1. Review Hints for Final

2. Descriptive Statistics: Describing a data set

3. How Does One Describe A Variable? Scale of Measurement Central Tendency Variability Shape of Distribution

4. Describing Sample Choice of Statistic Depends on Scale of Measurement Interval Ordinal or interval that is skewed or open-ended Mode Semi-Interquartile Range; Range Stan. Dev. Mean Central Tendency Median Nominal Variability Graphs Histogram; Freq. Poly. Bar Graph

5. Why Do We Need Descriptive Statistics? 1.To describe a group, as just reviewed 2.To describe where a person’s score falls in a group z score Percentile rank 3.To test assumptions of statistical tests Normality by graphs (recognize criteria) Homogeneity of variances

6. Inferential Statistics Psychology’s Truth Tool

7. Hypothesis Testing We want to know whether, say, two groups are different. The truth lies in the population values, which we do not have. We have to guess the population values from samples.

8. 11 Is the truth that 22 Men and women are different in competitiveness. WomenMen Competitiveness

9. 11 Or Men and women are NOT different in competitiveness. Women 22 Men

10.  If M Always Equaled  We wouldn’t need statistics. 

11. 11  22 Sample Means Would Reflect the Differences in Population  ’s WomenMen See how sample means lined up with population means.

12. 11  22 When Population  ’s Are the Same Women Men Sample M’s would also be the same.

13.  Alas, M May Be Greater Than  

14. ...Or M May Be Smaller Than  

15. 11   22 Such Random Differences May Mislead Us WomenMen Our sample means are quite different, but only by chance. We would falsely conclude there is a difference, which would be a Type __ error. I

16. 11  22 The Opposite is Also Possible We would conclude incorrectly that men and women do not differ in competitiveness. What kind of error is that? Type II

17. Solution: Hypothesis Testing Need to distinguish between chance variation and real differences. We do so by estimating how likely it is that the result* is simply a random chance variation. * In t and ANOVA the result is difference between means; in correlation/regression the result is relationship between IV(s) and DV.

18. Estimate of Chance: Distribution of Sample Means The variance (SD) of the sampling distributions (the standard error) provides an estimate of how much the sample means might vary from the population mean if only chance is operating on scores.

19. We Compare Obtained Mean Difference to the Estimate of Random Variability If mean difference is large enough compared to chance variation in means, we decide the difference is real. We need a criterion for “large enough.” The criterion is in terms of probability--how likely a difference that large is likely to happen by chance.

20. We Set the Probability by Alpha we decide that it is likely to be due to our experimental manipulation rather than due to chance. H 0 :  M =  F = 0 For alpha =.05 If is so extreme that it will only occur less than 5% of the time. 025

21. Statistical Decision-Making Steps 1.State the null and alternative hypotheses. 2.Find the critical value (t, F, r, R,   ). (To do so we need to choose alpha =.05 or.01, nondirectional or directional, and to figure out the degrees of freedom.) 3.Collect data and calculate obtained (t, F, r, R,   ). 4.Make a decision. If obtained (t, F, r, R,   ) is in the critical rejection region, reject H 0.

22. Step 1 Nondirectional H 0 =no effect (no difference between means or no relationship) H 1 =is some effect (is a difference between means or is a relationship) All tests this semester--t, F, r, R,  

23. Step 1 Directional Difference between means H 1 = mean 1 > mean 2 H 0 = mean 1 not > mean 2 (smaller or equal) Relationship H 1 = relationship >0 H 0 = relationship not >0 (inverse or equal) Can not use directional with F or R or  

24. Step 2 Set Alpha and Find Critical Value Alpha ( , p) is probability of Type I error (reject H 0 when it is false) Traditional procedure –Set alpha at.05 –Look up critical value in relevant Table (Alternative--use exact sig level SPSS provides)

25. Collect Data and Calculate Obtained Statistic Know how to calculate –One sample t –F from source table Know how to get SPSS to give you –Independent samples and related samples ts –Independent groups Fs –Two-way ANOVA, independent groups

26. Collect Data and Calculate Obtained Statistic 2 Know how to read SPSS output –Independent samples and related samples ts –Independent samples Fs –Two-way ANOVA, independent groups –Standard Multiple Regression (R) with two IVs –Chi Square (   )

27. Step 4 Make a Decision Traditional –Reject H 0 if obtained statistic in critical rejection region (i. e., more extreme for nondirectional test) –All statistics this semester--z, t, F, r,   Exact significance level –Reject H 0 if exact sig level is smaller than.05 –Can use when SPSS gives exact sig. level

28. Additional Tasks Step 0 Check assumptions and conditions Step 5 Follow-on tests –>2 groups--post hoc tests –Interaction--simple effect Step 6 Determine effect size

29. Assumptions All tests-- independence of observations –Determined when experimental procedure developed All parametric tests--distribution of sample means is normal –Will be with large samples (more than 30 per cell) –With small samples can only check sample distribution- -if it is symmetric, we guess population distribution is normal and therefore distribution of sample means will be normal.

30. Assumptions, cont. Homogeneity of variance –Levene’s in SPSS output (if you can cope with exact sig. Levels) –Fmax

31. Conditions, Problems Quasi-experiment Repeated measures Correlation/regression Chi-square

32. Effect Size Is estimate of how big effect is. Usefulness –If the effect is significant, effect size tells how big the effect is. –If the effect is nonsignificant, it gives a clue as to whether increasing power would lead to significance (i. e., whether result is truly nonsignificant or there is a Type II error). –Know how to calculate for correlation (r 2 and R 2 ).

33. Are Results Likely to Be Replicated? Type I error = alpha Type II error How to increase power –Larger sample size –Smaller variability (error) –Larger effect (e. g., difference between means)

34. Describing Results in APA Style The study was... The result was significant (not significant), statistic(df) = obtained value, p < (.05 or.01 or p = exact value). The nature of the differences was (which group(s) better, with post hoc test if necessary, or whether relationship positive or negative). The means and standard deviations were___________. The effect size, ____ = _____, which was __________. The effect size shows (for significant results, how big effect; for nonsignificant results, whether there might be a Type II error.

35. Choosing a Statistical Test Is the independent variable a nominal or interval scale of measurement? Interval interval Nominal Repeated Measures or Independent Samples? Independent Ind. t Rep. t Rep. ANOVA 2 Ind. ANOVA >2 2 Rep. Meas. Chi-square How many IVs? Scale of dependent variable? nominal interval How many groups in IV? Scale of DV? One-wayTwo-way 1 IV 2 IV >2 r Correlation R Multiple Regression 1 >1 How many groups in IV?

36. Structure Out of Chaos H: Tests Main H: Tests Followup Effect SizesAssumptions t t Cohen’s d r2r2 r2r2 Fmax F F Post-hoc Levene’s Simple E. r r R R R2R2 R2R2   skew Conditions Scatterplot 22 22

37. The End I still love statistics--do you know why?