problem 4)
A two-tailed test is conducted at the 5% significance level.
What is the
right tail percentile
required to reject the null hypothesis?
Problem 5)
What is the difference between an Type I and a Type II error?
Provide an example of both.
Chapter 10
Show all work
Problem 1)
Steven collected data from 20 college students on their emotional responses to classical music.
Students listened to two 30-second segments from “The Collection from the Best of Classical Music.”
After listening to a segment, the students rated it on a scale from 1 to 10, with 1 indicating that it “made them very sad” to 10 indicating that it “made them very happy.” Steve computes the total scores from each student and created a variable called “hapsad.”
Steve then conducts a one-sample t-test on the data, knowing that there is an established mean for the publication of others that have taken this test of 6.
The following is the scores:
5.0
5.0
10.0
3.0
13.0
13.0
7.0
5.0
5.0
15.0
14.0
18.0
8.0
12.0
10.0
7.0
3.0
15.0
4.0
3.0
Conduct a one-sample t-test.
What is the t-test score?
What is the mean?
Was the test significant?
If it was significant at what P-value level was it significant?
What is your null and alternative hypothesis? Given the results did you reject or fail to reject the null and why?
(Use instructions on page 437 of your textbook, under Hypothesis Tests with the t Distribution to conduct SPSS or Excel analysis).
Problem 2)
Billie wishes to test the hypothesis that overweight individuals tend to eat faster than normal-weight individuals.
To test this hypothesis, she has two assistants sit in a McDonald’s restaurant and identify individuals who order the Big Mac special for lunch.
The Big Mackers as they become known are then classified by the assistants as overweight, normal weight, or neither overweight nor normal weight.
The assistants identify 10 overweight and 10 normal weight Big Mackers.
The assistants record the amount of time it takes them to eight the Big Mac special.
1.0
585.0
1.0
540.0
1.0
660.0
1.0
571.0
1.0
584.0
1..
Assessment 3 ContextYou will review the theory, logic, and a.docxgalerussel59292
Assessment 3 Context
You will review the theory, logic, and application of t-tests. The t-test is a basic inferential statistic often reported in psychological research. You will discover that t-tests, as well as analysis of variance (ANOVA), compare group means on some quantitative outcome variable.
Recall that null hypothesis tests are of two types: (1) differences between group means and (2) association between variables. In both cases there is a null hypothesis and an alternative hypothesis. In the group means test, the null hypothesis is that the two groups have equal means, and the alternative hypothesis is that the two groups do not have equal means. In the association between variables type of test, the null hypothesis is that the correlation coefficient between the two variables is zero, and the alternative hypothesis is that the correlation coefficient is not zero.
Notice in each case that the hypotheses are mutually exclusive. If the null is false, the alternative must be true. The purpose of null hypothesis statistical tests is generally to show that the null has a low probability of being true (the p value is less than .05) – low enough that the researcher can legitimately claim it is false. The reason this is done is to support the allegation that the alternative hypothesis is true.
In this context you will be studying the details of the first type of test. This is the test of difference between group means. In variations on this model, the two groups can actually be the same people under different conditions, or one of the groups may be assigned a fixed theoretical value. The main idea is that two mean values are being compared. The two groups each have an average score or mean on some variable. The null hypothesis is that the difference between the means is zero. The alternative hypothesis is that the difference between the means is not zero. Notice that if the null is false, the alternative must be true. It is first instructive to consider some of the details of groups. Means, and difference between them.
Null Hypothesis Significance Test
The most common forms of the Null Hypothesis Significance Test (NHST) are three types of t tests, and the test of significance of a correlation. The NHST also extends to more complex tests, such as ANOVA, which will be discussed separately. Below, the null hypothesis and the alternative hypothesis are given for each of the following tests. It would be a valuable use of your time to commit the information below to memory. Once this is done, then when we refer to the tests later, you will have some structure to make sense of the more detailed explanations.
1. One-sample t test: The question in this test is whether a single sample group mean is significantly different from some stated or fixed theoretical value - the fixed value is called a parameter.
· Null Hypothesis: The difference between the sample group mean and the fixed value is zero in the population.
· Alternative hypothesis: T.
T test for two independent samples and inductionEmmanuel Buah
Recruitment and selection is important to find people who are a good fit for the organization to reduce costs from high turnover. A good recruitment system should be efficient, effective at finding suitable candidates, and fair by being non-discriminatory. Employers should do human resource planning to forecast needs and match available supply to demand to help with recruitment and development.
STATISTICS : Changing the way we do: Hypothesis testing, effect size, power, ...Musfera Nara Vadia
Researchers should take several steps to make statistical results meaningful:
1. Perform a power analysis to determine adequate sample size and ensure power is above .50, ideally .80. Power is the probability of detecting real effects.
2. Never set the alpha level lower than .05 and try to set it higher to .10 if acceptable.
3. Report effect sizes and confidence intervals to provide context around statistical significance. Effect sizes indicate the magnitude of differences between groups.
Assessment 3 – Hypothesis, Effect Size, Power, and t Tests.docxcargillfilberto
Assessment 3 – Hypothesis, Effect Size, Power, and
t
Tests
Complete the following problems within this Word document. Do not submit other files. Show your work for problem sets that require calculations. Ensure that your answer to each problem is clearly visible. You may want to highlight your answer or use a different type color to set it apart.
Hypothesis, Effect Size, and Power
Problem Set 3.1: Sampling Distribution of the Mean Exercise
Criterion:
Interpret population mean and variance.
Instructions:
Read the information below and answer the questions.
Suppose a researcher wants to learn more about the mean attention span of individuals in some hypothetical population. The researcher cites that the attention span (the time in minutes attending to some task) in this population is normally distributed with the following characteristics: 20
36
. Based on the parameters given in this example, answer the following questions:
1. What is the population mean (μ)? __________________________
2. What is the population variance
? __________________________
3. Sketch the distribution of this population. Make sure you draw the shape of the distribution and label the mean plus and minus three standard deviations.
Problem Set 3.2: Effect Size and Power
Criterion:
Explain effect size and power.
Instructions:
Read each of the following three scenarios and answer the questions.
Two researchers make a test concerning the effectiveness of a drug use treatment. Researcher A determines that the effect size in the population of males is
d
= 0.36; Researcher B determines that the effect size in the population of females is
d
= 0.20. All other things being equal, which researcher has more power to detect an effect? Explain. ______________________________________________________________________
Two researchers make a test concerning the levels of marital satisfaction among military families. Researcher A collects a sample of 22 married couples (
n
= 22); Researcher B collects a sample of 40 married couples (
n
= 40). All other things being equal, which researcher has more power to detect an effect? Explain. ______________________________________________________________________
Two researchers make a test concerning standardized exam performance among senior high school students in one of two local communities. Researcher A tests performance from the population in the northern community, where the standard deviation of test scores is 110 (
); Researcher B tests performance from the population in the southern community, where the standard deviation of test scores is 60 (
). All other things being equal, which researcher has more power to detect an effect? Explain. ______________________________________________________________________
Problem Set 3.3: Hypothesis, Direction, and Population Mean
Criterion:
Explain the relationship between hypothesis, tests, and population mean.
Instructions:
Read the following and answer the questions.
This document introduces parametric tests and provides information about the t-test. It defines parametric tests as those applied to normally distributed data measured on interval or ratio scales. Parametric tests make inferences about the parameters of the probability distribution from which the sample data were drawn. Examples of common parametric tests are provided, including the t-test. The t-test is used to compare two means from independent samples or correlated samples. Steps for conducting a t-test are outlined, including calculating the t-statistic and making decisions based on critical t-values. Two examples of using a t-test on experimental data are shown.
