Title stata.com
mean — Estimate means
Description Quick start Menu Syntax
Options Remarks and examples Stored results Methods and formulas
References Also see
Description
mean produces estimates of means, along with standard errors.
Quick start
Mean, standard error, and 95% confidence interval for v1
mean v1
Also compute statistics for v2
mean v1 v2
Same as above, but for each level of categorical variable catvar1
mean v1 v2, over(catvar1)
Weighting by probability weight wvar
mean v1 v2 [pweight=wvar]
Population mean using svyset data
svy: mean v3
Subpopulation means for each level of categorical variable catvar2 using svyset data
svy: mean v3, over(catvar2)
Test equality of two subpopulation means
svy: mean v3, over(catvar2)
test [email protected] = [email protected]
Menu
Statistics > Summaries, tables, and tests > Summary and descriptive statistics > Means
1
2 mean — Estimate means
Syntax
mean varlist
if
in
weight
, options
options Description
Model
stdize(varname) variable identifying strata for standardization
stdweight(varname) weight variable for standardization
nostdrescale do not rescale the standard weight variable
if/in/over
over(varlist
o
) group over subpopulations defined by varlist
o
SE/Cluster
vce(vcetype) vcetype may be analytic, cluster clustvar, bootstrap, or
jackknife
Reporting
level(#) set confidence level; default is level(95)
noheader suppress table header
display options control column formats, line width, display of omitted variables
and base and empty cells, and factor-variable labeling
coeflegend display legend instead of statistics
varlist may contain factor variables; see [U] 11.4.3 Factor variables.
bootstrap, collect, jackknife, mi estimate, rolling, statsby, and svy are allowed; see [U] 11.1.10 Prefix
commands.
vce(bootstrap) and vce(jackknife) are not allowed with the mi estimate prefix; see [MI] mi estimate.
Weights are not allowed with the bootstrap prefix; see [R] bootstrap.
aweights are not allowed with the jackknife prefix; see [R] jackknife.
vce() and weights are not allowed with the svy prefix; see [SVY] svy.
fweights, aweights, iweights, and pweights are allowed; see [U] 11.1.6 weight.
coeflegend does not appear in the dialog box.
See [U] 20 Estimation and postestimation commands for more capabilities of estimation commands.
Options
Model
stdize(varname) specifies that the point estimates be adjusted by direct standardization across the
strata identified by varname. This option requires the stdweight() option.
stdweight(varname) specifies the weight variable associated with the standard strata identified in
the stdize() option. The standardization weights must be constant within the standard strata.
nostdrescale prevents the standardization weights from being rescaled within the over() groups.
This option requires stdize() but is ignored if the over() option is not specified.
if/in/over
over(varlist
o
) specifies that estimates be computed for multiple subpopulations, which are identified
by the different values of the variables in varlist
o
. Only numeric, nonnegative, integer-valued
variables are allowed in over(varlist
o
).
mean — Estimate means 3
SE/Cluster
vce(vcetype) specifies the type of standard error reported, which includes types that are derived from
asymptotic theory (analytic), that allow for intragroup correlation (cluster clustvar), and that
use bootstrap or jackknife methods (bootstrap, jackknife); see [R] vce option.
vce(analytic), the default, uses the analytically derived variance estimator associated with the
sample mean.
Reporting
level(#); see [R] Estimation options.
noheader prevents the table header from being displayed.
display options: noomitted, vsquish, noemptycells, baselevels, allbaselevels,
nofvlabel, fvwrap(#), fvwrapon(style), cformat(% fmt), and nolstretch; see [R] Estima-
tion options.
The following option is available with mean but is not shown in the dialog box:
coeflegend; see [R] Estimation options.
Remarks and examples stata.com
Example 1
Using the fuel data from example 3 of [R] ttest, we estimate the average mileage of the cars
without the fuel treatment (mpg1) and those with the fuel treatment (mpg2).
. use https://www.stata-press.com/data/r18/fuel
. mean mpg1 mpg2
Mean estimation Number of obs = 12
Mean Std. err. [95% conf. interval]
mpg1 21 .7881701 19.26525 22.73475
mpg2 22.75 .9384465 20.68449 24.81551
Using these results, we can test the equality of the mileage between the two groups of cars.
. test mpg1 = mpg2
( 1) mpg1 - mpg2 = 0
F( 1, 11) = 5.04
Prob > F = 0.0463
4 mean — Estimate means
Example 2
In example 1, the joint observations of mpg1 and mpg2 were used to estimate a covariance between
their means.
