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19 - Chi-square - 04-03-08 - webct

19 - Chi-square - 04-03-08 - webct - Chi-Square Psyc110...

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4/3/2008 1 Chi-Square Psyc110 April 3, 2008 χ 2 Outline Very quick power review + meta-analysis Introduction to chi-square (two types) Hypothesis testing Basic formula for chi-square Calculation example: goodness of fit type Hands-on calculation practice Contingency table calculation and example Very Quick Statistical Power Review Power = (1 – β ), generally use .80 as benchmark From textbook: δ = d * √ N Use with Appendix D.5 to find power Power is determined by three key factors : (1) Effect size ( d ) (2) Sample size ( N ) (3) Alpha level ( α )
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4/3/2008 2 Mainstream Media Reporting of Psychological Research Yes, sometimes effect sizes are acknowledged But not often!! Researchers partly to blame (field’s emphasis on p - values) p < .001, but r (correlation between height and IQ) is only .03!! Practical significance (assuming causality): raising IQ from 100 to 130 would require a 14- foot increase in height! (Cohen, 1990) Meta-Analysis Quantitative way of combining results across many different studies Requires converting results of each study into a common metric (effect size or d !) Can give an estimate of overall effect in a particular area, but also what characteristics of studies might make certain ones have large effects and others small effects Janet Shibley Hyde Well-known meta-analysis on gender differences in mathematics performance (male score minus female score) Overall d = 0.15 (shown at right) Removing studies of very- high achievers, so including only representative samples: overall d = -.05 Variation within each gender is MUCH larger than the differences between them
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4/3/2008 3 Chi-Square: Introduction Used with frequency data (so: no means, no SD, no
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