This part of the thesis describes the methodology section which provides details of the research activities, data collection strategies, and administration of questionnaires and interviews to achieve the study objectives and address the problem. It discusses preparing and testing questionnaires, identifying persons responsible for data collection, and approaches for administering questionnaires and conducting interviews.
The document provides an overview of student's t-test, a statistical technique used to determine if there are significant differences between the means of two groups. It discusses the different types of t-tests, including one-sample, independent samples, and paired/correlated samples t-tests. Key steps for conducting each type of t-test are outlined, including calculating t-values, degrees of freedom, and comparing results to significance levels. The t-test is a commonly used hypothesis testing tool that allows testing assumptions about population means.
Marketing Research Hypothesis Testing.pptxxababid981
This document provides an overview of parametric and non-parametric hypothesis tests. It defines parametric tests as those that assume an underlying normal distribution, and lists common parametric tests like the z-test, t-test, F-test, and ANOVA. Non-parametric tests make no distributional assumptions and common examples discussed include the Mann-Whitney U test, chi-square test, and Kruskal-Wallis test. The document provides details on assumptions and procedures for conducting each of these important statistical hypothesis tests.
11 T(EA) FOR TWO TESTS BETWEEN THE MEANS OF DIFFERENT GROUPS11 .docxnovabroom
11 T(EA) FOR TWO TESTS BETWEEN THE MEANS OF DIFFERENT GROUPS
11: MEDIA LIBRARY
Premium Videos
Core Concepts in Stats Video
· Testing the Difference Between Two Sample Means
Lightboard Lecture Video
· Independent t Tests
Time to Practice Video
· Chapter 11: Problem 5
Difficulty Scale
(A little longer than the previous chapter but basically the same kind of procedures and very similar questions. Not too hard, but you have to pay attention.)
WHAT YOU WILL LEARN IN THIS CHAPTER
· Using the t test for independent means when appropriate
· Computing the observed t value
· Interpreting the t value and understanding what it means
· Computing the effect size for a t test for independent means
INTRODUCTION TO THE T TEST FOR INDEPENDENT SAMPLES
Even though eating disorders are recognized for their seriousness, little research has been done that compares the prevalence and intensity of symptoms across different cultures. John P. Sjostedt, John F. Schumaker, and S. S. Nathawat undertook this comparison with groups of 297 Australian and 249 Indian university students. Each student was measured on the Eating Attitudes Test and the Goldfarb Fear of Fat Scale. High scores on both measures indicate the presence of an eating disorder. The groups’ scores were compared with one another. On a comparison of means between the Indian and the Australian participants, Indian students scored higher on both of the tests, and this was due mainly to the scores of women. The results for the Eating Attitudes Test were t(544) = −4.19, p < .0001, and the results for the Goldfarb Fear of Fat Scale were t(544) = −7.64, p < .0001.
Now just what does all this mean? Read on.
Why was the t test for independent means used? Sjostedt and his colleagues were interested in finding out whether there was a difference in the average scores of one (or more) variable(s) between the two groups. The t test is called independent because the two groups were not related in any way. Each participant in the study was tested only once. The researchers applied a t test for independent means, arriving at the conclusion that for each of the outcome variables, the differences between the two groups were significant at or beyond the .0001 level. Such a small chance of a Type I error means that there is very little probability that the difference in scores between the two groups was due to chance and not something like group membership, in this case representing nationality, culture, or ethnicity.
Want to know more? Go online or to the library and find …
Sjostedt, J. P., Schumaker, J. F., & Nathawat, S. S. (1998). Eating disorders among Indian and Australian university students. Journal of Social Psychology, 138(3), 351–357.
LIGHTBOARD LECTURE VIDEO
Independent t Tests
THE PATH TO WISDOM AND KNOWLEDGE
Here’s how you can use Figure 11.1, the flowchart introduced in Chapter 9, to select the appropriate test statistic, the t test for independent means. Follow along the highlighted sequence of steps in Figure 1.
11 T(EA) FOR TWO TESTS BETWEEN THE MEANS OF DIFFERENT GROUPS11 .docxhyacinthshackley2629
A study compared eating disorder symptoms between 297 Australian and 249 Indian university students using the Eating Attitudes Test and Goldfarb Fear of Fat Scale. Indian students scored higher on both tests, especially women. Statistical analysis found the differences were highly significant (p < .0001) between the groups. However, the small effect size (-0.14) suggests the actual magnitude of the difference between memory technique groups was likely small.
Assignment 4Chapter 1010.1. In a t test for a single samp.docxssuser562afc1
Assignment 4
Chapter 10
10.1. In a t test for a single sample, the sample's mean is compared to the population .
10.2. When we use a paired-samples t test to compare the pretest and posttest scores for a group of 45 people, the degrees of freedom (df) are _____.
10.3. If we conduct a t test for independent samples, and n1 = 32 and n2 = 35, the degrees of freedom (df) are _____.
10.4. A researcher wants to study the effect of college education on people's earning by comparing the annual salaries of a randomly-selected group of 100 college graduates to the annual salaries of 100 randomly-selected group of people whose highest level of education is high school. To compare the mean annual salaries of the two groups, the researcher should use a t test for ______.
10.5. A training coordinator wants to determine the effectiveness of a program that makes extensive use of educational technology when training new employees. She compares the scores of her new employees who completed the training on a nationally-normed test to the mean score of all those in the country who took the same test. The appropriate statistical test the training coordinator should use for her analysis is the t
test for ______.
10.6. As part of the process to develop two parallel forms of a questionnaire, the persons creating the questionnaire may administer both forms to a group of students, and then use a t test for ______ samples to compare
the mean scores on the two forms.
Circle the correct answer:
10.7. A difference of 4 points between two homogeneous groups is likely to be more/less statistically significant than the same difference (of 4 points) between two heterogeneous groups, when all four groups are taking completing the same survey and have approximately the same number of subjects.
a.
10.8. A difference of 3 points on a 100-item test taken by two groups is likely to be more/less statistically significant than a difference of 3 points on a 30-item test taken by the same two groups.
10.9 When a t test for paired samples is used to compare the pretest and the posttest means, the number of pretest scores is thesame as/different thanthe number of post-test scores.
10.10. When we want to compare whether females' scores on the GMAT are different from males' scores, we should use a t test for paired samples/independentsamples.
10.11 In studies where the alternative (research) hypothesis is directional, the critical values for a one tailedtest/two-tailed testshould be used to determine the level of significance (i.e., the p value).
10.12 When the alternative hypothesis is: HA: u1=u2, the critical values for onetailed test/two-tailedtest should be used to determine the level of statistical significance.
10.13. In a study conducted to compare the test scores of experimental and control groups, a 50-item test is administered to both groups at the end of the study. The mean of the experimental group on the test is 1 point h ...
Chapter NineShow all workProblem 1)A skeptical paranorma.docxneedhamserena
Chapter Nine
Show all work
Problem 1)
A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO is less than 1 in every one thousand.
State the null hypothesis and the alternative hypothesis for a test of significance.
Problem 2)
At one school, the average amount of time that tenth-graders spend watching television each week is 18.4 hours.
The principal introduces a campaign to encourage the students to watch less television.
One year later, the principal wants to perform a hypothesis test to determine whether the average amount of time spent watching television per week has decreased.
Formulate the null and alternative hypotheses for the study described.
Problem 3)
A two-tailed test is conducted at the 5% significance level.
What is the P-value required to reject the null hypothesis?
Problem 4)
A two-tailed test is conducted at the 5% significance level.
What is the
right tail percentile
required to reject the null hypothesis?
