
HEDGES G CONFIDENCE LIMITSName:
with \( \bar{y}_{1} \), \( \bar{y}_{2} \), and \( s_{p} \) denoting the mean of sample 1, the mean of sample 2, and the pooled standard deviation, respectively. The formula for the pooled standard deviation is
with \( s_{1} \) and \( n_{1} \) denoting the standard deviation and number of observations for sample 1, respectively, and \( s_{2} \) and \( n_{2} \) denoting the standard deviation and number of observations for sample 2, respectively. The Hedge's g statistic expresses the difference of the means in units of the pooled standard deviation. It is typically used in the context where one of the samples is a control sample. That is, we are interested in the effect size relative to a control sample. The confidence interval for the Hedge's g statistic is
where
<SUBSET/EXCEPT/FOR qualification> where <y1> is the first response variable; <y2> is the second response variable; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
HEDGES G CONFIDENCE LIMITS Y1 Y2 SUBSET TAG = 1
That is, Cohen's d does not weight the standard deviations based on the sample sizes. These statistic are typically used to compare an experimental sample to a control sample. The Glass g statistic uses the standard deviation of the control sample rather than the pooled standard deviation. His argument for this is that experimental samples with very different standard deviations can result in significant differences in the g statistic for equivalent differences in the mean. So the Glass g statistic measures the difference in means in units of the control sample standard deviation. Hedge's g, Cohen's d, and Glass's g are interpreted in the same way. Cohen recommended the following rule of thumb
However, Cohen did suggest caution for this rule of thumb as the meaning of small, medium and large may vary depending on the context of a particular study. The Hedge's g statistic is generally preferred to Cohen's d statistic. It has better small sample properties and has better properties when the sample sizes are signigicantly different. For large samples where \( n_{1} \) and \( n_{2} \) are similar, the two statistics should be almost the same. The Glass g statistic may be preferred when the standard deviations are quite different.
LET A = HEDGES G Y1 Y2 In addition to the above LET commands, builtin statistics are supported for 20+ different commands (enter HELP STATISTICS for details).
Durlak (2009), "How to Select, Calculate, and Interpret Effect Sizes", Journal of Pediatric Psychology, Vol. 34, No. 9, pp. 917928. Hedges (1981), "Distribution Theory for Glass's Estimator of Effect Size and Related Estimators", Journal of Educational Statistics, Vol. 6, No. 2, pp. 107128. Cohen (1977), "Statistical Power Analysis for the Behavioral Sciences", Routledge. Glass (1976), "Primary, Secondary, and MetaAnalysis of Research", Educational Researcher, Vol. 5, pp. 38.
SKIP 25 READ AUTO83B.DAT Y1 Y2 DELETE Y2 SUBSET Y2 < 0 SET WRITE DECIMALS 5 . LET HG = HEDGES G Y1 Y2 LET HGSE = HEDGES G STANDARD ERROR Y1 Y2 LET HGLCL = HEDGES G LOWER CONFIDENCE LIMIT Y1 Y2 LET HGUCL = HEDGES G UPPER CONFIDENCE LIMIT Y1 Y2 . PRINT HG HGSE HGLCL HGUCL HEDGES G CONFIDENCE LIMITS Y1 Y2The following output is returned PARAMETERS AND CONSTANTS HG  1.62968 HGSE  0.14395 HGLCL  1.91183 HGUCL  1.34754 Confidence Limits for the Hedges G Statistic Response Variable 1: Y1 Response Variable 2: Y2 Summary Statistics for Variable 1: Number of Observations: 0 Sample Mean: 20.14458 Sample Standard Deviation: 6.41470 Summary Statistics for Variable 2: Number of Observations: 0 Sample Mean: 30.48101 Sample Standard Deviation: 6.10771 Pooled Standard Deviation 6.34260 Hedges G: 1.62968 Bias Corrected Hedges G: 1.62593 Standard Error for Hedges G: 0.14395  Confidence Z ZValue X Lower Upper Value (%) Value StdErr Limit Limit  50.000 0.674 0.09710 1.72678 1.53259 75.000 1.150 0.16560 1.79528 1.46409 80.000 1.282 0.18449 1.81417 1.44520 90.000 1.645 0.23678 1.86647 1.39290 95.000 1.960 0.28215 1.91183 1.34754 99.000 2.576 0.37080 2.00049 1.25888 99.900 3.291 0.47369 2.10337 1.15600  
Date created: 10/15/2018 Last updated: 12/11/2023 Please email comments on this WWW page to alan.heckert@nist.gov. 