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Significance and Meaningfulness

Significance and Meaningfulness. Effect Sizes. Significance vs. meaningfulness. Is your significant difference a real difference?. Significance vs. meaningfulness. Is your significant difference a real difference?. Significance vs. meaningfulness. Statistical Power .

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Significance and Meaningfulness

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  1. Significance and Meaningfulness Effect Sizes

  2. Significance vs. meaningfulness • Is your significant difference a real difference?

  3. Significance vs. meaningfulness • Is your significant difference a real difference?

  4. Significance vs. meaningfulness • Statistical Power

  5. Significance vs. meaningfulness • Statistical Power • Smaller difference between means reduces power • Larger SEM reduces power

  6. Significance vs. meaningfulness • Statistical Power • Smaller  reduces power

  7. 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

  8. 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 • = EFFECT SIZE

  9. Significance vs. meaningfulness • EFFECT SIZE - FORMULA

  10. Significance vs. meaningfulness • 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

  11. Significance vs. meaningfulness • EFFECT SIZE – from SPSS Mean difference to use T-Test SD’s to pool

  12. Significance vs. meaningfulness • EFFECT SIZE – from SPSS So…

  13. Significance vs. meaningfulness • EFFECT SIZE – from SPSS Substituting…

  14. Significance vs. meaningfulness • EFFECT SIZE – from SPSS Calculating…

  15. Significance vs. meaningfulness • 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)

  16. Statistical Power Maximizing the likelihood of significance

  17. 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 -  ( = type II error)

  18. Factors Affecting Statistical Power The big ones: • Effect size (bit obvious) • Select samples such that difference between them is maximized • Sample size • Most important: as n increases, SEM decreases, and test statistic then increases

  19. 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

  20. Calculating sample size a priori • Specify effect size • Set desired level of power • 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

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