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This document discusses one-tailed and two-tailed hypothesis tests. It explains that a one-tailed test looks for an increase or decrease in a parameter, while a two-tailed test looks for any change. If the claim uses words like "increased" or "decreased", it is a one-tailed test, while terms like "change" or "different" indicate a two-tailed test. A one-tailed test has a critical region in one tail, while a two-tailed test has critical regions in both tails. The example given is a one-tailed test comparing civil engineering and B.A. salaries, with the alternative hypothesis that engineering salaries are greater than B.A. salaries.
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Steps of hypothesis testingSelect the appropriate testSo far.docx
Steps of hypothesis testing
Select the appropriate test
So far we’ve learned a couple variation on z- and t-tests
See next slide for how to select
State your research hypothesis and your null hypothesis
State them in English
Then in math
Describe the NULL distribution
Starting here is where you be a skeptic and assume the null is true!
For one-sample tests, you will need to determine μ
(For two-tailed tests, you don’t need to worry about μ)
Compute the relevant standard error
Determine your critical value(s)
Keep in mind whether it is a directional or non-directional test
Compute the test statistic
Compare the test stat to the critical value(s) and make your decision
When to use each test
All of these tests require that the sampling distribution is normal
Either because population is normal or, thanks to central limit theorem, sample size is very large
All of these tests require that the measures be quantitative variables, that is interval/ratio
(Not all quantitative variables are normal, BUT all normal variables are quantitative. So if someone tells you a variable is normal, you know it is also quantitative.)
When to use each test, cont’d
1 Sample z-test
Comparing one sample mean to a population mean
And you do know σ (population SD)
2 sample z-test
Comparing two sample means to each other
And you do know σM1-M2 (standard error of difference of means)
1 sample t-test
Comparing one sample mean to a population mean
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2 sample t-test
Comparing two sample means to each other
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Dependent sample t-test
You have two scores coming from each person, such as if you measured them before and after an experimental manipulation.
Compute the differences between the two scores, then treat like a 1 sample t
What is α?
Put on your skeptic’s hat: you believe the null hypothesis is true
But you’re willing to be convinced you’re wrong
If the test statistic is sufficiently improbable, you will change your mind and decide the null hypothesis is false
What is “sufficiently” improbable?
When your test statistic is more extreme than your critical values
Critical values are selected so that only a small fraction of the entire distribution is more extreme than the critical values
This “small fraction” is called α
Conventionally, α is usually set to .05, that is 5%
Directionality of a test
Is a test simply about whether there a difference, regardless of direction?
If so, it is a non-directed, or undirected, or two-tailed test
Your α must be evenly split between the two tails
For the conventional α = .05, that means each tail should have .025 or 2.5% of the total distribution
Is the test predicting one mean will be bigger than another? Or is it predicting one mean will be less than another?
If so, it a directional, or directed, or one-tailed test
Put all your α in a single tail
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Step 3 of our procedure is a little awkward when we have one-tailed tests
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PAGE O&M Statistics – Inferential Statistics Hypothesis Test.docx
PAGE
O&M Statistics – Inferential Statistics: Hypothesis Testing
Inferential Statistics
Hypothesis testing
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In this week, we transition from confidence intervals and interval estimates to hypothesis testing, the basis for inferential statistics. Inferential statistics means using a sample to draw a conclusion about an entire population. A test of hypothesis is a procedure to determine whether sample data provide sufficient evidence to support a position about a population. This position or claim is called the alternative or research hypothesis.
“It is a procedure based on sample evidence and probability theory to determine whether the hypothesis is a reasonable statement” (Mason & Lind, pg. 336).
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Step 1
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State the alternate hypothesis – The alternate is represented as H1 or HA (H sub one or H sub A). The alternate hypothesis is the exact opposite of the null hypothesis and represents the conclusion supported if the null is rejected. The alternate will not contain an equal sign of the population parameter.
Most of the time, researchers construct tests of hypothesis with the anticipation that the null hypothesis will be rejected.
Step 2
Select a level of significance (α) which will be used when finding critical value(s).
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For example, a .05 alpha level means that we are 95% sure of the reliability of our findings, but there is still a 5% chance of being wrong (what is called the likelihood of committing a Type 1 error).
The level of significance is set by the individual performing the test. Common significance levels are .01, .05, and .10. It is important to always state what the chosen level of significance is.
Step 3
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Steps of hypothesis testingSelect the appropriate testSo far.docx
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Select the appropriate test
So far we’ve learned a couple variation on z- and t-tests
See next slide for how to select
State your research hypothesis and your null hypothesis
State them in English
Then in math
Describe the NULL distribution
Starting here is where you be a skeptic and assume the null is true!
