PSY 6290, Psychological Statistics: Anova
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Disclaimer: This study guide is not all inclusive; some topics may be added or omitted in a particular semester.

Review Material

1. What is the difference between a population and a sample?
2. What is the difference between a statistic and a parameter?
3. Why is randomly selecting a sample of individuals the 'ideal' way of obtaining a sample?
4. What are convenience samples?
5. What is the difference between a constant and a variable?
6. If given an example of a survey, be able to determine whether each variable is nominal, ordinal, interval, or ratio and whether each variable is qualitative or quantitative.
7. If given a description of a research study, be able to determine the independent variables, the dependent variables, covariates, and extraneous variables.
8. Know the 3 ways of  adjusting for extraneous variables.
9. Know the characteristics of the experimental, quasi-experimental, and observational studies.
10. If given a description of a research study, be able to determine whether it was an experimental, quasi-experimental, or observational study.
11. Know the difference between an operational definition and a hypothetical construct. Explain how research is limited by operational definitions.
12. Calculate the sample mean, sample variance, and sample standard deviation by hand.
13. Interpret the sample mean, sample variance, and sample standard deviation obtained from hand calculations.
14. Interpret the sample mean, sample variance, and sample standard deviation obtained via SPSS.

One Sample t Test

1. When should this test be used?
2. What are the assumptions of the test?
3. Can the results of the test be trusted if a particular assumption is not true?

T Test for Two Independent Samples—Equal Variances Assumed

1. When should this test be used?
2. What are the assumptions of the test?
3. Can the results of the test be trusted if a particular assumption is not true?

Welch's t Test for Two Independent Samples—Equal Variances Not Assumed

1. When should this test be used?
2. What are the assumptions of the test?
3. Can the results of the test be trusted if a particular assumption is not true?
4. The AWS t test is a modification of the t test for two independent samples. What modifications are made? Why are the modifications made?
5. The AWS df cannot be larger than ___.
6. The AWS df cannot be smaller than ___.

One-way ANOVA—Equal Variances Assumed

1. What is the general linear model?
2. What are the assumptions of the one-way anova?
3. Can the one-way anova results be trusted if a particular assumption is not valid?
4. What factors influence the numerator of the one-way anova F test?
5. What factors influence the denominator of the one-way anova F test?
6. What is the expected value of the one-way anova F if the null hypothesis is true?
7. What is the expected value of the one-way anova F if the null hypothesis is false?
8. When would this procedure be used?
9. What values does Cohen use to represent small, medium, and large effect sizes for d?
10. What values does Cohen use to represent small, medium, and large effect sizes for f?
11. If given a research scenario (i.e., number of groups, desired alpha level, expected effect size), be able to determine the necessary sample size for a specified power.
12. If given a research scenario, determine the predicted values based on the reduced model and on the full models. 
13. If given a research scenario, be able to use the one-way anova to test the null hypothesis by hand.
14. Identify the null and alternative hypotheses.
15. Identify the alpha level, calculate the degrees of freedom, and determine the critical value.
16. Determine the significance of the statistical test by comparing it to the critical value(s).
17. Calculate and interpret omega-squared.
18. Calculate f as a measure of effect size.
19. Calculate and interpret Cohen’s d or dmax as a measure of effect size.
20. Write a sentence that explains your results. The sentence will be graded for accuracy as well as APA format.
21. If given a research scenario, be able to use the one-way anova to test the null hypothesis based on the SPSS output.
22. Identify the null and alternative hypotheses.
23. State the full and reduced models.
24. Identify the alpha level.
25. Determine the significance of the statistical test by comparing the significance level to the alpha level.
26. Calculate and interpret omega-squared.
27. Calculate f as a measure of effect size.
28. Calculate and interpret Cohen’s d or dmax as a measure of effect size.
29. Write a sentence that explains your results. The sentence will be graded for accuracy as well as APA format.

Welch's One-way ANOVA—Equal Variances Not Assumed

1. When is it appropriate to use this test?
2. What assumptions are made by this test?
3. What are the null and alternative hypotheses?
4. If given a research scenario with SPSS output, be able to interpret the results. The sentence will be graded for accuracy as well as APA format.