. matrix list e(V)
symmetric e(V)[2,2]
mpg1 mpg2
mpg1 .62121212
mpg2 .4469697 .88068182
If the data were organized this way out of convenience but the two variables represent independent
samples of cars (coincidentally of the same sample size), we should reshape the data and use the
over() option to ensure that the covariance between the means is zero.
. use https://www.stata-press.com/data/r18/fuel
. stack mpg1 mpg2, into(mpg) clear
. rename _stack trt
. label define trt_lab 1 "without" 2 "with"
. label values trt trt_lab
. label var trt "Fuel treatment"
. mean mpg, over(trt)
Mean estimation Number of obs = 24
Mean Std. err. [95% conf. interval]
c.mpg@trt
without 21 .7881701 19.36955 22.63045
with 22.75 .9384465 20.80868 24.69132
. matrix list e(V)
symmetric e(V)[2,2]
c.mpg@ c.mpg@
1.trt 2.trt
[email protected] .62121212
[email protected] 0 .88068182
Now, we can test the equality of the mileage between the two independent groups of cars.
. test [email protected] = [email protected]
( 1) [email protected] - [email protected] = 0
F( 1, 23) = 2.04
Prob > F = 0.1667
mean — Estimate means 5
Example 3: standardized means
Suppose that we collected the blood pressure data from example 2 of [R] dstdize, and we wish to
obtain standardized high blood pressure rates for each city in 1990 and 1992, using, as the standard,
the age, sex, and race distribution of the four cities and two years combined. Our rate is really the
mean of a variable that indicates whether a sampled individual has high blood pressure. First, we
generate the strata and weight variables from our standard distribution, and then use mean to compute
the rates.
. use https://www.stata-press.com/data/r18/hbp, clear
. egen strata = group(age race sex) if inlist(year, 1990, 1992)
(675 missing values generated)
. by strata, sort: gen stdw = _N
. mean hbp, over(city year) stdize(strata) stdweight(stdw)
Mean estimation
N. of std strata = 24 Number of obs = 455
Mean Std. err. [95% conf. interval]
c.hbp@city#year
1 1990 .058642 .0296273 .0004182 .1168657
1 1992 .0117647 .0113187 -.0104789 .0340083
2 1990 .0488722 .0238958 .0019121 .0958322
2 1992 .014574 .007342 .0001455 .0290025
3 1990 .1011211 .0268566 .0483425 .1538998
3 1992 .0810577 .0227021 .0364435 .1256719
5 1990 .0277778 .0155121 -.0027066 .0582622
5 1992 .0548926 0 . .
The standard error of the high blood pressure rate estimate is missing for city 5 in 1992 because
there was only one individual with high blood pressure; that individual was the only person observed
in the stratum of white males 30–35 years old.
By default, mean rescales the standard weights within the over() groups. In the following, we
use the nostdrescale option to prevent this, thus reproducing the results in [R] dstdize.
. mean hbp, over(city year) stdize(strata) stdweight(stdw) nostdrescale
Mean estimation
N. of std strata = 24 Number of obs = 455
Mean Std. err. [95% conf. interval]
c.hbp@city#year
1 1990 .0073302 .0037034 .0000523 .0146082
1 1992 .0015432 .0014847 -.0013745 .004461
2 1990 .0078814 .0038536 .0003084 .0154544
2 1992 .0025077 .0012633 .000025 .0049904
3 1990 .0155271 .0041238 .007423 .0236312
3 1992 .0081308 .0022772 .0036556 .012606
5 1990 .0039223 .0021904 -.0003822 .0082268
5 1992 .0088735 0 . .
6 mean — Estimate means
Example 4: profile plots and contrasts
The first example in [R] marginsplot shows how to use margins and marginsplot to get profile
plots from a linear regression. We can similarly explore the data using marginsplot after mean with
the over() option. Here we use marginsplot to plot the means of systolic blood pressure for each
age group.
. use https://www.stata-press.com/data/r18/nhanes2, clear
. mean bpsystol, over(agegrp)
Mean estimation Number of obs = 10,351
Mean Std. err. [95% conf. interval]
c.bpsystol@agegrp
20--29 117.3466 .3247329 116.71 117.9831
30--39 120.2374 .4095845 119.4345 121.0402
40--49 126.9442 .532033 125.9013 127.9871
50--59 135.6754 .6061842 134.4872 136.8637
60--69 141.5227 .4433527 140.6537 142.3918
70+ 148.1765 .8321116 146.5454 149.8076
. marginsplot
Variables that uniquely identify means:
110
120
130
140
150
20–29 30–39 40–49 50–59 60–69 70+
Age group
Estimated means of bpsystol with 95% CIs
We see that the mean systolic blood pressure increases with age. We can use contrast to formally
test whether each mean is different from the mean in the previous age group using the ar. contrast
operator; see [R] contrast for more information on this command.
