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Survey of Statistical Methods

Survey of Statistical Methods. Wednesday, March 30, 2005. Sample Problem.

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Survey of Statistical Methods

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  1. Survey of Statistical Methods Wednesday, March 30, 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 • H0 : Mcontrol = Mlow =Mmedium =Mhigh • H1 : at least one Mi≠Mj

  4. Creating an ANOVA Summary Table for publication

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

  6. 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

  7. 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.

  8. 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

  9. 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 .

  10. 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

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

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

  13. 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”

  14. H01: M1 = M2accept • H02: M1 = M3reject • H03: M1 = M4accept • H04: M2 = M3accept • H05: M2 = M4accept • H06: M3 = M4reject

  15. An alternative way to analyze One-way ANOVAAnalyze -- General Linear Model --Univariate

  16. Output from:Analyze -- General Linear Model -- Univariate Output from:Analyze -- Compare Means -- One-Way ANOVA

  17. Running a Tukey HSD from:Analyze -- General Linear Model -- Univariate

  18. Tukey HSD Output from:Analyze -- General Linear Model --Univariate Tukey HSD Output from:Analyze --Compare Means --One-Way ANOVA

  19. Homework for next class • Write out the hypotheses for the 2 experiments described on the next 2 slides. • For each, did the researcher use a within-subjects or a between-subjects design? • Create an SPSS database for each study (you will need to create 2 separate databases… you can not accomplish this task with only one) and bring that data with you to class on Friday. We will be working with this data during Fridays lab session.

  20. Study #1 • Purpose • To determine if the type of stimuli used can effect a persons’ reaction time. • Design • 15 subjects were randomly assigned to complete a simple reaction time task under one of the following 3 conditions: • Auditory stimuli • Visual stimuli • Proprioceptive stimuli

  21. Study #2 • Purpose • To determine if the type of stimuli used can effect a persons’ reaction time. • Design • A simple reaction time task was completed by 5 subjects on 3 separate days with one of 3 different stimuli (auditory, visual and proprioceptive). The order for the presentation of the stimuli was randomized.

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