Problem 5)
What is the difference between an Type I and a Type II error?
Provide an example of both.
Chapter 10
Show all work
Problem 1)
Steven collected data from 20 college students on their emotional responses to classical music.
Students listened to two 30-second segments from “The Collection from the Best of Classical Music.”
After listening to a segment, the students rated it on a scale from 1 to 10, with 1 indicating that it “made them very sad” to 10 indicating that it “made them very happy.” Steve computes the total scores from each student and created a variable called “hapsad.”
Steve then conducts a one-sample t-test on the data, knowing that there is an established mean for the publication of others that have taken this test of 6.
The following is the scores:
5.0
5.0
10.0
3.0
13.0
13.0
7.0
5.0
5.0
15.0
14.0
18.0
8.0
12.0
10.0
7.0
3.0
15.0
4.0
3.0
a)
Conduct a one-sample t-test.
What is the t-test score?
What is the mean?
Was the test significant?
If it was significant at what P-value level was it significant?
b)
What is your null and alternative hypothesis? Given the results did you reject or fail to reject the null and why?
(Use instructions on page 349 of your textbook, under Hypothesis Tests with the t Distribution to conduct SPSS or Excel analysis).
Problem 2)
Billie wishes to test the hypothesis that overweight individuals tend to eat faster than normal-weight individuals.
To test this hypothesis, she has two assistants sit in a McDonald’s restaurant and identify individuals who order the Big Mac special for lunch.
The Big Mackers as they become known are then classified by the assistants as overweight, normal weight, or neither overweight nor normal weight.
The assistants identify 10 overweight and 10 normal weight Big Mackers.
The assistants record the amount of time it takes them to eight the Big Mac special.
1.0
585.0
1.0
540.0
1.0
660.0
1.0
571.0
1.0
584.0
1.0
653.0
1.0
574.0
1.0
569.0
1.0
619.
Student's t-test is used to determine if two population means are statistically different based on random samples from those populations. It calculates a ratio of the difference between sample means to the variability within each sample. If the t-value is large enough based on the sample sizes and pre-set significance level (often 0.05), then the population means are considered statistically different. The t-test is commonly used to compare outcomes before and after an intervention or between treated and control groups.
Student's t-test is used to determine if two population means are statistically different based on random samples from those populations. It calculates a ratio of the difference between two sample means over the variability within each sample. If the t-value is large enough based on the sample sizes and pre-set significance level (often 0.05), then the population means are considered statistically different. The t-test is commonly used to compare outcomes before and after an intervention or between treated and untreated groups.
PSY520 – Module 5Answer Sheet Submit your answers in the.docxwoodruffeloisa
PSY520 – Module 5
Answer Sheet
Submit your answers in the boxes provided. No credit will be given for responses not found in the correct answer area.
Chapter 13:
13.6It’s well established, we’ll assume, that lab rats require an average of 32 trials in a complex water maze before reaching a learning criterion of three consecutive errorless trials. To determine whether a mildly adverse stimulus has any effect on performance, a sample of seven lab rats were given a mild electrical shock just before each trial.
Question:
Steps:
Calculations or Logic:
Answer:
Given that X 5 34.89 and s 5 3.02, test the null hypothesis with t , using the .05 level of significance.
What is the research hypothesis?
What is the null hypothesis?
Is this a one-tailed or two-tailed test?
What are the degrees of freedom?
What is the t critical for .05 significance?
What is the calculated t?
Do you accept or reject the null hypothesis?
Construct a 95 percent confidence interval for the true number of trials required to learn the water maze.
Interpret this confidence interval.
13.8Assume that on average, healthy young adults dream 90 minutes each night, as inferred from a number of measures, including rapid eye movement (REM) sleep. An investigator wishes to determine whether drinking coffee just before going to sleep affects the amount of dream time. After drinking a standard amount of coffee, dream time is monitored for each of 28 healthy young adults in a random sample. Results show a sample mean, X, of 88 minutes and a sample standard deviation, s, of 9 minutes.
Question:
Steps:
Calculations or Logic:
Answer:
Use t to test the null hypothesis at the .05 level of significance.
What is the research hypothesis?
What is the null hypothesis?
Is this a one-tailed or two-tailed test?
What are the degrees of freedom?
What is the t critical for .05 significance?
What is the calculated t?
Do you accept or reject the null hypothesis?
If appropriate (because the null hypothesis has been rejected), construct a 95 percent confidence interval and interpret this interval.
13.9In the gas mileage test described in this chapter, would you prefer a smaller or a larger sample size if you were the car manufacturer? Why? a vigorous prosecutor for the federal regulatory agency? Why
Question:
Smaller or Larger?
Why?
In the gas mileage test described in this chapter, would you prefer a smaller or a larger sample size if you were the car manufacturer?
In the gas mileage test described in this chapter, would you prefer a smaller or a larger sample size if you were a vigorous prosecutor for the federal regulatory agency?
13.10Even though the population standard deviation is unknown, an investigator uses z rather than the more appropriate t to test a hypothesis at the .05 level of significance.
Question:
Larger or smaller?
Is the true level of significance larger or smaller than .05
Is the true critical value larger or smaller than that for the cr ...
Week 5 Lecture 14 The Chi Square TestQuite often, patterns of .docxcockekeshia
Week 5 Lecture 14
The Chi Square Test
Quite often, patterns of responses or measures give us a lot of information. Patterns are generally the result of counting how many things fit into a particular category. Whenever we make a histogram, bar, or pie chart we are looking at the pattern of the data. Frequently, changes in these visual patterns will be our first clues that things have changed, and the first clue that we need to initiate a research study (Lind, Marchel, & Wathen, 2008).
One of the most useful test in examining patterns and relationships in data involving counts (how many fit into this category, how many into that, etc.) is the chi-square. It is extremely easy to calculate and has many more uses than we will cover. Examining patterns involves two uses of the Chi-square - the goodness of fit and the contingency table. Both of these uses have a common trait: they involve counts per group. In fact, the chi-square is the only statistic we will look at that we use when we have counts per multiple groups (Tanner & Youssef-Morgan, 2013). Chi Square Goodness of Fit Test
The goodness of fit test checks to see if the data distribution (counts per group) matches some pattern we are interested in. Example: Are the employees in our example company distributed equal across the grades? Or, a more reasonable expectation for a company might be are the employees distributed in a pyramid fashion – most on the bottom and few at the top?
The Chi Square test compares the actual versus a proposed distribution of counts by generating a measure for each cell or count: (actual – expected)2/actual. Summing these for all of the cells or groups provides us with the Chi Square Statistic. As with our other tests, we determine the p-value of getting a result as large or larger to determine if we reject or not reject our null hypothesis. An example will show the approach using Excel.
Regardless of the Chi Square test, the chi square related functions are found in the fx Statistics window rather than the Data Analysis where we found the t and ANOVA test functions. The most important for us are:
· CHISQ.TEST (actual range, expected range) – returns the p-value for the test
· CHISQ.INV.RT(p-value, df) – returns the actual Chi Square value for the p-value or probability value used.
· CHISQ.DIST.RT(X, df) – returns the p-value for a given value.
When we have a table of actual and expected results, using the =CHISQ.TEST(actual range, expected range) will provide us with the p-value of the calculated chi square value (but does not give us the actual calculated chi square value for the test). We can compare this value against our alpha criteria (generally 0.05) to make our decision about rejecting or not rejecting the null hypothesis.
If, after finding the p-value for our chi square test, we want to determine the calculated value of the chi square statistic, we can use the =CHISQ.INV.RT(probability, df) function, the value for probability is .
