t-test.pptx
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The document discusses the student's t-test, which is used to test the significance of small samples with less than 30 observations. Specifically, it outlines two variants of the t-test statistic: 1) to test the difference between a sample mean and population mean, and 2) to test the difference between the means of two samples drawn from the same normal population. Formulas are provided for calculating the t-test statistic in each case.
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1. An independent samples t-test was conducted to determine if there were differences in anxiety scores between male and female participants before a major competition.
2. The results of the t-test showed no significant difference between the mean anxiety scores of males (M=17, SD=4.58) and females (M=18, SD=3.16), t(8)=0.41, p>0.05.
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ناوی کۆلێژ : زانکۆی پۆلیتەکنیکی ئەندازیاری هەولێر
ناوی بەشی زانستی : ئەندازیاری شارستانی
ناوی بابەت : Engineering Statistics
ناوی قوتابی : بهزاد بهرام صابر
ناوی مامۆستای بابەت : دلڤین حسن عمر
رێکەوتی پێشکەش کردن : ١٥ / ٦ / ٢٠٢٠
Ch6 Testing the Difference between Means, Variances
The document discusses various statistical tests for comparing means and variances between two populations or groups. It provides formulas and examples for:
1. Testing the difference between two means with large independent samples using the z-test. This assumes normal distributions and known or large sample sizes.
2. Testing differences between two means with small independent samples using a t-test. This allows for unknown and unequal variances between populations.
3. Testing differences between two variances using an F-test, which compares the ratio of the two sample variances to an F distribution.
4. Calculating confidence intervals for the difference between two means with large or small independent samples.
Trochim, W. M. K. (2006). Internal validity.httpwww.socialres
Trochim, W. M. K. (2006). Internal validity.
http://www.socialresearchmethods.net/kb/intval.php
Please follow link:^^^^^
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Molly, an administrator with a regional organization that advocates for alternatives to long-term prison sentences for nonviolent offenders, asked a team of researchers to conduct an outcome evaluation of a new vocational rehabilitation program for recently paroled prison inmates. The primary goal of the program is to promote full-time employment among its participants.
To evaluate the program, the evaluators decided to use a quasi-experimental research design. The program enrolled 30 individuals to participate in the new program. Additionally, there was a waiting list of 30 other participants who planned to enroll after the first group completed the program. After the first group of 30 participants completed the vocational program (the “intervention” group), the researchers compared those participants’ levels of employment with the 30 on the waiting list (the “comparison” group).
In order to collect data on employment levels, the probation officers for each of the 60 people in the sample (those in both the intervention and comparison groups) completed a short survey on the status of each client in the sample. The survey contained demographic questions that included an item that inquired about the employment level of the client. This was measured through variables identified as none, part-time, or full-time. A hard copy of the survey was mailed to each probation officer and a stamped, self-addressed envelope was provided for return of the survey to the researchers.
After the surveys were returned, the researchers entered the data into an SPSS program for statistical analysis. Because both the independent variable (participation in the vocational rehabilitation program) and dependent variable (employment outcome) used nominal/categorical measurement, the bivariate statistic selected to compare the outcome of the two groups was the Pearson chi-square.
After all of the information was entered into the SPSS program, the following output charts were generated:
TABLE 1. CASE PROCESSING SUMMARY
Cases
Valid
Missing
Total
N
Percent
N
Percent
N
Percent
Program
Participation
*Employment
59
98.3%
1
1.7%
60
100.0%
TABLE 2. PROGRAM PARTICIPATION *EMPLOYMENT CROSS TABULATION
Employment
Total
None
Part-Time
Full-Time
Program
Participation
Intervention
Group
Count % within Program Participation
5
16.7%
7
23.3%
18
60.0%
30
100.0%
Comparison
Group
Count % within Program Participation
16
55.2%
7
24.1%
6
20.7%
29
100.0%
Total
Count % within Program Participation
21
35.6%
14
23.7%
24
40.7%
59
100.0%
TABLE 3. CHI-SQUARE TESTS
Value
df
Asymp. Sig. (2-sided)
Pearson Chi-Square
11.748a
2
.003
Likelihood Ratio
12.321
2
.002
Linear-by-Linear Association
11.548
1
.001
N of Valid Cases
59
a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 6.88.
The first table, titled Case ...
Qt notes by mj
- The document discusses key concepts in statistics including population, sampling, parameters, statistics, hypothesis testing, and different statistical tests.
- It defines population, sample, population parameters (mean, variance), sample statistics (mean, variance), and the differences between them.
- Hypothesis testing is explained as determining if a population parameter is likely to be true by stating the null and alternative hypotheses, criteria for decision making, computing a test statistic, and making a conclusion.
- Common statistical tests covered include the t-test, F-test, chi-square test, and z-test; and their applications to comparing means, variances, goodness of fit, and independence.