Multiple Comparisons

1. Why is it usually necessary to conduct multiple comparisons following a one-way anova?
2. When is it unnecessary to conduct multiple comparisons following a one-way anova?
3. If told the number of groups, be able to determine the number of pairwise comparisons that are possible.
4. If told the number of groups, be able to determine the maximum number of orthogonal contrasts.
5. If given two specific comparisons, be able to determine whether they are orthogonal contrasts or not.
6. What is Simpson’s Paradox?
7. If given descriptive statistics (i.e., M, SD, and n) and a research hypothesis, be able to conduct a test for a complex contrast or a pairwise comparison.
8. What are the assumptions of the REGWQ multiple comparison procedure—as implemented in SPSS?
9. What are the assumptions of the Welch t test with a Bonferroni adjustment—as implemented in SPSS?
10. Write an APA format results section if given SPSS output containing a one-way anova and REGWQ output.
11. Write an APA format results section if given SPSS output containing a one-way anova and t test output—including a Bonferroni, Dunn-Sidak, or Holm adjustment.
12. Be able to determine the familywise error rate if given the number of comparisons that are conducted and the alpha level used with each of the comparisons.
13. Be able to determine the per-comparison alpha level that would be needed for a specific number of contrasts and a specific familywise alpha—using the Bonferroni method.
14. Be able to determine the per-comparison alpha level that would be needed for a specific number of contrasts and a specific familywise alpha—using the Dunn-Sidak method.
15. Be able to determine the per-comparison alpha level that would be needed for a specific number of contrasts and a specific familywise alpha using Holm's method.
    

Trend Analysis

1. When is it appropriate to use trend analysis rather than multiple comparisons?
2. If given descriptive statistics, a table of orthogonal polynomials, and the appropriate critical value table, be able to conduct a trend analysis by hand.
3. Be able to determine the tests of trend that are possible when told the number of groups.
4. Be able to determine the tests of trend that are appropriate when told the number of groups.
5. Be able to draw a graph that demonstrates what a linear, quadratic, cubic, linear & quadratic, linear and cubic relationships would look like.
6. Write an APA format results section if given SPSS output containing a one-way anova and trend analysis.

1. How many F tests are produced when a two-way anova is calculated?
2. Know how to calculate each of the F tests associated with a two-way anova—using the complex contrast approach. Means, standard deviations, and sample sizes for each cell would be provided.
3. Be able to determine whether there is a main effect for “A”, for “B”, or for “AB” when given a plot of cell means.
4. What are the full and reduced models for the A, B, and AB F tests—using the Type III Sum of Squares?
5. What are the full and reduced models for the A, B, and AB F tests—using the Type II Sum of Squares?
6. What are the full and reduced models for the A, B, and AB F tests—using the Type I Sum of Squares?
7. What are the numerator and denominator degrees of freedom for the A, B, and AB F tests?
8. How does the familywise error rate differ from the experimentwise error rate and the per-comparison error rate?
9. Be able to describe the necessary follow-up analyses when the AB interaction test is not significant—(alpha level used for each test, type of test, what data are included in each analysis).
10. Be able to describe the necessary follow-up analyses when the AB interaction test is significant—(alpha level used for each test, type of test, what data are included in each analysis).
11. Be able to interpret the SPSS output for the two-way anova and the follow-up analyses (e.g., APA results section) when there is a significant interaction.
12. Be able to interpret the SPSS output for the two-way anova and the follow-up analyses (e.g., APA results section) when there is not a significant interaction.
13. Be able to determine the recommended sample size for each cell as well as the total sample size if given information about the # levels of A, # levels of B, the alpha used, the desired effect size, and the F test that is of greatest interest.
14. Be able to determine whether the power of a particular F test is higher or lower than another F test—for a specific cell size.
15. What are the three possible reasons that we would have unequal sample sizes in our design?
16. Which of the Sum of Squares approaches is recommended? Why?