Week 6 DQ1. What is your research questionIs there a differen.docxcockekeshia
Week 6 DQ
1. What is your research question?
Is there a difference between the math utility of a male and a female?
2. What is the null hypothesis for your question?
Hn There is no difference in the math utility between male and female.
Alternative hypotheses can also be created in the case the null hypothesis is proven incorrect. Two alternative hypotheses are:
Ha1 Feales have a higher math utility.
Ha2 Males have a higher math utility.
3. What research design would align with this question?
According to Frankfort-Nachmias and Leon-Guerrero (2015) a descriptive research design would be best for this type of study.
4. What comparison of means test was used to answer the question (be sure to defend the use of the test using the article you found in your search)?
The independent-samples T test was used to analyze the means for this data.
5. What dependent variable was used and how is it measured?
The dependent variable is the student’s math utility. It is measured from -3.51 to 1.31(University high school longitudinal study dataset. (2009).
6. What independent variable is used and how is it measured?
Either male (1) of female (2) (University high school longitudinal study dataset. (2009).
7. If you found significance, what is the strength of the effect?
The significance was 0.0000. This is much better than the standard of .05 significance as outlined by Frankfort-Nachmias and Leon-Guerrero (2015).
8. Identify your research question and explain your results for a lay audience, what is the answer to your research question?
My research question was “Is there a difference between the math utility of a male and a female?” Based on the analysis of the means (or average) through testing using the independent-samples T test there was no measurable difference between the math utility of male or females. This leads us to accept the null hypothesis of “There is no difference in the math utility between male and female” as true.
Group Statistics
T1 Student's sex
N
Mean
Std. Deviation
Std. Error Mean
T1 Scale of student's mathematics utility
Male
9453
.0140
1.01962
.01049
Female
9349
-.0481
.97291
.01006
Independent Samples Test
Levene's Test for Equality of Variances
t-test for Equality of Means
F
Sig.
t
df
Sig. (2-tailed)
Mean Difference
Std. Error Difference
95% Confidence Interval of the Difference
Lower
Upper
T1 Scale of student's mathematics utility
Equal variances assumed
17.400
.000
4.276
18800
.000
.06216
.01454
.03367
.09066
Equal variances not assumed
4.277
18775.932
.000
.06216
.01453
.03367
.09065
University high school longitudinal study dataset. (2009).
References
Frankfort-Nachmias, C., & Leon-Guerrero, A. (2015). Social statistics for a diverse society (7th ed.). Thousand Oaks, CA: Sage Publications.
University high school longitudinal study dataset. (2009). Retrieved from class.waldenu.edu
The t Test for Related Samples
The t Test for Related Samples
Program Transcript
MAT.
Happiness Data SetAuthor Jackson, S.L. (2017) Statistics plain ShainaBoling829
Happiness Data Set
Author: Jackson, S.L. (2017) Statistics plain and simple. (4th ed.). Boston, MA: Cengage Learning.
I attach the previous essay so you have idea on how to do this assignment. It is similar to the assignment last week.
Assignment Content
1.
Top of Form
As you get closer to the final project in Week 6, you should have a better idea of the role of statistics in research. This week, you will calculate a one-way ANOVA for the independent groups. Reading and interpreting the output correctly is highly important. Most people who read research articles never see the actual output or data; they read the results statements by the researcher, which is why your summary must be accurate.
Consider your hypothesis statements you created in Part 2.
Calculate a one-way ANOVA, including a Tukey's HSD for the data from the Happiness and Engagement Dataset.
Write a 125- to 175-word summary of your interpretation of the results of the ANOVA, and describe how using an ANOVA was more advantageous than using multiple t tests to compare your independent variable on the outcome. Copy and paste your Microsoft® Excel® output below the summary.
Format your summary according to APA format.
Submit your summary, including the Microsoft® Excel® output to the assignment.
Reference/Module:
Module 13: Comparing More Than Two Groups
Using Designs with Three or More Levels of an Independent Variable
Comparing More than Two Kinds of Treatment in One Study
Comparing Two or More Kinds of Treatment with a Control Group
Comparing a Placebo Group to the Control and Experimental Groups
Analyzing the Multiple-Group Design
One-Way Between-Subjects ANOVA: What It Is and What It Does
Review of Key Terms
Module Exercises
Critical Thinking Check AnswersModule 14: One-Way Between-Subjects Analysis of Variance (ANOVA)
Calculations for the One-Way Between-Subjects ANOVA
Interpreting the One-Way Between-Subjects ANOVA
Graphing the Means and Effect Size
Assumptions of the One-Way Between-Subjects ANOVA
Tukey's Post Hoc Test
Review of Key Terms
Module Exercises
Critical Thinking Check AnswersChapter 7 Summary and ReviewChapter 7 Statistical Software Resources
In this chapter, we discuss the common types of statistical analyses used with designs involving more than two groups. The inferential statistics discussed in this chapter differ from those presented in the previous two chapters. In Chapter 5, single samples were being compared to populations (z test and t test), and in Chapter 6, two independent or correlated samples were being compared. In this chapter, the statistics are designed to test differences between more than two equivalent groups of subjects.
Several factors influence which statistic should be used to analyze the data collected. For example, the type of data collected and the number of groups being compared must be considered. Moreover, the statistic used to analyze the data will vary depending on whether the study involves a between-subjects design (designs in ...
2016 Symposium Poster - statistics - FinalBrian Lin
This document discusses common pitfalls in statistical analysis and provides examples to illustrate typical mistakes. It notes that statistical significance does not always imply practical significance. Even with the same means and variances, different datasets can have very different distributions. Correlation does not necessarily indicate causation. Qualitative scales should not always be treated as quantitative variables. Choosing the appropriate statistical test is important to get the right results. Sample size calculations depend on study details and objectives. Involving statisticians early in the research process helps ensure proper experimental design and analysis.
Chapter NineShow all workProblem 1)A skept.docxneedhamserena
Chapter Nine
Show all work
Problem 1)
A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO is less than 1 in every one thousand.
State the null hypothesis and the alternative hypothesis for a test of significance.
Problem 2)
At one school, the average amount of time that tenth-graders spend watching television each week is 18.4 hours.
The principal introduces a campaign to encourage the students to watch less television.
One year later, the principal wants to perform a hypothesis test to determine whether the average amount of time spent watching television per week has decreased.
Formulate the null and alternative hypotheses for the study described.
Problem 3)
A two-tailed test is conducted at the 5% significance level.
What is the P-value required to reject the null hypothesis?
Problem 4)
A two-tailed test is conducted at the 5% significance level.
What is the
right tail percentile
required to reject the null hypothesis?
Problem 5)
What is the difference between an Type I and a Type II error?
Provide an example of both.
Chapter 10
Show all work
Problem 1)
Steven collected data from 20 college students on their emotional responses to classical music.
Students listened to two 30-second segments from “The Collection from the Best of Classical Music.”
After listening to a segment, the students rated it on a scale from 1 to 10, with 1 indicating that it “made them very sad” to 10 indicating that it “made them very happy.” Steve computes the total scores from each student and created a variable called “hapsad.”
Steve then conducts a one-sample t-test on the data, knowing that there is an established mean for the publication of others that have taken this test of 6.
The following is the scores:
5.0
5.0
10.0
3.0
13.0
13.0
7.0
5.0
5.0
15.0
14.0
18.0
8.0
12.0
10.0
7.0
3.0
15.0
4.0
3.0
Conduct a one-sample t-test.
What is the t-test score?
What is the mean?
Was the test significant?
If it was significant at what P-value level was it significant?
What is your null and alternative hypothesis? Given the results did you reject or fail to reject the null and why?