T test-for-a-mean
The document discusses the t-test, which is used to test hypotheses about population means when the population standard deviation is unknown. It is similar to the z-test but uses the sample standard deviation instead of the population standard deviation. The t-test uses degrees of freedom to determine critical values from a t-distribution table. Examples are provided to demonstrate how to perform a t-test, including stating hypotheses, finding critical values, computing the test statistic, making a decision, and summarizing results.
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1. An independent samples t-test was conducted to determine if there were differences in anxiety scores between male and female participants before a major competition.
2. The results of the t-test showed no significant difference between the mean anxiety scores of males (M=17, SD=4.58) and females (M=18, SD=3.16), t(8)=0.41, p>0.05.
3. Therefore, the null hypothesis that there is no difference between male and female anxiety scores before a major competition was not rejected.
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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.
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1. Statistical analysis involves collecting, organizing, analyzing data, and drawing inferences about populations based on samples. It includes both descriptive and inferential statistics.
2. The document defines key terms used in statistical analysis like population, sample, statistical analysis, and discusses various statistical measures like mean, median, mode, interquartile range, and standard deviation.
3. The purposes of statistical analysis are outlined as measuring relationships, making predictions, testing hypotheses, and summarizing results. Both parametric and non-parametric statistical analyses are discussed.
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ناوی کۆلێژ : زانکۆی پۆلیتەکنیکی ئەندازیاری هەولێر
ناوی بەشی زانستی : ئەندازیاری شارستانی
ناوی بابەت : Engineering Statistics
ناوی قوتابی : بهزاد بهرام صابر
ناوی مامۆستای بابەت : دلڤین حسن عمر
رێکەوتی پێشکەش کردن : ١٥ / ٦ / ٢٠٢٠
Ch6 Testing the Difference between Means, Variances
The document discusses various statistical tests for comparing means and variances between two populations or groups. It provides formulas and examples for:
1. Testing the difference between two means with large independent samples using the z-test. This assumes normal distributions and known or large sample sizes.
2. Testing differences between two means with small independent samples using a t-test. This allows for unknown and unequal variances between populations.
3. Testing differences between two variances using an F-test, which compares the ratio of the two sample variances to an F distribution.
4. Calculating confidence intervals for the difference between two means with large or small independent samples.
Trochim, W. M. K. (2006). Internal validity.httpwww.socialres
Trochim, W. M. K. (2006). Internal validity.
http://www.socialresearchmethods.net/kb/intval.php
Please follow link:^^^^^
Social Work Research: Chi Square
Molly, an administrator with a regional organization that advocates for alternatives to long-term prison sentences for nonviolent offenders, asked a team of researchers to conduct an outcome evaluation of a new vocational rehabilitation program for recently paroled prison inmates. The primary goal of the program is to promote full-time employment among its participants.
To evaluate the program, the evaluators decided to use a quasi-experimental research design. The program enrolled 30 individuals to participate in the new program. Additionally, there was a waiting list of 30 other participants who planned to enroll after the first group completed the program. After the first group of 30 participants completed the vocational program (the “intervention” group), the researchers compared those participants’ levels of employment with the 30 on the waiting list (the “comparison” group).
In order to collect data on employment levels, the probation officers for each of the 60 people in the sample (those in both the intervention and comparison groups) completed a short survey on the status of each client in the sample. The survey contained demographic questions that included an item that inquired about the employment level of the client. This was measured through variables identified as none, part-time, or full-time. A hard copy of the survey was mailed to each probation officer and a stamped, self-addressed envelope was provided for return of the survey to the researchers.
After the surveys were returned, the researchers entered the data into an SPSS program for statistical analysis. Because both the independent variable (participation in the vocational rehabilitation program) and dependent variable (employment outcome) used nominal/categorical measurement, the bivariate statistic selected to compare the outcome of the two groups was the Pearson chi-square.
After all of the information was entered into the SPSS program, the following output charts were generated:
TABLE 1. CASE PROCESSING SUMMARY
Cases
Valid
Missing
Total
N
Percent
N
Percent
N
Percent
Program
Participation
*Employment
59
98.3%
1
1.7%
60
100.0%
TABLE 2. PROGRAM PARTICIPATION *EMPLOYMENT CROSS TABULATION
Employment
Total
None
Part-Time
Full-Time
Program
Participation
Intervention
Group
Count % within Program Participation
5
16.7%
7
23.3%
18
60.0%
30
100.0%
Comparison
Group
Count % within Program Participation
16
55.2%
7
24.1%
6
20.7%
29
100.0%
Total
Count % within Program Participation
21
35.6%
14
23.7%
24
40.7%
59
100.0%
TABLE 3. CHI-SQUARE TESTS
Value
df
Asymp. Sig. (2-sided)
Pearson Chi-Square
11.748a
2
.003
Likelihood Ratio
12.321
2
.002
Linear-by-Linear Association
11.548
1
.001
N of Valid Cases
59
a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 6.88.
