2. Significance and Meaningfulness Effect Size & Statistical Power 1

3. 1. Effect Size How “meaningful” is the significant difference? 1

4. KNR 445 Statistics Effect sizes Slide 3 Significance vs. meaningfulness  As sample size increases, likelihood of significant difference increases The fact that this sample size is buried down here in the denominator of the test statistic means that as n  , p  0. So if your sample is big enough, it will generate significant results 1 2

5. KNR 445 Statistics Effect sizes Slide 4 Significance vs. meaningfulness  As sample size increases, likelihood of significant difference increases  So statistical difference does not always mean important difference  What to do about this?  Calculate a measure of the difference that is standardized to be expressed in terms of the variability in the 2 samples, but independent of sample size  = EFFECT SIZE 1

6. Effect Size  EFFECT SIZE - FORMULA KNR 445 Statistics Effect sizes Slide 5 1 2

7. KNR 445 Statistics Effect sizes Slide 6 Effect Size  EFFECT SIZE – from SPSS  Using appendix B data set 2, and submitting DV salary to test of difference across gender, gives the following output (squashed here to fit): T-Test 1

8. KNR 445 Statistics Effect sizes Slide 7 Effect Size  EFFECT SIZE – from SPSS T-Test SD’s to pool Mean difference to use 1

9. KNR 445 Statistics Effect sizes Slide 8 Effect Size  EFFECT SIZE – from SPSS So… 1 2 so

10. KNR 445 Statistics Effect sizes Slide 9 Effect Size  EFFECT SIZE – from SPSS Substituting… 1 2

11. KNR 445 Statistics Effect sizes Slide 10 Effect Size  EFFECT SIZE – from SPSS Calculating… 1

12. KNR 445 Statistics Effect sizes Slide 11 Effect Size  From Cohen, 1988:  d =.20 is small  d =.50 is moderate  d =.80 is large  So our effect size of.25 is small, and concurs on this occasion with the insignificant result  The finding is both insignificant and small  (a pathetic, measly, piddling little difference of no consequence whatsoever – trivial and beneath us) 1 2

13. 2. Statistical Power Maximizing the likelihood of significance 1 2 3 4

14. KNR 445 Statistics Effect sizes Slide 13 Statistical Power  The likelihood of getting a significant relationship when you should (i.e. when there is a relationship in reality)  Recall from truth table, power = 1 -  1 Truth Table Reality (unknown) Null TrueNull False Decision Accept Null Type II error (β) Reject Null Type I error (α) Power = 1 - β (1- type II error)

15. KNR 445 Statistics Effect sizes Slide 14 Factors Affecting Statistical Power The big ones:  Effect size (bit obvious)  Select samples such that difference between them is maximized  Combines the effects of sample SD (need to decrease) and mean difference (need to increase)  Sample size  Most commonly discussed: as n increases, SE M decreases, and test statistic then increases 1 2

16. KNR 445 Statistics Effect sizes Slide 15 Factors Affecting Statistical Power The others:  Level of significance  Smaller , less power  Larger , more power  1-tailed vs. 2-tailed tests  With good a priori info (i.e. research literature), selecting 1-tailed test increases power  Dependent samples  Correlation between samples reduces standard error, and thus increases test statistic 1 2 3

17. KNR 445 Statistics Effect sizes Slide 16 Calculating sample size a priori 1. Specify effect size 2. Set desired level of power 3. Enter values for effect size and power in appropriate table, and generate desired sample size:  Applet for calculating sample size based on above: http://www.stat.uiowa.edu/~rlenth/Power/  Applets for seeing power acting (and interacting) with sample size, effect size, etc… http://statman.stat.sc.edu/~west/applets/power.html http://acad.cgu.edu/wise/power/powerapplet1.html http://www.stat.sc.edu/%7Eogden/javahtml/power/power.html 1