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Solomon effect sizes for meta-analysis

Source: R/solomon_from_summary.R
solomon_effect_sizes.Rd

[Stable] Computes standardized treatment effects for the pretested and unpretested pairs of a Solomon four-group study, with sampling variances in the yi/vi form that meta-analysis software reads.

Usage

solomon_effect_sizes(
  n,
  mean_post,
  sd_post,
  mean_pre = NULL,
  sd_pre = NULL,
  r = NULL
)

Arguments

n

Sample sizes of the four groups, in the order pretested treated, pretested control, unpretested treated, unpretested control.

mean_post, sd_post

Posttest means and standard deviations of the four groups.

mean_pre, sd_pre

Pretest means and standard deviations of the two pretested groups (treated, control). Optional; without them only the unpretested pair is returned.

r

Pre-post correlation in the pretested groups, needed with mean_pre and sd_pre.

Value

A data frame with one row per pair: the estimator, yi (effect size), vi (sampling variance), sei (standard error), and the group sizes.

Details

Pretested pair. The effect size is Morris's (2008) \(d_{ppc2}\): the difference between the treated and control groups' mean pre-post change, divided by the pooled pretest standard deviation and multiplied by a small-sample bias correction (Eqs. 8-10). The correction here is the exact form (Eq. 22). Its sampling variance is Eq. 25, which needs the pre-post correlation r, assumed equal in the two groups. Morris (2008, p. 374) found that Eq. 25 was within 3% of the simulated variance in most conditions. When the treatment inflates posttest variance, however, it underestimated the true variance by 21% to 48% (p. 380), and a correlation that differs between the groups can make it less accurate still.

Unpretested pair. The effect size is Hedges's g for the two posttest groups, with the pooled posttest standard deviation. Its variance comes from the same noncentral t argument that Morris (2008, pp. 371-373) uses for Eq. 25, following Hedges (1981), without the pretest adjustment.

Variances are evaluated at the estimated effect size. The two rows use different standardizers (the pretest SD and the posttest SD), so their difference is not a clean measure of pretest sensitization.

References

Hedges, L. V. (1981). Distribution theory for Glass's estimator of effect size and related estimators. Journal of Educational Statistics, 6(2), 107–128. https://doi.org/10.3102/10769986006002107

Morris, S. B. (2008). Estimating effect sizes from pretest-posttest-control group designs. Organizational Research Methods, 11(2), 364–386. https://doi.org/10.1177/1094428106291059

See also

solomon_from_summary()

Examples

# Pretested pair: the first study in Morris (2008, Table 1);
# unpretested pair: hypothetical.
solomon_effect_sizes(
  n = c(20, 20, 20, 20),
  mean_post = c(38.5, 19.7, 36.0, 25.0),
  sd_post = c(11.6, 14.8, 13.0, 14.0),
  mean_pre = c(30.6, 23.1),
  sd_pre = c(15.0, 13.8),
  r = 0.47
)
#>                          pair             estimator        yi        vi
#> 1 Pretested (O1-O2 vs. O3-O4) d_ppc2 (Morris, 2008) 0.7684476 0.1157400
#> 2     Unpretested (O5 vs. O6)            Hedges's g 0.7980613 0.1103048
#>         sei n_treated n_control
#> 1 0.3402058        20        20
#> 2 0.3321217        20        20