(Use instructions on page 437 of your textbook, under Hypothesis Tests with the t Distribution to conduct SPSS or Excel analysis).
Problem 2)
Billie wishes to test the hypothesis that overweight individuals tend to eat faster than normal-weight individuals.
To test this hypothesis, she has two assistants sit in a McDonald’s restaurant and identify individuals who order the Big Mac special for lunch.
The Big Mackers as they become known are then classified by the assistants as overweight, normal weight, or neither overweight nor normal weight.
The assistants identify 10 overweight and 10 normal weight Big Mackers.
The assistants record the amount of time it takes them to eight the Big Mac special.
1.0
585.0
1.0
540.0
1.0
660.0
1.0
571.0
1.0
584.0
1..
Assessment 3 ContextYou will review the theory, logic, and a.docxgalerussel59292
Assessment 3 Context
You will review the theory, logic, and application of t-tests. The t-test is a basic inferential statistic often reported in psychological research. You will discover that t-tests, as well as analysis of variance (ANOVA), compare group means on some quantitative outcome variable.
Recall that null hypothesis tests are of two types: (1) differences between group means and (2) association between variables. In both cases there is a null hypothesis and an alternative hypothesis. In the group means test, the null hypothesis is that the two groups have equal means, and the alternative hypothesis is that the two groups do not have equal means. In the association between variables type of test, the null hypothesis is that the correlation coefficient between the two variables is zero, and the alternative hypothesis is that the correlation coefficient is not zero.
Notice in each case that the hypotheses are mutually exclusive. If the null is false, the alternative must be true. The purpose of null hypothesis statistical tests is generally to show that the null has a low probability of being true (the p value is less than .05) – low enough that the researcher can legitimately claim it is false. The reason this is done is to support the allegation that the alternative hypothesis is true.
In this context you will be studying the details of the first type of test. This is the test of difference between group means. In variations on this model, the two groups can actually be the same people under different conditions, or one of the groups may be assigned a fixed theoretical value. The main idea is that two mean values are being compared. The two groups each have an average score or mean on some variable. The null hypothesis is that the difference between the means is zero. The alternative hypothesis is that the difference between the means is not zero. Notice that if the null is false, the alternative must be true. It is first instructive to consider some of the details of groups. Means, and difference between them.
Null Hypothesis Significance Test
The most common forms of the Null Hypothesis Significance Test (NHST) are three types of t tests, and the test of significance of a correlation. The NHST also extends to more complex tests, such as ANOVA, which will be discussed separately. Below, the null hypothesis and the alternative hypothesis are given for each of the following tests. It would be a valuable use of your time to commit the information below to memory. Once this is done, then when we refer to the tests later, you will have some structure to make sense of the more detailed explanations.
1. One-sample t test: The question in this test is whether a single sample group mean is significantly different from some stated or fixed theoretical value - the fixed value is called a parameter.
· Null Hypothesis: The difference between the sample group mean and the fixed value is zero in the population.
· Alternative hypothesis: T.
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Introduction to AI for Nonprofits with Tapp Network
Chapter 5 t-test
1. Chapter 5: Comparing two means using the t-test
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Upon completion of this chapter, you should be able to:
explain what is the t-Test and its use in hypothesis testing
demonstrate using the t-Test for INDEPENDENT MEANS
identify the assumptions for using the t-test
demonstrate the use of the t-Test for DEPENDENT MEANS
CHAPTER OVERVIEW
What is the t-test?
The hypothesis tested using the t-
test
Using the t-test for independent
means
Assumptions that must be observed
when using the t-test
Summary
Key Terms
References
Chapter 1: Introduction
Chapter 2: Descriptive Statistics
Chapter 3: The Normal Distribution
Chapter 4: Hypothesis Testing
Chapter 5: T-test
Chapter 6: Oneway Analysis of Variance
Chapter 7: Correlation
Chapter 8: Chi-Square
This chapter introduces you to the t-test which is statistical tool used to test the significant
differences between the means of two groups. The independent t-test is used when the
means of two groups when the sample is drawn from two different or independent
samples. The dependent or pairwise t-test is used when the sample is tested twice the
means are compared.
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What is the T-Test?
The t-test was developed by a statistician, W.S.
Gossett (1878-1937) who worked in a brewery in Dublin,
Ireland. His pen name was ‘student’ and hence the term
‘student’s t-test’ which was published in the scientific
journal, Biometrika in 1908. The t-test is a statistical tool
used to infer differences between small samples based on
the mean and standard deviation.
In many educational studies, the researcher is
interested in testing the differences between means on
some variable. The researcher is keen to determine
whether the differences observed between two samples
represents a real difference between the populations from
which the samples were drawn. In other words, did the observed difference just
happen by chance when, in reality, the two populations do not differ at all on the
variable studies.
or example, a teacher wanted to find out whether the Discovery method of
teaching science to primary school children was more effective than the Lecture
method. She conducted an experiment among 70 primary school children of which 35
pupils were taught using the Discovery method and 35 children were taught using the
Lecture method. The results of the study showed that subjects in the Discovery group
scored 43.0 marks while subjects in the Lecture method group score 38.0 marks on a
the science test. Yes, the Discovery group did better than the Lecture group. Does the
difference between the two groups represent a real difference or was it due to
chance? To answer this question, the t-test is often used by researchers.
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The Hypothesis Tested Using the T-Test
How do we go about establishing whether the differences in the two means are
statistically significant or due to chance? You begin by formulating a hypothesis
about the difference. This hypothesis states that the two means are equal or the
difference between the two means is zero and is called the null hypothesis.
Using the null hypothesis, you begin testing the significance by saying:
"There is no difference in the score obtained in science between subjects in the
Discovery group and the Lecture group".
More commonly the null hypothesis may be stated as follows:
a) Ho : U1 = U2 which translates into 43.0 = 38.0
b) Ho : U1 ─ U2 = 0 which translate into 43.0 ─ 38.0 = 0
If you reject the null hypothesis, it means that the difference between the two
means have statistical significance
If you do not reject the null hypothesis, it means that the difference between
the two means are NOT statistically significant and the difference is due to
chance.
Note:
For a null hypothesis to be accepted, the difference between the two means need not
be equal to zero since sampling may account for the departure from zero. Thus, you
can accept the null hypothesis even if the difference between the two means is not
zero provided the difference is likely to be due to chance. However, if the difference
between the two means appears too large to have been brought about by chance, you
reject the null hypothesis and conclude that a real difference exists.
LEARNING ACTIVITY
a) State TWO null hypothesis in your area of interest
that can be tested using the t-test.
b) What do you mean when you reject or do not reject
the null hypothesis?
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Using the T-Test for INDEPEDENT MEANS
The t-test is a powerful statistic that enables you to determine that the
differences obtained between two groups is statistically significant. When two groups
are INDEPENDENT of each other; it means that the sample drawn came from two
populations. Other words used to mean that the two groups are independent are
"unpaired" groups and "unpooled” groups.
a) What is meant by Independent Means or Unpaired Means?
Say for example you conduct a study to determine the spatial reasoning ability
of 70 ten-year old children in Malaysia. The sample consisted of 35 males and 35
females. See figure 5.1. The sample of 35 males was drawn from the population of ten
year old males in Malaysia and the sample of 35 females was drawn from the
population of ten year olds females in Malaysia.
Note that they are independent samples because they come from two completely
different populations.
Figure 5.1 Samples drawn from two independent populations
Population of ten year old
MALES in Malaysia
Population of ten year old
FEMALES in Malaysia
Sample of 35 MALES Sample of 35 FEMALES
Research Question:
"Is there a significant difference in spatial reasoning between male and female ten
year old children?"