The first table, titled Case ...
Qt notes by mj
- The document discusses key concepts in statistics including population, sampling, parameters, statistics, hypothesis testing, and different statistical tests.
- It defines population, sample, population parameters (mean, variance), sample statistics (mean, variance), and the differences between them.
- Hypothesis testing is explained as determining if a population parameter is likely to be true by stating the null and alternative hypotheses, criteria for decision making, computing a test statistic, and making a conclusion.
- Common statistical tests covered include the t-test, F-test, chi-square test, and z-test; and their applications to comparing means, variances, goodness of fit, and independence.
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The t-test is used to test the significant difference between two sample means. It was introduced by William Sealy Gosset under the pen name 'student t'. There are two types of t-tests: the independent sample t-test compares two independent groups, while the dependent sample t-test compares two dependent or paired groups. To perform a t-test, the researcher states the null hypothesis, calculates the t-value, finds the degrees of freedom, and compares the calculated t-value to the tabulated value to determine if the null hypothesis can be rejected or retained.
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In the t test for independent groups, ____.we estimate µ1 µ2.docx
In the t test for independent groups, ____.
we estimate µ1 µ2
we estimate 2
we estimate X1-X2
df = N 1
Exhibit 14-1
A professor of women's studies is interested in determining if stress affects the menstrual cycle. Ten women are randomly sampled for an experiment and randomly divided into two groups. One of the groups is subjected to high stress for two months while the other lives in a relatively stress-free environment. The professor measures the menstrual cycle (in days) of each woman during the second month. The following data are obtained.
High stress
20
23
18
19
22
Relatively stress free
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31
25
26
30
Refer to Exhibit 14-1. The obtained value of the appropriate statistic is ____.
tobt = 4.73
tobt = 4.71
tobt = 3.05
tobt = 0.47
Refer to Exhibit 14-1. The df for determining tcrit are ____.
4
9
8
3
Refer to Exhibit 14-1. Using = .052 tail, tcrit = ____.
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+2.506
±2.462
±2.306
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accept H0; stress does not affect the menstrual cycle
retain H0; we cannot conclude that stress affects the menstrual cycle
retain H0; stress affects the menstrual cycle
reject H0; stress affects the menstrual cycle
Refer to Exhibit 14-1. Estimate the size of the effect. = ____
0.8102
0.6810
0.4322
0.5776
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the test has more power
the data are easier to analyze
the experiment does not need to know population parameters
the test has less power
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correlated t test
t test for independent groups
sign test
test of variance
If n1 = n2 and n is relatively large, then the t test is relatively robust against ____.
violations of the assumptions of homogeneity of variance and normality
violations of random samples
traffic violations
violations by the forces of evil
Exhibit 14-3
Five students were tested before and after taking a class to improve their study habits. They were given articles to read which contained a known number of facts in each story. After the story each student listed as many facts as he/she could recall. The following data was recorded.
Before
10
12
14
16
12
After
15
14
17
17
20
Refer to Exhibit 14-3. The obtained value of the appropriate statistic is ____.
3.92
3.06
4.12
2.58
Refer to Exhibit 14-3. What do you conclude using = 0.052 tail?
reject H0; the class appeared to improve study habits
retain H0; the class had no effect on study habits
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accept H0; the class appeared to improve study habits
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the raw score populations are normally distributed
the variances of the raw score populations are the same
the mean of the populations differ
the raw score popul.
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1. The document discusses hypothesis testing, including defining the null and alternative hypotheses, types of errors, test statistics, and testing differences between population means and differences between two samples.
2. Examples are provided to demonstrate hypothesis testing for one and two sample means. This includes stating the hypotheses, significance level, test statistic, critical region, and conclusion.
3. Assignments are given applying hypothesis testing to compare lung destruction between smokers and non-smokers, serum complement activity between disease and normal subjects, and podiatric problems between elderly diabetic and non-diabetic patients.
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1. The document discusses key concepts in statistics including populations, samples, descriptive statistics, inferential statistics, qualitative and quantitative data, and scales of measurement.
2. It provides examples of statistical tests that can be used including one-sample t-tests, two-sample t-tests, paired t-tests, one-way ANOVA tests, and examples of how they can be applied.
3. The guidelines for designing a statistical study are outlined including identifying variables of interest, developing a data collection plan, collecting and describing data, and interpreting results.
