*! version 1.0.1 March 2024

help for miesizePaul A Tiffin (March 2024)

Effect size estimation using imputed data

Syntax

Cohen's d and Hedges' g effect size estimation using imputed data

miesize
varname
[if] [in],
by(varlist:groupvar) [countdown]

Glass' delta effect size estimation using imputed data

miesize
varname
[if] [in],
by(varlist:groupvar) [glass countdown]

Options

options

Main
by specifies the groupvar that defines the two groups that miesize will use to estimate the effect sizes

countdown specifies that a countdown of analysis steps remaining will be displayed

glass report Glass' Delta (Smith and Glass 1977) using each group's standard deviation

level(#) set a confidence level between 10 and 99.99%; default is level(95)

Description

miesize calculates effect sizes for a binary variable from multiply imputed data in wide format. The estimates and standard errors
(used to calculate the confidence intervals) are recombined using Rubin's rules (Rubin 2004). These rules are applied such
that the average point estimate for the effect size is calculated from the imputed datasets. The pooled standard error, and hence confidence
intervals, are calculated in such a way that accounts for both variance between the imputed datasets, as well as the variance within them. Pooled
effect-sizes and confidence intervals for Cohen's d (Cohen 1988), Hedges'g (Hedges 1981) and Glass' Delta (Smith and Glass 1977) are given.

Remarks

miesize can calculate two sample effect sizes from multiply imputed data in wide format. The command can handle situations where
either one or both variables (namely the outcome and grouping variables) are imputed. When neither variable is detected as imputed
then the esize command for non-imputed data will be invoked. The imputed data should be in the 'wide' format that stata provides.
That is, imputed variables are named sequentially as "_m_varname" where m is the imputation number. For example, "_2_price" where this
is the second imputed dataset for the variable "price".

Do not confuse the by() option with the by prefix, which is not supported by miesize

See also [R] esize.

Examples

creating some some missing values then performing multiple imputation

. sysuse auto

. mi set wide

. replace price=. if make=="Dodge Colt" | make=="Toyota Celica"

. replace foreign=. if _n==11 | _n==3

. mi register imputed price foreign

. mi impute chained (reg) price (logit) foreign= mpg trunk weight length displacement , add(2) burnin(5)

Estimating two sample Cohen's d and Hedges' g effect sizes on the imputed datasets

. miesize price, by(foreign)

Estimating a two sample Glass' Delta effect size on the imputed datasets with a countdown provided during the analysis

. miesize price, by(foreign) countdown glass

Stored results

Scalars

r(pooled_se_d) pooled standard error for Cohen's d

r(pt_est_d) pooled point estimate for Cohen's d

r(ub_d) upper confidence limit for the estimate of Cohen's d

r(lb_d) lower confidence limit for the estimate of Cohen's d

r(pooled_se_g) pooled standard error for Hedges' g

r(pt_est_g) pooled point estimate for Hedges' g

r(ub_g) upper confidence limit for the estimate of Hedges' g

r(lb_g) lower confidence limit for the estimate of Hedges' g

r(pooled_se_g1) pooled standard error for Glass's Delta for group 1

r(pt_est_g1) pooled point estimate for Glass's Delta for group 1

r(ub_g1) upper confidence limit for the estimate of Glass' group 1 Delta

r(lb_g1) lower confidence limit for the estimate of Glass' group 1 Delta

r(pooled_se_g2) pooled standard error for Glass's Delta for group 2

r(pt_est_g2) pooled point estimate for Glass's Delta for group 2

r(ub_g2) upper confidence limit for the estimate of Glass' group 2 Delta

r(lb_g2) lower confidence limit for the estimate of Glass' group 2 Delta

r(by_var) the grouping variable used in the by statement

r(varname) the outcome variable used in the command

Author

Paul Alexander Tiffin

The Hull York Medical School and Department of Health Sciences, University of York, York, UK.

E-mail: paul.tiffin@york.ac.uk

Acknowledgements

Many thanks to Drs Lewis Paton (the Hull York Medical School),
Nick Cox (Durham University), Yulia Marchenko (StataCorp LLC) and Mr Fraser Wiggins (University of York, Clinical Trials Unit) for feedback and advice on an earlier version of the code for
this command.

References

Cohen, J. 1988.
Statistical Power Analysis for the Behavioral Sciences. 2nd ed.
Hillsdale, NJ: Erlbaum.

Hedges, L. V. 1981.
Distribution theory for Glass's estimator of effect size and related estimators.
Journal of Educational Statistics 6: 107-128.

Rubin, J. 2004.
Multiple imputation for nonresponse in surveys.
Hoboken, NJ: John Wiley & Sons.

Smith, M. L., and G. V. Glass. 1977.
Meta-analysis of psychotherapy outcome studies.
American Psychologist 32: 752-760.