For one-sample tests, you will need to determine μ
(For two-tailed tests, you don’t need to worry about μ)
Compute the relevant standard error
Determine your critical value(s)
Keep in mind whether it is a directional or non-directional test
Compute the test statistic
Compare the test stat to the critical value(s) and make your decision
When to use each test
All of these tests require that the sampling distribution is normal
Either because population is normal or, thanks to central limit theorem, sample size is very large
All of these tests require that the measures be quantitative variables, that is interval/ratio
(Not all quantitative variables are normal, BUT all normal variables are quantitative. So if someone tells you a variable is normal, you know it is also quantitative.)
When to use each test, cont’d
1 Sample z-test
Comparing one sample mean to a population mean
And you do know σ (population SD)
2 sample z-test
Comparing two sample means to each other
And you do know σM1-M2 (standard error of difference of means)
1 sample t-test
Comparing one sample mean to a population mean
You only know s (sample SD)
2 sample t-test
Comparing two sample means to each other
You only know s1 and s2 (sample SDs)
Dependent sample t-test
You have two scores coming from each person, such as if you measured them before and after an experimental manipulation.
Compute the differences between the two scores, then treat like a 1 sample t
What is α?
Put on your skeptic’s hat: you believe the null hypothesis is true
But you’re willing to be convinced you’re wrong
If the test statistic is sufficiently improbable, you will change your mind and decide the null hypothesis is false
What is “sufficiently” improbable?
When your test statistic is more extreme than your critical values
Critical values are selected so that only a small fraction of the entire distribution is more extreme than the critical values
This “small fraction” is called α
Conventionally, α is usually set to .05, that is 5%
Directionality of a test
Is a test simply about whether there a difference, regardless of direction?
If so, it is a non-directed, or undirected, or two-tailed test
Your α must be evenly split between the two tails
For the conventional α = .05, that means each tail should have .025 or 2.5% of the total distribution
Is the test predicting one mean will be bigger than another? Or is it predicting one mean will be less than another?
If so, it a directional, or directed, or one-tailed test
Put all your α in a single tail
Special note on one-tailed tests
Step 3 of our procedure is a little awkward when we have one-tailed tests
How do you descr.
Hypothesis
In this document, I have tried to illustrate most of the hypothesis testing like 1 sample,2 samples, etc, which I have covered to analyze the machine learning algorithms. I have focused on Independent statistical testing.
Now the question is why we use statistical testing? the answer is that we use statistical testing for significance analysis of our results, which I am going to deliver
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The document provides an overview of statistical hypothesis testing and various statistical tests used to analyze quantitative and qualitative data. It discusses types of data, key terms like null hypothesis and p-value. It then outlines the steps in hypothesis testing and describes different tests of significance including standard error of difference between proportions, chi-square test, student's t-test, paired t-test, and ANOVA. Examples are provided to demonstrate how to apply these statistical tests to determine if differences observed in sample data are statistically significant.
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“It is a procedure based on sample evidence and probability theory to determine whether the hypothesis is a reasonable statement” (Mason & Lind, pg. 336).
This Week in Relation to the Course
Hypothesis testing is at the heart of research. In this week, we examine and practice a procedure to perform tests of hypotheses comparing a sample mean to a population mean and a test of hypotheses comparing two sample means.
The Five-Step Procedure for Hypothesis Testing (you need to show all 5 steps – these contain the same information you would find in a research paper – allows others to see how you arrived at your conclusion and provides a basis for subsequent research).
Step 1
State the null hypothesis – equating the population parameter to a specification. The null hypothesis is always one of status quo or no difference. We call the null hypothesis H0 (H sub zero). It is the hypothesis that contains an equality.
State the alternate hypothesis – The alternate is represented as H1 or HA (H sub one or H sub A). The alternate hypothesis is the exact opposite of the null hypothesis and represents the conclusion supported if the null is rejected. The alternate will not contain an equal sign of the population parameter.
Most of the time, researchers construct tests of hypothesis with the anticipation that the null hypothesis will be rejected.
Step 2
Select a level of significance (α) which will be used when finding critical value(s).
The level you choose (alpha) indicates how confident we wish to be when making the decision.
For example, a .05 alpha level means that we are 95% sure of the reliability of our findings, but there is still a 5% chance of being wrong (what is called the likelihood of committing a Type 1 error).
The level of significance is set by the individual performing the test. Common significance levels are .01, .05, and .10. It is important to always state what the chosen level of significance is.
Step 3
Identify the test statistic – this is the formula you use given the data in the scenario. Simply put, the test statistic may be a Z statistic, a t statistic, or some other distribution. Selection of the correct test statistic will depend on the nature of the data being tested (sample size, whether the population standard deviation is known, whether the data is known to be normally distributed).
The sampling distribution of the test statistic is divided into t.
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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:
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· 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.