Statistics for Medical students
This document provides an overview of key concepts in statistics. It discusses how statistics is used to collect, organize, summarize, present, and analyze numerical data to derive valid conclusions. It defines common statistical terminology like data, quantitative vs. qualitative data, measures of central tendency (mean, median, mode), measures of variability (range, standard deviation), the normal distribution curve, and coefficient of variation. The document also explains common statistical tests like the z-test, t-test, ANOVA, chi-square test and concepts like sensitivity and specificity. Overall, the document serves as a high-level introduction to foundational statistical methods and analyses.
The t test
1) The document presents information on different types of t-tests including the single sample t-test, independent sample t-test, and dependent/paired sample t-test. Equations and examples are provided for each.
2) The single sample t-test compares the mean of a sample to a hypothesized population mean. The independent t-test compares the means of two independent samples. The dependent t-test compares the means of two related samples, such as pre-and post-test scores.
3) A z-test is also discussed and compared to t-tests. The z-test is used when the population standard deviation is known and sample sizes are large, while t-tests are used
Research methodology
The document summarizes the key differences between a t-test and a z-test. A t-test is used when the sample size is small and the population variance is unknown, while a z-test is used for large sample sizes where the population variance can be assumed to be known. The t-test follows a t-distribution and the z-test follows a normal distribution. Both tests are used to determine if the means of two datasets differ significantly.
In the t test for independent groups, ____.we estimate µ1 µ2.docx
In the t test for independent groups, ____.
we estimate µ1 µ2
we estimate 2
we estimate X1-X2
df = N 1
Exhibit 14-1
A professor of women's studies is interested in determining if stress affects the menstrual cycle. Ten women are randomly sampled for an experiment and randomly divided into two groups. One of the groups is subjected to high stress for two months while the other lives in a relatively stress-free environment. The professor measures the menstrual cycle (in days) of each woman during the second month. The following data are obtained.
High stress
20
23
18
19
22
Relatively stress free
26
31
25
26
30
Refer to Exhibit 14-1. The obtained value of the appropriate statistic is ____.
tobt = 4.73
tobt = 4.71
tobt = 3.05
tobt = 0.47
Refer to Exhibit 14-1. The df for determining tcrit are ____.
4
9
8
3
Refer to Exhibit 14-1. Using = .052 tail, tcrit = ____.
+2.162
+2.506
±2.462
±2.306
Refer to Exhibit 14-1. Using = .052 tail, your conclusion is ____.
accept H0; stress does not affect the menstrual cycle
retain H0; we cannot conclude that stress affects the menstrual cycle
retain H0; stress affects the menstrual cycle
reject H0; stress affects the menstrual cycle
Refer to Exhibit 14-1. Estimate the size of the effect. = ____
0.8102
0.6810
0.4322
0.5776
A major advantage to using a two condition experiment (e.g. control and experimental groups) is ____.
the test has more power
the data are easier to analyze
the experiment does not need to know population parameters
the test has less power
Which of the following tests analyzes the difference between the means of two independent samples?
correlated t test
t test for independent groups
sign test
test of variance
If n1 = n2 and n is relatively large, then the t test is relatively robust against ____.
violations of the assumptions of homogeneity of variance and normality
violations of random samples
traffic violations
violations by the forces of evil
Exhibit 14-3
Five students were tested before and after taking a class to improve their study habits. They were given articles to read which contained a known number of facts in each story. After the story each student listed as many facts as he/she could recall. The following data was recorded.
Before
10
12
14
16
12
After
15
14
17
17
20
Refer to Exhibit 14-3. The obtained value of the appropriate statistic is ____.
3.92
3.06
4.12
2.58
Refer to Exhibit 14-3. What do you conclude using = 0.052 tail?
reject H0; the class appeared to improve study habits
retain H0; the class had no effect on study habits
retain H0; we cannot conclude that the class improved study habits
accept H0; the class appeared to improve study habits
Which of the following is (are) assumption(s) underlying the use of the F test?
the raw score populations are normally distributed
the variances of the raw score populations are the same
the mean of the populations differ
the raw score popul.
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Hypothesis Test _Two-sample t-test, Z-test, Proportion Z-test
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- 2. Test of significance for small samples: If the sample size is less than 30 i.e., n < 30, the sample may be regarded as small sample. And in the following some of important test for small samples are listed. 1. Students’ t -test. 2. F-test. 3. Chi-square test. 1. t -Test: The student’s t – test for a small sample have two different variant of test statistics depend up on the means. 1. Test 1: Test of significance of the difference between sample mean and population mean. And the test statistic defined as follows: where 𝒙 is the sample mean, 𝜇 is the population mean from which the sample has been drawn, s is the sample SD and n denotes the number of observations in the sample. Note:
- 8. 2. Test 2: Test of significance of the difference between means of two samples drawn from the same normal population. And the test statistic defined as follows: with Here 𝒙1 and 𝒙2 are two sample means, 𝑠1 and 𝑠2 are two sample SDs, 𝑛1 and 𝑛1 denote the number of observations in both the samples.