Survey of Statistical Methods

1. Survey of Statistical Methods Monday, March 28, 2005

2. Sample Problem • A physiologist has conducted an experiment to evaluate the effect of 3 different concentrations of a hormone X on aggressive behavior. Ten rats were randomly assigned to one of 4 conditions. Rats were injected with either a low concentration, medium concentration, or a high concentration of hormone X, or with a placebo substance. The number of aggressive encounters were counted over a 20-minute period. Using =.05, determine how hormone X effects aggressive behavior.

3. Sample Data

4. What Hypothesis is being tested? X X • H0 : M = μ • H1 : M≠μ • H0 : M1 = M2 • H1 : M1≠M2 • H0 : M1 = M2 =M3 =M4 • H1 : at least one Mi≠Mj

5. Sample Data • H0 : Mcontrol = Mlow =Mmedium =Mhigh • H1 : at least one Mi≠Mj

6. What is ANOVA? • ANalysis Of VAriance • A method to tests hypotheses involving more than two means • Developed by Sir Ronald Fisher (1890-1962) • "To call in the statistician after the experiment is done may be no more than asking him to perform a postmortem examination: he may be able to say what the experiment died of." Indian Statistical Congress, Sankhya, ca 1938

7. A little ANOVA THEORY

8. Sample data file: hormone_study_data.sav If the research design is “between subjects”…. In order to run a One-Way ANOVA, data is entered this way

9. To run the analysis:Analyze -- Compare Means -- One-Way ANOVA

10. The F-ratio is robust to violation of the assumption of homogeneity of variance if the sample N’s are equal. If the sample N’s are not equal you must look at the results here. If p<.05 you have violated the assumption.

12. Creating an ANOVA Summary Table for publication

13. dfnum = [# levels of IV] - 1 = 3 • dfden = (N - 1) - dfnum = 36

15. Obtained F = 22.77 Accept H0 Reject H0 2.84 • Evaluate the outcome • Since the obtained F falls within the critical region, we reject the null hypothesis

16. Steps for Analysis (cont.) • Conclusion • Hormone X has a significant effect on aggressive behavior. • In order to determine which concentration produces the greatest change we need to conduct a post-hoc analysis.

17. Post-Hoc Analyses • A test of the statistical significance of differences between individual group means calculated after obtaining a significant F-ratio. • Some typical Post-Hoc analyses include; • Fisher's LSD • Dunnett • Newman-Keuls • Tukey • Scheffe Test

18. J.W. Tukey Tukey HSD Procedure • Developed in 1953 • Called Tukey HSD(Honestly Significant Difference) • Designed to compare all possible pairs of means while maintaining the Type I error at .

19. Multiple t-tests H01: MP = ML H02: MP = MM H03: MP = MH H04: ML = MM H05: ML = MH H06: MM = MH familywise=6*(.05)=.30 Tukey HSD H01: MP = ML H02: MP = MM H03: MP = MH H04: ML = MM H05: ML = MH H06: MM = MH familywise=.05 Controlling Type I Error

23. H01: MP = MLaccept • H02: MP = MMreject • H03: MP = MHreject • H04: ML = MMreject • H05: ML = MHreject • H06: MM = MHreject

25. Steps for Analysis (cont.) • Conclusion • Hormone X had a significant effect on aggressive behavior. Figure 1 summarizes these effects.

26. Sample Problem #2 • The same course is administered by 4 different instructors at a University. At the end of the semester, each student takes the same exam. The question is “Did the students’ performance differ between instructors?” • Data is in the file “instructor.sav”

27. Assignment for Wednesday • Conduct an analysis of this data and bring your results with you to class on Wednesday.