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Descriptive Analyses

Descriptive Analyses. Introduction to analysis Modal study characteristics Effect size distribution Weighted mean effect size Heterogeneity. Introduction to Analysis. The way that you analyze your effect is independent of the actual effect size that you use

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Descriptive Analyses

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  1. Descriptive Analyses • Introduction to analysis • Modal study characteristics • Effect size distribution • Weighted mean effect size • Heterogeneity

  2. Introduction to Analysis • The way that you analyze your effect is independent of the actual effect size that you use • Will therefore use T in our formulas to represent the effect size, and sT2 to represent the variance of the effect size • Can substitute d, r, or the odds ratio for T in any of the formulas

  3. Introduction to Analysis • Each study should only contribute a single effect size to your descriptive analyses • Can average together effect sizes from different experiments or different response measures to get an overall effect size for the study • Will be assuming a fixed-effects model for all of our analyses

  4. Modal Study Characteristics • A meta-analyst will commonly report the characteristics of the typical study in the analysis • If you have coded moderator variables, this can be done by reporting the modal value of the most important moderators

  5. Effect Size Distribution • You will commonly want to look at the distribution of effect sizes in your sample to determine if there are any outliers • Should examine the reports corresponding to the outliers to determine why their effect size is unusual • Could be a calculation error • Could be examining a different effect • Could be valid data

  6. Effect Size Distribution • Should decide what to do with each outlier • Drop from analysis • Correct or adjust • Leave as it is • Patterns in the distribution can be used to determine moderators • You can choose to provide a graph of the distribution in your writeup, but it is not necessary

  7. Weighted Mean Effect Size • The weight given to each study is generally equal to the inverse of the variance • Weighted mean calculated using the formula

  8. Weighted Mean Effect Size • The variance of the mean effect size can be computed using the formula • The mean effect size follows a normal distribution, so the mean and standard error can be used to perform hypothesis tests and compute confidence intervals

  9. Heterogeneity Analyses • You can compute the heterogeneity statistic Q to measure the amount of variability in your studies using the formula • Q follows a chi-square distribution with k-1 degrees of freedom, where k is the number of effect sizes

  10. Heterogeneity Analyses • A significant Q indicates there is more variability in your effect sizes then you’d expect due to chance alone • Mean effect size alone doesn’t fully describe the population • Implies the need for moderator analyses • Q is also sometimes called the “homogeneity statistic” • Prefer “heterogeneity” since larger values of Q indicate greater heterogeneity

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