Null Hypothesis or Ho:
"There is no significant difference in spatial reasoning between male and female
ten year old children"
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b) Formula for the Independent T-Test
Note that the formula for the t-test shown below is a ratio. It is Group 1 mean (i.e.
males) minus Group 2 mean (i.e. females) divided by the Standard Error multiplied by
Group 1 mean minus Group 2 mean.
Computation of the Standard Error
Use the formula below. To compute the standard error (SE), you take the variance
(i.e. standard deviation squared) for Group 1 and divide it by the number of subjects
in that group minus "1". Do the same for Group 2. Than add these two values and take
the square root.
The top part of the equation is the
difference between the two means
The bottom part of the equation is
the Standard Error (SE) which is a
measure of the variability of
dispersion of the scores.
This is the formula for the
Standard Error:
Combine the two
formulas and you get
this version of the t-test
formula:
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b) Example:
The results of the study are as follow:
Let's try using the formula:
t =
2
= ------------- = 4.124
0.485
Note:
The t-value will be positive if the mean for Group I is larger or more than (>) the
mean of Group 2 and negative if it is smaller or less than (<).
c) What do you do after computing the t-value?
Once you compute the t-value (which is 4.124) you look up the t-value in The
Student's t-test Probabilities or The Table of Critical Values for Student’s T-Test
which tells us whether the ratio is large enough to say that the difference between the
groups is significant. In other words the difference observed is not likely due to
chance or sampling error.
Alpha Level: As with any test of significance, you need to set the alpha level.
In most educational and social research, the "rule of thumb" is to set the alpha
level at .05. This means that 5% of the time (five times out of a hundred) you
would find a statistically significant difference between the means even if
there is none ("chance").
Degrees of Freedom: The t-test also requires that we determine the degrees of
freedom (df) for the test. In the t-test, the degrees of freedom is the sum of the
subjects or persons in both groups minus 2. Given the alpha level, the df, and
the t-value, you look up in the Table (available as an appendix in the back of
12 -10
4.0 1
0.1177 + 0.1177
4.0 2
(35-1) (35-1)
2
=
+
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most statistics texts) to determine whether the t-value is large enough to be
significant.
d) Look up in the Table of Critical Values for Student's t-test shown on the right:
The df is 70 minus 2 = 68. You take the nearest df which is 70 and read the
column for the two-tailed alpha of 0.050. See Table 5.1.
The t-value you obtained is 4.124. The critical value shown is 1.677. Since,
the t-values is greater than the critical value of 1.677, you Reject Ho and conclude
that the difference between the means for the two groups is different. In other words,
males scored significantly higher than females on the spatial reasoning test.
However, you do not have to go through this tedious process, as statistical
computer programs such as SPSS, provides the significance test results, saving you
from looking them up in the Table of Critical Values.
Table 5. 1: Table of Critical Values for Student's t-test
Tailed
Two 0.250 0.100 0.050 0.025 0.010 0.005
One 0.500 0.200 0.100 0.050 0.020 0.010
df
30 0.683 1.310 1.697 2.042 2.457 2.750
40 0.681 1.303 1.684 2.021 2.423 2.704
50 0.679 1.299 1.676 2.009 2.403 2.678
60 0.679 1.296 1.671 2.000 2.390 2.660
70 0.678 1.294 1.667 1.994 2.381 2.648
80 0.678 1.292 1.664 1.990 2.374 2.639
90 0.677 1.291 1.662 1.987 2.368 2.632
100 0.677 1.290 1.660 1.984 2.364 2.626
100 0.674 1.282 1.645 1.960 2.326 2.576
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Assumptions that Must be Observed when Using the T-Test
While the t-test has been described as a robust statistical tool, it is based on a
model that makes several assumptions about the data that must be met prior to
analysis. Unfortunately, students conducting research tend not to report whether their
data meet the assumptions of the t-test. These assumptions need are be observed,
because the accuracy of your interpretation of the data depends on whether
assumptions are violated. The following are three main assumptions that are generic
to all t-tests.
Instrumentation (Scale of Measurement)
The data that you collect for the dependent variable should be based on an
instrument or scale that is continuous or ordinal. For example, scores that
you obtain from a 5-point Likert scale; 1,2,3,4,5 or marks obtained in a
mathematics test, the score obtained on an IQ test or the score obtained on
an aptitude test.
Random Sampling
The sample of subjects should be randomly sampled from the population
of interest.
Normality
The data come from a distribution that has one of those nice bell-shaped
curves known as a normal distribution. Refer to Chapter 3: The Normal
Distribution which provides both graphical and statistical methods for
assessing normality of a sample or samples.
Sample Size
Fortunately, it has been shown that if the sample size is reasonably large,
quite severe departures from normality do not seem to affect the
LEARNING ACTIVITY
a) Would you reject Ho if you had set the alpha at 0.01 for a
two-tailed test?
b) When do you use the one-tailed test and two-tailed t-test?
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conclusions reached. Then again what is a reasonable sample size? It has
been argued that as long as you have enough people in each group
(typically greater or equal to 30 cases) and the groups are close to equal in
size, you can be confident that the t-test will be a good, strong tool for
getting the correct conclusions. Statisticians say that the t-test is a "robust"
test. Departure from normality is most serious when sample sizes are
small. As sample sizes increase, the sampling distribution of the mean
approaches a normal distribution regardless of the shape of the original
population.
Homogeneity of Variance.
It has often been suggested by some researchers that homogeneity of
variance or equality of variance is actually more important than the
assumption of normality. In other words, are the standard deviations of the
two groups pretty close to equal? Most statistical software packages
provide a "test of equality of variances" along with the results of the t-test
and the most common being Levene's test of homogeneity of variance
(see Table 5.2).
Levene's Test 95% Confidence
of Equality Interval
of Variances
F Sig t d Sign. Mean Std. Error Upper Lower
Two-tail Difference Difference
Equal
Variances 3.39 .080 .848 20 .047 1.00 1.18 -1.46 3.46
Assumed
Unequal
Variances .848 16.70 .049 1.00 1.18 -1.49 3.40
Assumed
Table 5.2 Levene’s Test of Equality of Variances
Begin by putting forward the null hypothesis that:
"There are no significant differences between the variances of the two
groups" and you set the significant level at .05.
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If the Levene statistic is significant, i.e. LESS than .05 level (p < .05), then the null
hypothesis is:
REJECTED and one accepts the alternative hypothesis and conclude that
the VARIANCES ARE UNEQUAL. [The unequal variances in the SPSS
output is used]
If the Levene statistic is not significant, i.e. MORE than .05 level (p > .05),
then you DO NOT REJECT (or Accept) the null hypothesis and conclude
that the VARIANCES ARE EQUAL. [The equal variances in the SPSS
output is used]
The Levene test is robust in the face of departures from normality. The Levene's test
is based on deviations from the group mean.
SPSS provides two options'; i.e. "homogeneity of variance assumed" and
"homogeneity of variance not assumed" (see Table below).
The Levene test is more robust in the face of non-normality than more
traditional tests like Bartlett's test.
Let’s examine an EXAMPLE:
In the CoPs Project, an Inductive Reasoning scale consisting of 11 items was
administered to 946 eighteen year. One of the research questions put forward is:
"Is there a significant difference between in inductive reasoning between
male and female subjects"?
To establish the statistical significance of the means of these two groups, the t-
test was used. Using SPSS.
LEARNING ACTIVITY
Refer to the table above. Based on the Levene’s Test of
Homogeneity of variance, what is your conclusion. Explain.
