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### Table B-8Bias of the ES indexes as a function of the correlation (r) between pretest and post-test

r | d_{hb} | d_{hw} | d_{b} | d_{g} | d_{s1} | d_{s2} | d_{s3} |
---|---|---|---|---|---|---|---|

.00 | 0.0016 | −0.1476 | 0.0000 | −0.1465 | 0.0016 | 0.0016 | −0.1352 |

.25 | 0.0019 | −0.1474 | 0.0001 | −0.0919 | 0.0015 | 0.0019 | −0.1295 |

.50 | 0.0015 | −0.1474 | −0.0001 | −0.0001 | 0.0011 | 0.0019 | −0.1118 |

.75 | 0.0017 | −0.1469 | 0.0000 | 0.2905 | 0.0011 | 0.0027 | −0.0635 |

*Note.*See Tables 1 and 2 in the main report for definitions of each ES index. Bias is defined as the*M*difference between the estimate of the ES and the parametric value.*d*_{b}=Becker’s standardized mean difference;*d*_{g}=Gibbons’s standardized mean difference.*d*_{hb}=Hedges’s standardized mean difference using the between-studies degrees of freedom.*d*_{hw}=Huedo-Medina and Johnson’s standardized mean difference using the within-study degrees of freedom.*d*_{s1}=Standardized mean difference proposed by Shadish (See Table 2, No. 10).*d*_{s2}=Standardized mean difference proposed by Shadish using the standard deviation from ANOVA results (See Table 2, No. 11).*d*_{s3}=Standardized mean difference proposed by Shadish using the standard deviation from ANCOVA results (See Table 2, No. 12).*d*_{tch}=the standardized mean difference in change-score metric from*t*_{d}.*d*_{tra}=standardized mean difference in raw-score metric form*t*_{d}.