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

__Syntax__

Effect sizes for two independent samples using groups

**esize** __two__**sample** *varname* [*if*] [*in*]**,** **by(***groupvar***)** [*options*]

Effect sizes for two independent samples using variables

**esize** __unp__**aired** *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* [**,** __l__**evel(***#***)**]

*options* Description
-------------------------------------------------------------------------
Main
__coh__**ensd** report Cohen's d (1988)
__hed__**gesg** report Hedges's g (1981)
__gla__**ssdelta** report Glass's Delta (Smith and Glass 1977) using each
group's standard deviation
__pbc__**orr** report the point-biserial correlation coefficient
(Pearson 1909)
**all** report all estimates of effect size
__une__**qual** use unequal variances
__w__**elch** use Welch's (1947) approximation
__l__**evel(***#***)** set confidence level; default is **level(95)**
-------------------------------------------------------------------------
**by** is allowed with **esize**; see **[D] by**.

__Menu__

__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.