analyses:morris2008

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analyses:morris2008 [2017/03/19 13:09] 127.0.0.1 external edit |
analyses:morris2008 [2021/11/08 13:17] (current) Wolfgang Viechtbauer |
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Morris (2008) discusses various ways for computing a (standardized) effect size measure for pretest posttest control group designs, where the characteristic, | Morris (2008) discusses various ways for computing a (standardized) effect size measure for pretest posttest control group designs, where the characteristic, | ||

- | As described by Becker (1988), we can compute the standardized mean change (with raw score standardization) for a treatment and control group with $$g_T = c(n_T-1) \frac{\bar{x}_{post,(1988) who uses $d$ to denote this).)) | + | As described by Becker (1988), we can compute the standardized mean change (with raw score standardization) for a treatment and control group with $$g_T = c(n_T-1) \frac{\bar{x}_{post,, 1988, who uses $d$ to denote this). There was (and sometimes still is) some inconsistency in notation when referring to the biased and the bias-corrected version of standardized mean difference / change measures, but I would say the general trend has been to use $d$ for the biased version and $g$ for the bias-corrected version and this is the notation I am also using here.)) |

Morris (2008) uses five studies from a meta-analysis on training effectiveness by Carlson and Schmidt (1999) to illustrate these computations. We can create the same dataset with: | Morris (2008) uses five studies from a meta-analysis on training effectiveness by Carlson and Schmidt (1999) to illustrate these computations. We can create the same dataset with: | ||

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==== The Actual Meta-Analysis ==== | ==== The Actual Meta-Analysis ==== | ||

- | For the actual meta-analysis part, we simply pass the ''a fixed-effects model can be fitted with: | + | For the actual meta-analysis part, we simply pass the ''an equal-effects model can be fitted with: |

<code rsplus> | <code rsplus> | ||

- | rma(yi, vi, data=dat, method="FE", digits=2) | + | rma(yi, vi, data=dat, method="EE", digits=2) |

</ | </ | ||

<code output> | <code output> | ||

- | Fixed-Effects Model (k = 5) | + | Equal-Effects Model (k = 5) |

- | Test for Heterogeneity: | + | I^2 (total heterogeneity / total variability): |

+ | H^2 (total variability / sampling variability): | ||

+ | | ||

+ | Test for Heterogeneity: | ||

Q(df = 4) = 4.43, p-val = 0.35 | Q(df = 4) = 4.43, p-val = 0.35 | ||

Model Results: | Model Results: | ||

- | estimate se zval pval ci.lb ci.ub | + | estimate se zval pval ci.lb ci.ub |

- | 0.95 0.14 6.62 < 0.67 1.23 *** | + | 0.95 0.14 6.62 < 0.67 1.23 *** |

--- | --- | ||

- | Signif. codes: ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 | + | Signif. codes: '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 |

</ | </ | ||

Note that these results are slightly different than the ones in Table 5 due to the different ways of estimating the sampling variances. | Note that these results are slightly different than the ones in Table 5 due to the different ways of estimating the sampling variances. | ||

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==== Alternative Estimates ==== | ==== Alternative Estimates ==== | ||

- | In his article, Morris (2008) discusses two other ways of computing an effect size measure for pretest posttest control group designs. The second approach that pools the two pretest SDs actually can be more efficient under certain conditions. However, that approach assumes that the true pretest SDs are equal for the two groups. That may not be the case. The approach given above does not make that assumption and therefore is more broadly applicable (but may be less efficient). | + | In his article, Morris (2008) discusses two other ways of computing an effect size measure for pretest posttest control group designs. The second approach that pools the two pretest SDs actually can be more efficient under certain conditions. However, that approach assumes that the true pretest SDs are equal for the two groups. That may not be the case. The approach given above does not make that assumption and therefore is more broadly applicable (but may be slightly less efficient). |

If you really want to use the approach with pooled pretest SDs, then this can be done as follows: | If you really want to use the approach with pooled pretest SDs, then this can be done as follows: | ||

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5 0.44 0.16 | 5 0.44 0.16 | ||

</ | </ | ||

- | The '' | + | The ''''vi'' above and the ones given in Table 5 (column $\hat{\sigma}^2(d_{ppc2})$ in Morris, 2008) differ slightly. |

==== Pretest Posttest Correlations ==== | ==== Pretest Posttest Correlations ==== |

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