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1、 EFFECT SIZES 效应量的选用与分析 参考文献： Cohen J (1988)“Statistical power analysis for the behavioral sciences” . New Jersey: Lawrenced Erlbaum Associates, Inc. Publishers. pp 283-286 Durlak, J. A. (2009). How to select, calculate, and interpret effect sizes. Journal of pediatric psychology, jsp004. Levine, T.
2、 R., & Hullett, C. R. (2002). Eta squared, partial eta squared, and misreporting of effect size in communication research. Human Communication Research, 28(4), 612-625. Thompson, B. (2007). Effect sizes, confidence intervals, and confidence intervals for effect sizes. Psychology in the Schools, 44,
3、423432. Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science: a practical primer for t-tests and ANOVAs. Frontiers in psychology, 4. 郑昊敏, 温忠麟, & 吴艳. (2011). 心理学常用效应量的选用与分析. 心理科学进 展, 19(012), 1868-1878 . 1 Effect Size 2014/11/13 minfang_zhao ZhaoMF What are effec
4、t sizes？ There are many different types of ESs but those discussed here provide information about the magnitude and direction of the difference between two groups or the relationship between two variables. An ES can be a difference between means, a percentage, or a correlation (Vacha-Hasse & Thompso
5、n, 2004). It allows us to move beyond the simplistic Does it work or not? to the far more sophisticated How well does it work in a range of contexts？ 2 Effect Size 2014/11/13 ZhaoMF Types of Effect Sizes Mean Differences between Groups Cohens d Hedges g Correlation/Regression Pearsons r and R2 Cohen
6、s f2 Contingency tables Odds Ratio 3 Effect Size 2014/11/13 ZhaoMF Types of Effect Sizes ANOVA or GLMs Eta-squared Omega squared Intraclass correlation (rater equality) Chi-square tests Phi(2 binary variables) Cramers Phi or V (categorical variables) 4 Effect Size 2014/11/13 ZhaoMF Cohens d Standard
7、izes ES of the difference between two means d ranges from -to + interpretation: the difference between the mean values is d standard deviations, Cohen (1988) 5 Effect Size 2014/11/13 ZhaoMF Cohens d 6 d值总是作为一种标准的平均数差异的估计,与当前样 本无关。 (Cohen, 1992) Effect Size 2014/11/13 ZhaoMF Hedges g & Glasss 7 Speci
8、al Cases For small sample sizes use Hedges g For unequal group variances, use Glasss uses sample SD of the control group only so that effect sizes would not differ under equal means and unequal variances(Rosenthal, 1991). Effect Size 2014/11/13 ZhaoMF Correction positively biased estimators of an ES
9、 when sample sizes are small. Practically speaking, the correction amounts to a 4% reduction in effect when the total sample size is 20 and around 2% when N=50 (Hedges & Olkin, 1985). 校正部分，不同的研究可能使用的 校正部分不一样，可以参考相关领 域研究的校正方式。 Pearsons r 8 used in the context of correlationmeasuring association betwe
10、en 2 continuous variables. Interpretation: For every 1-unit standard deviation change in x, there is a r-unit standard deviation change in y. Effect Size 2014/11/13 ZhaoMF Odds Ratio 9 Used in the context of binary/categorical outcomes Odds of being in one group (eg. success) relative to the odds of
11、 being in a different group (eg. failure) OR ranges from 0 to OR1 indicates an increase in odds relative to the reference group OR 2 ) (R x C tables) measures the inter-correlation of the variables, but is biased since it increases with the number of cells. Increase in R and C will indicate a strong
12、 association, which is just an artifact of the type of variable used. Effect Size 2014/11/13 ZhaoMF Pearsons R2 12 used in the context of regressionmeasuring how well a regression line fits to a given data regression line fits to a given data R : linear association between 2 continuous variables R2
13、:(Coefficient of Determination) proportion of shared variability between 2 or more variables Interpretation: R2 *100% is percent variance of the outcome y that can be explained by the linear regression model (i.e. indicates how well the linear regression line fits the data) Effect Size 2014/11/13 Zh
14、aoMF Cohens f2 13 Used in multiple linear regression, Standardized effect size is the proportion of explained variance over unexplained variance Estimate is biased and overestimates the effect size for ANOVA (unbiased estimate is Omega-Squared) Effect Size 2014/11/13 ZhaoMF Eta Squared(2) and partia
15、l Eta Squared(p2 ) 14 Used with ANOVA family and GLMs Measures the degree of association in the sample Partial eta-squared is the proportion of the total variability attributable to a given factor. Interpretation: 2*100% is percent of the variance in y explained by the variance in x (similar to the R2 interpretation for linear regression (Dattalo,2008) 2 is biased and on average overestimates the variance explained in the population, but decreases as the sample size gets larger. Caution!: SPSS show ONLY p2 (偏eta 方) 关于两者区别参考：Levine, T. R.,