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T test, Student’s t Test, Key Takeaways, Uses of t-test / Application , Type of t-test, Type of t-test Cont.., One-tailed or two-tailed t-test, Which t-test to Use, t-test Formula, The t-score, Understanding P-values, Degrees of Freedom, How is the t-distribution table used, Example, Example Cont.., Different t-test Formulae, Different t-test Formulae Cont.., Reference.
T test, independant sample, paired sample and anova
The document discusses various statistical analyses that can be performed in SPSS, including t-tests, ANOVA, and post-hoc tests. It provides details on one-sample t-tests, independent t-tests, paired t-tests, one-way ANOVA tests, and evaluating assumptions like normality. Examples are given on how to conduct these tests in SPSS and how to interpret the output. Guidance is provided on follow-up post-hoc tests that can be used after ANOVA to examine differences between specific groups.
hypothesis.pptx
Hypothesis testing involves setting up a null hypothesis and alternative hypothesis, determining a significance level, calculating a test statistic, identifying the critical region, computing the test statistic value based on a sample, and making a decision to reject or fail to reject the null hypothesis. The z-test is used when the sample size is large and the population standard deviation is known, while the t-test is used for small samples when the population standard deviation is unknown. Both tests involve calculating a test statistic and comparing it to critical values to determine if there is sufficient evidence to reject the null hypothesis. Limitations include that the tests only indicate differences and not the reasons for them, and inferences are based on probabilities rather than certainty.
Data Normality (1).pptx
This document defines data and different data types. It discusses prerequisites for data analysis including sample selection, normality, and homogeneity of variance. It then explains what normality refers to and aspects of the normal distribution curve. It provides details on testing for normality in SPSS including steps to run the analysis and outputs to examine like skewness, kurtosis, normality tests, and plots. An example output analyzing sample characteristics is also included.
Data presenatation
This document defines and provides examples of different types of data:
- Discrete and categorical data can be counted and sorted into categories.
- Nominal data involves assigning codes to values. Ordinal data allows values to be ranked.
- Interval and continuous data can be measured and ordered on a scale.
- Frequency tables, pie charts, bar charts, dot plots and histograms are used to summarize different types of data. Outliers, symmetry, skewness and scatter plots are also discussed.
Common statistical tests and applications in epidemiological literature
This document provides an overview of common statistical tests and applications in epidemiological literature. It describes the different types of data, including nominal, ordinal and continuous data. It also discusses describing data through distributions and other characteristics. Hypothesis testing and the concepts of null and alternative hypotheses are explained. Types of errors in statistical testing like Type I and Type II errors are defined. Specific statistical tests like the student's t-test and chi-square analysis are outlined along with examples of their applications. Practice questions related to hypothesis testing and p-values are also included.
Common statistical tests and applications in epidemiological literature
This document provides an overview of common statistical tests and applications in epidemiological literature. It describes the different types of data, such as nominal, ordinal, and continuous data. It also discusses describing data through distributions and other characteristics. Hypothesis testing and the concepts of null and alternative hypotheses are explained. Types of errors in statistical testing like Type I and Type II errors are defined. Specific statistical tests like the Student's t-test and chi-square analysis are outlined along with examples of their applications. Practice questions related to hypothesis testing and p-values are provided at the end.
univariate and bivariate analysis in spss
this slide will help to perform various tests in spss targeting univariate and bivariate analysis along with the way of entering and analyzing multiple responses.
Week 5 Lecture 14 The Chi Square TestQuite often, patterns of .docx
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 .
Epidemiological study design and it's significance
This document provides an overview of parametric statistical tests, including the t-test, ANOVA, Pearson's correlation coefficient, and Z-test. It describes the assumptions, calculations, and procedures for each test. The t-test is used to compare means of small samples and can be used for one sample, two independent samples, or paired samples. ANOVA allows comparison of multiple population means and is used when more than two groups are involved. Pearson's correlation measures the strength of association between two continuous variables. The Z-test, which is used for larger samples, can be applied to compare means or proportions.
Statistical test
Statistical tests provide a mechanism for making quantitative decisions about processes by determining if there is enough evidence to reject conjectures. Common statistical tests include correlational tests, comparison of means tests, regression tests, and non-parametric tests. Two-sample tests compare two independent samples, while paired tests compare two related samples by looking at differences between pairs. One-tailed and two-tailed tests determine rejection regions. ANOVA tests examine differences between group means. One-way ANOVA compares two independent groups, while two-way ANOVA compares groups with two independent variables and their interactions.
Bgy5901
This document provides definitions and explanations of key concepts in biostatistics and statistical hypothesis testing, including:
- Types of data/variables, measures of central tendency, measures of dispersion
- Descriptive vs inferential statistics, populations and samples
- Assumptions of parametric tests, tests of normality, homogeneity of variance
- Components of hypothesis testing, types of errors, significance levels and p-values
- T-tests, ANOVA, within-subjects and between-subjects designs
Stat2013
The document provides information about performing chi-square tests and choosing appropriate statistical tests. It discusses key concepts like the null hypothesis, degrees of freedom, and expected versus observed values. Examples are provided to illustrate chi-square tests for goodness of fit and comparison of proportions. The document also compares parametric and non-parametric tests, providing examples of when each would be used.