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THE SPSS STEPS to answer the Research Question.
SPSS OUTPUTS:
Output #1:
The ‘Group statistics’ table above reports that the mean values on the variable
(inductive reasoning) for the two different groups (males and females). Here, we see
that the 495 females in the sample scored 8.99 while the 451 males had a mean score
of 7.95 on inductive reasoning. The standard deviation for the males is 3.46 while
that for the females is 3.14. The scores for the females are less dispersed compared to
the males.
SPSS PROCEDURES for the independent groups t-test:
1. Select the Analyze menu.
2. Click on Compare Means and then Independent-
Samples T Test ....to open the Independent Samples
T Test dialogue box.
3. Select the test variable(s). [i.e. Inductive Reasoning] and
then click on the button to move the variables into
the Test Variables(s): box
4. Select the grouping variables [i.e. gender] and click on
the button to move the variable into the Grouping Variable:
box
5. Click on the Define Groups ....command pushbutton to
open the Define Groups sub-dialogue box.
6. In the Group 1: box, type the lowest value for the variable
[i.e. 1 for 'males'], then tab. Enter the second value for the
variables [i.e. 2 for 'females'] in the Group 2: box.
7. Click on Continue and then OK.
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GROUP STATISTICS
The question remains: Is this sample difference in inductive reasoning large
enough to convince us that there it is a real significant difference in inductive
reasoning ability between the population 18 year old females and the population of 18
year-old males?
Output #2:
Let’s examine this output in two parts:
First is to determine that the data meet the "Homogeneity of Variance" assumption
you can use the Levene's Test and set the alpha at 0.05. The alpha obtained is 0.054
which is greater (>) than 0.05 and you do not Reject the Ho: and conclude that the
variances are equal. Hence, you have not violated the "Homogeneity of Variance"
assumption.
Levene's Test 95% Confidence
of Equality Interval
of Variances
F Sig t d Sign. Mean Std. Error Upper Lower
Two-tail Difference Difference
Equal
Variances 4.720 .030 -4.875 944 .000 -1.0468 -2.147 -1.4682 -.6254
Assumed
Unequal
Variances -4.853 911.4 .049 -1.0468 -2.146 -1.4701 -.6234
Assumed
INDUCTIVE N Mean Std. Deviation Std. Error Mean
GENDER Male 451 7.9512 3.4618 2.345
Female 495 8.9980 3.1427 3.879
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SECOND is to examine the following:
The SPSS output below displays the results of the t-test to test whether or not
the difference between the two sample means is significantly different from
zero.
Remember the null hypothesis states that there is no real difference between
the means (Ho: X1 = X2).
Any observed difference just occurred by chance.
Interpretation:
t-value
This "t" value tells you how far away from 0, in terms of the number of standard
errors, the observed difference between the two sample means falls. The "t" value is
obtained by dividing the difference in the Means ( - 1.0468) by the Std. Error (-.2147)
which is equal to - 4.875
p-value
If the p-value as shown in the "sig (2 tailed) column is smaller than your chosen alpha
level you do not reject the null hypothesis and argue that there is a real difference
between the populations. In other words, we can conclude, that the observed
difference between the samples is statistically significant.
Mean Difference
This is the difference between the means (labelled "Mean Difference"); i.e. 7.9512 –
8.9980 = – 1.0468.
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Using the T-Test for Dependent Means
The Dependent means t-test or the Paired t-test or the Repeated measures
t-test is used when you have data from only one group of subjects. i.e. each subject
obtains two scores under different conditions. For example, when you give a pre-test
and after a particular treatment or intervention you give the same subjects a post-test.
In this form of design, the same subjects obtain a score on the pretest and, after some
intervention or manipulation obtain a score on the posttest. Your objective is to
determine whether the difference between means for the two sets of scores is the same
or different.
You want to find answers to the following:
Research Questions:
Is there a significant difference in pretest and posttest scores in mathematics
for subjects taught using visualisation techniques?
Null Hypotheses:
There is no significant difference between the pretest and the posttest scores in
mathematics for subjects taught using visualisation techniques.
Treatment: Students taught using
Visualisation techniques
Note: The pretest and posttest should be similar or equivalent
PRETEST
POSTTEST
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The top part of the equation is the sum of the
difference between the two means divided by ‘n’
or the number of subjects
FORMULA OF THE DEPENDENT t-TEST
d
t =
sd
n
Let’s look at an EXAMPLE where the formula is applied:
A researcher wanted to determine if teaching 12 year children memory techniques
improved their performance in science. Randomly selected 12 year olds were trained
in memory techniques for two weeks and the results of the study is shown in the table
below:
Student Science
Pretest
Science
Posttest
Paired
difference
d d ²
1 12 18 6 36
2 10 14 4 16
3 15 19 4 16
4 9 15 6 36
5 11 14 3 9
6 13 17 4 16
7 14 16 2 4
8 11 13 2 4
9 10 16 4 16
10 9 12 3 9
Ʃd = 38 Ʃ d ² = 162
Standard deviation = 0.443
Ʃ d = 38
Ʃ d ² = 162
The 4th
column in the table above shows the difference, d, between the science pretest
and the science posttest scores for each of the 10 students sampled. You refer to each
The bottom part of the equation is the
Standard Deviation (sd) which is a measure of
the variability of dispersion of the scores divided
by the square root of ‘n’ or the number of
subjects.
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difference as a paired difference because it is the difference of a pair of observations.
For example, student #1 got 12 on the pretest and 18 on the posttest, giving a paired
difference of d = 18 – 12 = 6 marks, an increase in 6 marks as a result of the memory
techniques training.
If the null hypothesis is true, the paired differences between the pretest and
the posttest for the 10 students sampled should average about 0 (zero).
If the paired differences is greater than zero, the null hypothesis is false.
STEPS IN THE COMPUTATION OF THE T-VALUE
Step 1:
You begin by computing the d
d = Ʃ (posttest score – pretest score ) = 38 = 3.80
number of students 10
Step 2:
Next is to compute the value of sd.
sd =
= 1.399
Step 3:
Applying the t-test for Dependent Means formula:
d 3.80
t = = = 8.589
sd 1.399 √ 10
√ n
Ʃd² ─ (Ʃd)² ∕ n
n – 1
162 ─ (38)² ∕ n
n – 1
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Excerpt of the Table of Critical Values for Student's t-test
Tailed
Two 0.100 0.050 0.025 0.010 0.005
One 0.200 0.100 0.050 0.020 0.010
df
9 1.383 1.833 2.262 2.821 3.250
10 1.372 1.812 2.228 2.764 3.169
11 1.363 1.796 2.201 2.718 3.106
12 1.356 1.782 2.179 2.681 3.055
Step 4:
Having computed the t-value (which is 8.589) you look up the t-value in The Table
of Critical Values for Student's t-test or The Table of Significance which tells us
whether the ratio is large enough to say that the difference between the groups is
significant. In other words the difference observed is not likely due to chance or
sampling error.
Alpha Level:
The researcher set the alpha level at 0.05. This means that 5% of the time (five out of
a hundred) you would find a statistically significant difference between the means
even if there is none ("chance").
Degrees of Freedom:
The t-test also requires that we determine the degrees of freedom (df) for the test. In
the t-test, the degrees of freedom is the sum of the subjects or persons which is 10
minus 1 = 9. Given the alpha level, the df, and the t-value, you look up in the Table
(available as an appendix in the back of most statistics texts) to determine whether the
t-value is large enough to be significant.
