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Schmidt & Hunter Approach to r

Schmidt & Hunter Approach to r. Bare Bones. Statistical Artifacts. Extraneous factors that influence observed effect Sampling error* Reliability Range restriction Computational error Dichotomization of variables *addressed in the analysis. Bare Bones r.

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Schmidt & Hunter Approach to r

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  1. Schmidt & Hunter Approach to r Bare Bones

  2. Statistical Artifacts • Extraneous factors that influence observed effect • Sampling error* • Reliability • Range restriction • Computational error • Dichotomization of variables *addressed in the analysis

  3. Bare Bones r • Find weighted mean and variance: • Note sample size weight. • Note that for unit weights, the weighted variance estimator is the sample, not population, estimate.

  4. Confidence Interval for Mean There are k studies, with Ni observations. This is not the only formula they use, but it’s the best one IMHO.

  5. Estimated Sampling Error Variance • The variance of r Estimated variance for a study. Estimated sampling variance for a meta-analysis. Note mean r is constant.

  6. Variance of Rho Classical Test Theory Sampling Error A definition

  7. Estimated Variance of rho Note that the variance of rho will be called tau-squared by Hedges - To find the variance of infinite-sample correlations, find the variance of r in the meta-analysis and subtract sampling error variance. Schmidt would be quick to add that part of the estimated variance is artifactual.

  8. Credibility Interval The credibility interval and the confidence interval are quite different things. The CI is a standard statistical estimate (intended to contain rho). The CR is a Bayesian estimate (intended to contain a percentage of the values of a random variable).

  9. Bare-Bones Example (1)

  10. Bare-Bones Example (2)

  11. BB Example (3) Recall unwighted or unit weighted mean = .30. Why are they different?

  12. BB Example (4)

  13. BB Example (5)

  14. Interpretation • Schmidt says this is a random-effects meta-analysis. (I agree.) • People interpret the Credibility Interval, but typically do not recognize that it is poortly estimated.

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