## Stata 15 help for esizei

```
[R] esize -- Effect size based on mean comparison

Syntax

Effect sizes for two independent samples using groups

esize twosample varname [if] [in], by(groupvar) [options]

Effect sizes for two independent samples using variables

esize unpaired varname1 == varname2 [if] [in], [options]

Immediate form of effect sizes for two independent samples

esizei #obs1 #mean1 #sd1 #obs2 #mean2 #sd2 [, options]

Immediate form of effect sizes for F tests after an ANOVA

esizei #df1 #df2 #F [, level(#)]

options           Description
-------------------------------------------------------------------------
Main
cohensd         report Cohen's d (1988)
hedgesg         report Hedges's g (1981)
glassdelta      report Glass's Delta (Smith and Glass 1977) using each
group's standard deviation
pbcorr          report the point-biserial correlation coefficient
(Pearson 1909)
all             report all estimates of effect size
unequal         use unequal variances
welch           use Welch's (1947) approximation
level(#)        set confidence level; default is level(95)
-------------------------------------------------------------------------
by is allowed with esize; see [D] by.

esize

Statistics > Summaries, tables, and tests > Classical tests of
hypotheses > Effect size based on mean comparison

esizei

Statistics > Summaries, tables, and tests > Classical tests of
hypotheses > Effect-size calculator

Description

esize calculates effect sizes for comparing the difference between the
means of a continuous variable for two groups.  In the first form, esize
calculates effect sizes for the difference between the mean of varname
for two groups defined by groupvar.  In the second form, esize calculates
effect sizes for the difference between varname1 and varname2, assuming
unpaired data.

esizei is the immediate form of esize; see immed.  In the first form,
esizei calculates the effect size for comparing the difference between
the means of two groups.  In the second form, esizei calculates the
effect size for an F test after an ANOVA.

Options

+------+
----+ Main +-------------------------------------------------------------

by(groupvar) specifies the groupvar that defines the two groups that
esize will use to estimate the effect sizes.  Do not confuse the by()
option with the by prefix; you can specify both.

cohensd specifies that Cohen's d (1988) be reported.

hedgesg specifies that Hedges's g (1981) be reported.

glassdelta specifies that Glass's Delta (Smith and Glass 1977) be
reported.

pbcorr specifies that the point-biserial correlation coefficient (Pearson
1909) be reported.

all specifies that all estimates of effect size be reported.  The default
is Cohen's d and Hedges's g.

unequal specifies that the data not be assumed to have equal variances.

welch specifies that the approximate degrees of freedom for the test be
obtained from Welch's formula (1947) rather than Satterthwaite's
approximation formula (1946), which is the default when unequal is
specified.  Specifying welch implies unequal.

level(#) specifies the confidence level, as a percentage, for confidence
intervals.  The default is level(95) or as set by set level.

Examples

---------------------------------------------------------------------------
Setup
. webuse depression

Effect size for two independent samples using by()
. esize twosample qu1, by(sex)

Effect size by race for two independent samples using by()
. by race, sort: esize twosample qu1, by(sex) all

Estimate bootstrap confidence intervals for effect sizes
. bootstrap r(d) r(g), reps(1000) nodots nowarn:  esize twosample
qu1, by(sex)

---------------------------------------------------------------------------
Setup
. webuse fuel

Effect size for two independent samples using unpaired
. esize unpaired mpg1==mpg2

Immediate form of esizei for comparing two means based on Kline (2013,
tables 4.2 and 4.3); obs1=30, mean1=13, sd1=2.74, obs2=30, mean2=11,
sd2=2.24
. esizei 30 13 2.74 30 11 2.24

Immediate form of esizei for the results of an ANOVA based on Smithson
(2001, 623); df_num=4, df_den=50, F=4.2317
. esizei 4 50 4.2317, level(90)

---------------------------------------------------------------------------

Video example

Tour of effect sizes

Stored results

esize and esizei for comparing two means store the following in r():

Scalars
r(d)            Cohen's d
r(lb_d)         lower confidence bound for Cohen's d
r(ub_d)         upper confidence bound for Cohen's d
r(g)            Hedges's g
r(lb_g)         lower confidence bound for Hedges's g
r(ub_g)         upper confidence bound for Hedges's g
r(delta1)       Glass's Delta for group 1
r(lb_delta1)    lower confidence bound for Glass's Delta for group 1
r(ub_delta1)    upper confidence bound for Glass's Delta for group 1
r(delta2)       Glass's Delta for group 2
r(lb_delta2)    lower confidence bound for Glass's Delta for group 2
r(ub_delta2)    upper confidence bound for Glass's Delta for group 2
r(r_pb)         point-biserial correlation coefficient
r(lb_r_pb)      lower confidence bound for the point-biserial
correlation coefficient
r(ub_r_pb)      upper confidence bound for the point-biserial
correlation coefficient
r(N_1)          sample size n_1
r(N_2)          sample size n_2
r(df_t)         degrees of freedom
r(level)        confidence level

esizei for F tests after ANOVA stores the following in r():

Scalars
r(eta2)         eta-squared
r(lb_eta2)      lower confidence bound for eta-squared
r(ub_eta2)      upper confidence bound for eta-squared
r(epsilon2)     epsilon-squared
r(omega2)       omega-squared
r(level)        confidence level

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.

Kline, R. B. 2013.  Beyond Significance Testing: Statistics Reform in the
Behavioral Sciences.  Washington, DC: American Psychological
Association.

Pearson, K. 1909.  On a new method of determining correlation between a
measured character A, and a character B, of which only the percentage
of cases wherein B exceeds (or falls short of) a given intensity is
recorded for each grade of A.  Biometrika 7: 96-105.

Satterthwaite, F. E. 1946.  An approximate distribution of estimates of
variance components.  Biometrics Bulletin 2: 110-114.

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

Smithson, M. 2001.  Correct confidence intervals for various regression
effect sizes and parameters: The importance of noncentral
distributions in computing intervals.  Educational and Psychological
Measurement 61: 605-632.

Welch, B. L. 1947.  The generalization of `student's' problem when
several different population variances are involved. Biometrika 34:
28-35.

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