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Social Statistics: ANOVA

Social Statistics: ANOVA. Review. This week. When to use F statstic How to compute and interpret Using FTEST and FDIST functions How to use the ANOVA. The problem with t-tests…. We could compare three groups with multiple ttests: M1 vs. M2, M1 vs. M3, M2 vs. M3. What is ANOVA?.

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Social Statistics: ANOVA

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  1. Social Statistics: ANOVA

  2. Review S519

  3. This week • When to use F statstic • How to compute and interpret • Using FTEST and FDIST functions • How to use the ANOVA S519

  4. The problem with t-tests… • We could compare three groups with multiple ttests: M1 vs. M2, M1 vs. M3, M2 vs. M3 S519

  5. What is ANOVA? • “Analysis of Variance” • A hypothesis-testing procedure used to evaluate mean differences between two or more treatments (or populations). • Related to: t-tests using independent-measures or repeated- measures design. • Advantages: • 1) Can work with more than two samples. • 2) Can work with more than one independent variable S519

  6. What is ANOVA? • In ANOVA an independent or quasi-independent variable is called a factor. • Factor = independent (or quasi-independent) variable. • Levels = number of values used for the independent variable. • One factor → “single-factor design” • More than one factor → “factorial design” S519

  7. What is ANOVA? • An example of a single-factor design • A example of a two-factor design S519

  8. F value • Variance between treatments can have two interpretations: • Variance is due to differences between treatments. • Variance is due to chance alone. This may be due to individual differences or experimental error. S519

  9. Three Types of ANOVA • Independent measures design: Groups are samples of independent measurements (different people) • Dependent measures design: Groups are samples of dependent measurements (usually same people at different times; also matched samples) “Repeated measures” • Factorial ANOVA (more than one factor) S519

  10. Excel: ANOVA • Three different ANOVA: • Anova: single factor - independent • Anova: two factors with replication - factorial • Anova: two factors without replication - dependent S519

  11. Example (independent) • Three groups of preschoolers and their language scores, whether they are overall different? S519

  12. F test steps • Step1: a statement of the null and research hypothesis • One-tailed or two-tailed (there is no such thing in ANOVA) S519

  13. F test steps • Step2: Setting the level of risk (or the level of significance or Type I error) associated with the null hypothesis • 0.05 S519

  14. F test steps • Step3: Selection of the appropriate test statistics • See Figure 11.1 (S-p227) • Simple ANOVA (independent) S519

  15. F test steps • Between-group degree of freedom=k-1 • k: number of groups • Within-group degree of freedom=N-k • N: total sample size S519

  16. F test steps • Step4: determination of the value needed for rejection of the null hypothesis using the appropriate table of critical values for the particular statistic • Table B3 (S-p363) • df for the denominator = n-k=30-3=27 • df for the numerator = k-1=3-1=2 S519

  17. F test steps • Step5: comparison of the obtained value and the critical value • If obtained value > the critical value, reject the null hypothesis • If obtained value < the critical value, accept the null hypothesis • 8.80 and 3.36 S519

  18. F test steps • Step6 and 7: decision time • What is your conclusion? Why? • How do you interpret F(2, 27)=8.80, p<0.05 S519

  19. Example (dependent) Five participants took a series of test on a new drug S519

  20. F test steps • Step1: a statement of the null and research hypothesis • One-tailed or two-tailed (there is no such thing in ANOVA) S519

  21. F test steps • Step2: Setting the level of risk (or the level of significance or Type I error) associated with the null hypothesis • 0.05 S519

  22. F test steps • Step3: Selection of the appropriate test statistics • See Figure 11.1 (S-p227) • Simple ANOVA (independent) S519

  23. F test steps • Between-group degree of freedom=k-1 • k: number of groups • Within-group degree of freedom=N-k • N: total sample size • Between-subject degree of freedom=n-1 • n: number of subjects • Error degree of freedom=(N-k)-(n-1) S519

  24. F test steps • Step4: determination of the value needed for rejection of the null hypothesis using the appropriate table of critical values for the particular statistic • Table B3 (S-p363) • df for the denominator = (N-k)-(n-1)=16-4=12 • df for the numerator = k-1=4-1=3 S519

  25. F test steps • Step5: comparison of the obtained value and the critical value • If obtained value > the critical value, reject the null hypothesis • If obtained value < the critical value, accept the null hypothesis • 24.88 and 3.49 S519

  26. F test steps • Step6 and 7: decision time • What is your conclusion? Why? • How do you interpret F(3, 12)=24.88, p<0.05 S519

  27. Factorial ANOAVA • Next week S519

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