1. Analyzing the Results of an Experiment… -not straightforward.. –Why not?

2. Variability and Random/chance outcomes

3. Inferential Statistics Statistical analysis appropriate for inferring causal relationships and effects. Many different formulas…which one do you use?

4. Inferential Stat selection -Determine that you are analyzing the results of an experimental manipulation, not a correlation Identify the IV and DV. The IV Will always be nominal on some level, even when it may seem to be continuous..low, medium and high doses of a drug

5. Inf. Stat Selection What is the scale of the DV? –Scale of DV -Statistic to use Nominal Chi-squared OrdinalMann-Whitney U-test ContinuousT-test or ANOVA

6. t-test or ANOVA? How many levels of the IV are there? 2 levelsmore than 2 levels T-test or ANOVAANOVA

7. There are different forms of T-tests and ANOVA’s: Did the Study Use a Within Group or Between group Experimental Design? Between GroupWithin Group Only 2 levels of the IVUnpaired t-tests (or “t for independent samples”). “Paired t-tests ( or “t for dependent samples”) Or…ANOVA ( the basic ANOVA is fitted for between group designs) Or…Within group ANOVA (often referred to as a “repeated measures ANOVA”) More than 2 levels of the IV ANOVARepeated Measures ANOVA

8. In some ways all inferential Stats are similar. They calculate the probability that a result was due to the IV as opposed to random variability… Let’s focus on the Basic ANOVA since it is likely to be the statistic you may use most commonly.

9. ANOVA ANOVA produces an F-value. F values are the ratio of overall between group Variability to the Mean within group variability Between Var. (+ chance) / Mean within grp. Variability (+ chance) What does this mean?

10. Lets suppose: Experiment- IV marijuana –Control –Placebo control –Low dose –High dose

11. Dependent Variable is: Performance on a short term memory task measured number correct out of 10 test items. 9 subjects in each group

12. Possible out come 1

13. Possible Outcome 1 ControlPlaceboLow doseHigh dose 4222 5333 6445 5643 5554 6544 4454 3466 7335

14. Distribution of scores for control sample

15. Placebo scores

16. Low dose scores

17. High dose scores

18. The population distribution of scores

19. F value relatively low High low placebo control Between grp. Var w/in grp. var

20. Now consider this: Possible Outcome 2 ControlPlaceboLow doseHigh dose 4222 5333 6445 5643 5554 6544 4454 3466 7335

21. Distribution of scores for control sample

22. Placebo scores

23. Low dose scores

24. High dose scores

25. F value relatively High High low placebo control Between grp. Var w/in grp. var

26. The high F value reflects Logic! Distribution of score are much more obviously separated, and in this case are completely non-overlapping Low F values indicate highly overlapping score distributions

27. So how do we decide if an F value is large enough to consider the result as causal? We consult a table of established probabilities of different F values, within the context of Degree of freedom terms:

30. ANOVA Significance table

33. Where is/are the difference (s)?

34. Inferential Statistics

35. The story of “Scratch”

36. Why not jus use repeated t-tests? Probability pyramiding 15 t-tests required for this data set Post-hocs include compensations for repeated testing of a large data set

37. After all this where so we stand? We can still be wrong.

40. Factors that affect “power.” Sample size

41. One vs two-tailed testing

43. Effect size