Step 5:
The t-value obtained is 8.589 which is greater than the critical value shown which is
1.833 (one tailed). Hence, the null hypothesis [Ho:] is Rejected and Ha: is accepted
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which states Mean 1 > than Mean 2. It can be concluded that the difference between
the means is different. In other words, there is overwhelming evidence that a "gain"
has taken place on the science posttest as a result of training students on memory
techniques.
Again, you do not have to go through this tedious process, as statistical
computer programs such as SPSS, provides the significance test
results, saving you from looking them up in a table.
Note: Misapplication of the Formula
A common error made by some research students is the misapplication of the
formula. Researchers who have Dependent Samples fail to recognise this fact,
and inappropriately apply the t-test for Independent Groups to test the
hypothesis that X¹ = X² = 0. If an inappropriate Independent Groups t-test is
performed with Dependent Groups the standard error will be greatly
overestimated and significant differences between the two means may be
considered "non-significant" (Type 1 Error).
The opposite error, mistaking non-significant differences for significant ones
(Type 2 Error), may be made if the Independent Groups t-test is applied to
Dependent Groups t-test. Thus, when using the t-test, you need to recognise
and distinguish Independent and Dependent samples.
Using SPSS: T-Test for Dependent Means
EXAMPLE:
In a study, a researcher was keen to determine if teaching note-taking techniques
improved achievement in history. A sample of 22 students selected for the study and
taught note-taking techniques for a period of 4 weeks. The research questions put
forward is:
"Is there a significant difference in performance in history before and after the
treatment?" i.e. You wish to determine whether the difference between the means
for the two sets of score is the same or different.
To establish the statistical significance of the means obtained on the pretest
and posttest, the dependent-samples or paired t-test was used.
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Data was collected from the same group of subjects on both conditions and
each subject obtains a score on the pretest, and after the treatment (or intervention or
manipulation), a score on the posttest.
Ho: U1 = U2 or Ha: U1 = U2
You will notice that the syntax for the Independent Groups t-test is different from that
of the Dependent groups t-test. In the case of the Independent Groups t-test you have
a grouping variable so you can distinguish between Group 1 and Group 2 whereas
this is not found with the Dependent groups t -test.
The following are the SPSS OUTPUTS:
Paired Sample Statistics
HISTORY TEST N Mean Std. Deviation Std. Error Mean
Pair Pretest 40 43.15 12.97 2.05
Posttest 40 63.98 13.16 2.08
The ‘Paired sample statistics’ table above reports that the mean values on the variable
(history test) for the pretest and posttest. The posttest mean is higher (63.98) than the
posttest mean (43.15) indicating improved performance in the history test after the
SPSS PROCEDURES for the dependent groups t-test:
1. Select the Analyze menu.
2. Click on Compare Means and then Paired-Samples T Test
....to open the Paired-Sample T Test dialogue box.
3. Select the test variable(s). [i.e. History Test] and
then press the button to move the variables into
the Paired Variables: box
4. Click on Continue and then OK.
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treatment. The standard deviation for the pretest 2.05 and is very close to the standard
deviation for the posttest which is 2.08.
The question remains: Is this mean difference large enough to convince us that there
it is a real significant difference in performance in history a consequence of teaching
note taking techniques)?
Paired Differences
Mean Std . Std. Error t df Sig. (2 tailed)
Difference Deviation Mean Lower Upper
Pair Pretest -20.83 15.65 2.47 -25.83 -15.82 -8.43 39 .000
Posttest
t-Value
This "t" value tells you how far away from 0, in terms of the number of standard
errors, the observed difference between the two sample means falls. The "t" value is
obtained by dividing the Mean difference ( - 20.83) by the Std. Error (2.47) which is
equal to – 8.43.
p-value
The p-value shown in the "sig (2 tailed) column is smaller than your chosen alpha
level (0.05) and so you Reject the null hypothesis and argue that there is a real
difference between the pretest and posttest.
In other words, we can conclude, that the observed difference between the two
means is statistically significant.
Mean Difference
This is the difference between the means 43.15 – 63.98 = – 20.83 which students did
significantly better on the posttest.
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ATTITUDE N Mean Std. Deviation Std. Error Mean
Pair Pretest 22 8.50 3.33 .71
Posttest 22 13.86 2.75 .59
Paired Differences
Mean Std . Std. Error t df Sig.
Deviation Mean Lower Upper (2 tailed)
Pair Pretest -5.36 2.90 .62 -6.65 -4.08 -8.66 21 .000
1 Posttest
LEARNING ACTIVITY
t-Test for Dependent Means or Groups
T-test
Page 3 of 5
CASE STUDY 1:
In a study, a researcher was interested in finding out
whether attitude towards science would be enhanced when
students are taught science using the Inquiry Method. A
sample of 22 students were administered an attitude toward
science scale before the experiment. The treatment was
conducted for one semester and after which the same
attitude scale was administered to the same group of
students.
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ANSWER THE FOLLOWING QUESTIONS:
1. State a null hypothesis for the above study.
2. State an alternative hypothesis for the above study.
3. Briefly describe the 'Paired Sample Statistics' table with regards to
the means and variability of scores.
4. What is the conclusion of the null hypothesis stated in (1).
5. What is the conclusion of the alternative hypothesis stated in (2).
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GENDER
N Mean Std. Deviation Std. Error Mean
Male 1966 6.9410 2.2858 5.155E-02
Female 2438 6.8351 2.4862 5.035E-02
Levene's Test t-test for
for Equality Equality of
of Variances Means
F Sig. t df Sig. Mean Std. Error
2-tailed Difference Difference
Equal 19.408 .000 1.456 4402 .145 .1059 7.271E-02
Equal 1.469 4327 .142 .1059 7.206E-02
LEARNING ACTIVITY
t-Test for Independent Means or Groups
T-test
CASE STUDY 2:
A researcher was interested in finding out about the
creative thinking skills of secondary school students. He
administered a 10 item creative thinking to a sample of
4400 sixteen year old students drawn from all over
Malaysia
e 3 of 5
24. Chapter 5: Comparing two means using the t-test
24
ANSWER THE FOLLOWING QUESTIONSE:
1. State a null hypothesis for the above study.
2. State an alternative hypothesis for the above study.
3. Briefly describe the 'Group Statistics' table with regards to
the means and variability of scores.
4. Is there evidence for homogeneity of variance? Explain.
5. What would you do if the significance level is 0.053?
6. What is the conclusion of the null hypothesis stated in (1).
7. What is the conclusion of the alternative hypothesis stated in (2).
SUMMARY
The t-test was developed by a statistician, W.S. Gossett (1878-1937) who
worked in a brewery in Dublin, Ireland.
Researchers are keen to determine whether the differences observed between
two samples represents a real difference between the populations from which
the samples were drawn.
The t-test is a powerful statistic that enables you to determine that the
differences obtained between two groups is statistically significant.
When two groups are INDEPENDENT of each other; it means that the sample
drawn came from two populations. Other words used to mean that the two
groups are independent are "unpaired" groups and "unpooled” groups..
In most educational and social research, the "rule of thumb" is to set the alpha
level at .05. This means that 5% of the time (five times out of a hundred) you
would find a statistically significant difference between the means even if
there is none ("chance").
25. Chapter 5: Comparing two means using the t-test
25
This "t" value tells you how far away from 0, in terms of the number of
standard errors, the observed difference between the two sample means falls.
The Dependent means t-test or the Paired t-test or the Repeated measures t-test
is used when you have data from only one group of subjects. i.e. each subject
obtains two scores under different conditions.
KEY WORDS:
T-test
Independent groups
Dependent groups
Paired groups
t-value
Levene’s test
Critical values
Alpha level
Degress of freedom
One tailed
Two tailed
Null hypothesis
Alternative hypothesis