Non-parametric Statistical tests for Hypotheses testing
A complete guidelines for Non-parametric Statistical tests for Hypotheses testing with relevant examples which covers Meaning of non-parametric test, Types of non-parametric test, Sign test, Rank sum test, Chi-square test, Wilcoxon signed-ranks test, Mc Nemer test, Spearman’s rank correlation, statistics,
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Hypothesis
Hypotheses are assumptions that can be tested scientifically. A null hypothesis assumes no difference or relationship, while an alternative hypothesis predicts a difference or relationship. Statistical tests determine if results reject the null hypothesis. A Type I error rejects a true null hypothesis, while a Type II error fails to reject a false null hypothesis. Two-tailed tests consider results higher or lower than predicted, while one-tailed tests consider only one direction of difference. Common statistical tests include z-tests, t-tests, chi-squared tests, and F-tests.
Hypothesis
Hypotheses are assumptions that can be tested scientifically. A null hypothesis assumes no difference or relationship, while an alternative hypothesis predicts a difference or relationship. Statistical tests determine if results reject the null hypothesis. A Type I error rejects a true null hypothesis, while a Type II error fails to reject a false null hypothesis. Two-tailed tests consider results higher or lower than predicted, while one-tailed tests consider only one direction of difference. Common statistical tests include z-tests, t-tests, chi-squared tests, and F-tests.
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One-tailed-Test-or-Two-tailed-Test(1).pdf
- 1. One-tailed or Two-tailed Tests In Statisticshypothesistesting,weneed to judgewhether itis a one-tailed or atwo-tailed test so thatwecan findthecritical valuesin tables such asStandardNormal zDistribution Tableand t DistributionTable.And then,by comparingteststatisticvaluewiththecritical valueor whether statisticvaluefallsin thecritical region,wemakea conclusion either to rejectthenull hypothesisor to fail to rejectthenull hypothesis. Howcan wetell whether itisa one-tailed ora two-tailedtest? Itdependson theoriginalclaim in thequestion.Aone-tailedtestlooksfor an “increase”or “decrease”in theparameter whereas a two-tailed testlooks for a “change” (could beincreaseor decrease) in the parameter. Therefore,if weseewords suchas“increased,greater,larger,improved andso on”,or “decreased,less,smallerandso on”intheoriginal claimof a question (>,<areusedin H1), a one-tail testisapplied.If wordssuch as“change,thesame,different/differenceand soon” are used in theclaimof thequestion(≠is used in H1),a two-tailed testisapplied. In a one-tailed test,thecritical regionhasjustonepart (thegreen areabelow).Itcan bea left- tailed testor a right-tailed test.Left-tailed test:Thecritical regionisin theextremeleftregion (tail)under thecurve.Right-tailed test:Thecritical regionisin theextremerightregion(tail) under thecurve. rcriticalregion critical region Left-tailed test Right-tailed test Sign used in H1: ˂ Sign used in H1: >
- 2. In two-tailed test,the critical region hastwo parts(thered areasbelow)which are in the two extreme gerions (tails)underthecurve. Two-tailed test Sign used in H1:≠ Example: Thetrue valueof onetypeof degreeordiplomacannotbequantitatively measured,butwecan measureitsrelativeimpacton starting salary.GraduatesfromQuebecuniversitieswith a B.A.or B.Sc. degreehavea mean annual startingsalary of $28,300.Sixty-fiveQuebecgraduateswith a civil engineering degreearerandomly selected.Theirstarting salarieshavea meanof $36,300. If thestandard deviation is$1670,usea 0.01level of significanceto testthe claimthatQuebec graduateswith a civil engineeringdegreehavea mean startingsalarythatis greaterthanthe mean forgraduateswith a B.A.orB.Sc.degreefromQuebec. The underlined partof thequestionaboveistheoriginal claimof thisquestion. Thewords “greater than”showthatitis a one-tailed (righttail) testandthesignusedin H1 is“>”.Thenull hypothesisand thealternativehypothesisare: H0: µ = 28,300 H1: µ > 28,300 Note:In MATH1257 ElementaryStatistics,wealwaysuse“=”sign forthenull hypothesisand the sign of thealternativehypothesisisbasedon theoriginal claimof thequestion. In PSYC 2126 & 2127,weneed to decideon thesymbol used in alternativehypothesisdepending on the
- 3. original claimof thequestion first,and then theoppositesymbol will beused in null hypothesis. So,the null hypothesisand alternativehypothesisshouldbe: H0: µ ≤ 28,300 H1: µ > 28,300