1. If given a research question, be able to determine whether it is an anova question or an ancova question.
2. How do the full and reduced models for a one-way anova and a one-way ancova differ?
3. How are the calculations of the slope for the reduced ancova model and the slope for the full ancova model different?
4. How are the calculations of the intercept(s) for the reduced ancova model and the full ancova model different?
5. Graphically demonstrate each of the following situations.
6. The covariate is related to the dependent variable, but there is no effect of the independent variable.
7. The covariate is related to the dependent variable, the slopes are homogenous, and there is an effect of the independent variable.
8. The covariate is related to the dependent variable, the slopes are heterogeneous, and there is an effect of the independent variable.
9. The covariate is not related to the dependent variable, but there is an effect of the independent variable.
10. The covariate is not related to the dependent variable, and there is no effect of the independent variable.
11. What are the numerator and denominator degrees of freedom for the one-way ancova test?
12. What are the assumptions of the one-way ancova test?
13. What are the implications of the assumptions for the one-way ancova test?
14. What are the situations that lead to dependence between the treatment (Independent variable) and the covariate? Would such dependence prevent us from using the ancova test?
15. What preliminary tests are recommended before conducting the one-way ancova?
16. What are the desired results for each of the preliminary tests of the one-way ancova?
17. If given SPSS output, be able to determine the results for each of the preliminary tests as well as the ancova and pairwise comparisons on the adjusted means (e.g., APA results section).
18. Be able to compare the results of a one-way ancova and pairwise comparisons on the adjusted means to the results of a one-way anova and pairwise comparisons. Know why the two procedures might result in different conclusions.  

1. Be able to determine whether a factor would be considered fixed or random.
2. Be able to determine whether the design is a nested design or a crossed design.
3. Be able to determine the appropriate sources of variability (i.e., rows of the mean square table) for a particular design.
4. Be able to create the appropriate expected mean square table for one-way, two-way, and three-way designs.
5. Be able to determine the expected mean square for a specific effect, e.g., E(MSA), using the expected mean square table.
6. Be able to determine the appropriate numerator and denominator of an F ratio.

1. What are the three situations that lead to a repeated measures design?
2. If given a specific study, be able to determine whether the data are repeated or between subjects.
3. Explain why it is inappropriate to analyze repeated measures data using a between-subjects anova.

Univariate Approach

1. Be able to create the expected mean square table for a one-way repeated measures anova.
2. Be able to determine the expected mean square of an effect.
3. Be able to determine the appropriate numerator and denominator of the F test for a repeated measures anova.
4. What are the assumptions of the one-way repeated measures anova test?
5. Why is it necessary to use a Greenhouse-Geiser or Huynh-Feldt adjustment for a repeated measures anova?
6. What statistical procedure is used to conduct pairwise comparisons with repeated measures data?
7. How should you control the familywise alpha to .05?
8. Be able to interpret the SPSS output for a one-way repeated measures anova-univariate approach.

Multivariate Approach

1. What are the assumptions of the one-way repeated measures anova test?
2. What statistical procedure is used to conduct pairwise comparisons with repeated measures data?
3. How should you control the familywise alpha to .05?
4. Know which of the Multivariate F tests to interpret if you are using the multivariate approach to a one-way repeated measures anova.
5. Be able to interpret the SPSS output for a one-way repeated measures anova-multivariate approach.

Univariate Approach

1. Be able to create an expected mean square table for a two-way repeated measures design where both factors are repeated.
2. Be able to determine the appropriate numerator and denominator of an F test from a two-way repeated measures design where both factors are repeated.
3. Know the assumptions of the two-way repeated measures design where both factors are repeated.
4. Be able to interpret the SPSS output for a two-way repeated measures anova-univariate approach-when both factors are repeated.
5. Be able to create an expected mean square table for a two-way repeated measures design where one factor is repeated.
6. Be able to determine the appropriate numerator and denominator of an F test from a two-way repeated measures design where one factor is repeated.
7. Know the assumptions of the two-way repeated measures design where one factor is repeated.
8. Be able to interpret the SPSS output for a two-way repeated measures anova-univariate approach-when one factor is repeated.

Multivariate Approach

1. What are the assumptions of the two-way repeated measures anova-multivariate approach--when both factors are repeated?
   
2. Be able to interpret the SPSS output for a two-way repeated measures anova-multivariate approach-when both factors are repeated.
3. Know the assumptions of the two-way repeated measures design where one factor is repeated.
4. Be able to interpret the SPSS output for a two-way repeated measures anova-multivariate approach-when one factor is repeated.

Reminders
The SPSS output may contain follow-up tests when the interaction is significant.
The SPSS output may contain follow-up tests when the interaction is not significant.

 Psy 3020 | Psy 4070  | Psy 6280  | Psy 6290  | Psy 6560  | Computer Labs | Statistical Resources
Home | Quantitative Psychology | Psychology Dept.  | MTSU  | Dr. Fuller  | Teaching  Resources APA Public Resources  | ASA Resources  | Habitat for Humanity  | Expanding Your Horizons