mean — Estimate means 7
. contrast ar.agegrp#c.bpsystol, effects nowald
Contrasts of means
Contrast Std. err. t P>|t| [95% conf. interval]
agegrp#
c.bpsystol
(30--39
vs
20--29) 2.89081 .5226958 5.53 0.000 1.866225 3.915394
(40--49
vs
30--39) 6.706821 .6714302 9.99 0.000 5.390688 8.022954
(50--59
vs
40--49) 8.731263 .8065472 10.83 0.000 7.150275 10.31225
(60--69
vs
50--59) 5.847282 .7510133 7.79 0.000 4.375151 7.319413
(70+
vs
60--69) 6.653743 .9428528 7.06 0.000 4.80557 8.501917
The first row of the output reports that the mean systolic blood pressure for the 30–39 age group
is 2.89 higher than the mean for the 20–29 age group. The mean for the 40–49 age group is 6.71
higher than the mean for the 30–39 age group, and so on. Each of these differences is significantly
different from zero.
We can include both agegrp and sex in the over() option to estimate means separately for men
and women in each age group.
. mean bpsystol, over(agegrp sex)
Mean estimation Number of obs = 10,351
Mean Std. err. [95% conf. interval]
c.bpsystol@agegrp#sex
20--29#Male 123.8862 .4528516 122.9985 124.7739
20--29#Female 111.2849 .3898972 110.5206 112.0492
30--39#Male 124.6818 .5619855 123.5802 125.7834
30--39#Female 116.2207 .5572103 115.1284 117.3129
40--49#Male 129.0033 .7080788 127.6153 130.3912
40--49#Female 125.0468 .7802558 123.5174 126.5763
50--59#Male 136.0864 .855435 134.4096 137.7632
50--59#Female 135.3164 .8556015 133.6393 136.9935
60--69#Male 140.7451 .6059786 139.5572 141.9329
60--69#Female 142.2368 .6427981 140.9767 143.4968
70+#Male 146.3951 1.141126 144.1583 148.6319
70+#Female 149.6599 1.189975 147.3273 151.9924
8 mean — Estimate means
. marginsplot
Variables that uniquely identify means:
110
120
130
140
150
20–29 30–39 40–49 50–59 60–69 70+
Age group
Male
Female
Estimated means of bpsystol with 95% CIs
Are the means different for men and women within each age group? We can again perform the
tests using contrast. This time, we will use r.sex to obtain contrasts comparing men and women
and use @agegrp to request that the tests are performed for each age group.
. contrast r.sex#c.bpsystol@agegrp, effects nowald
Contrasts of means
Contrast Std. err. t P>|t| [95% conf. interval]
sex@agegrp#
c.bpsystol
(Female
vs
Male)
20--29 -12.60132 .5975738 -21.09 0.000 -13.77268 -11.42996
(Female
vs
Male)
30--39 -8.461161 .7913981 -10.69 0.000 -10.01245 -6.909868
(Female
vs
Male)
40--49 -3.956451 1.053648 -3.76 0.000 -6.021805 -1.891097
(Female
vs
Male)
50--59 -.7699782 1.209886 -0.64 0.525 -3.141588 1.601631
(Female
vs
Male)
60--69 1.491684 .8834022 1.69 0.091 -.2399545 3.223323
(Female
vs
Male)
70+ 3.264762 1.648699 1.98 0.048 .0329927 6.496531
mean — Estimate means 9
Using a 0.05 significance level, we find that the mean systolic blood pressure is different for men
and women in all age groups except the fifties and sixties.
Video example
Descriptive statistics in Stata
Stored results
mean stores the following in e():
Scalars
e(N) number of observations
e(N over) number of subpopulations
e(N stdize) number of standard strata
e(N clust) number of clusters
e(k eq) number of equations in e(b)
e(df r) sample degrees of freedom
e(rank) rank of e(V)
Macros
e(cmd) mean
e(cmdline) command as typed
e(varlist) varlist
e(stdize) varname from stdize()
e(stdweight) varname from stdweight()
e(wtype) weight type
e(wexp) weight expression
e(title) title in estimation output
e(clustvar) name of cluster variable
e(over) varlist from over()
e(vce) vcetype specified in vce()
e(vcetype) title used to label Std. err.
e(properties) b V
e(estat
cmd) program used to implement estat
e(marginsnotok) predictions disallowed by margins
Matrices
e(b) vector of mean estimates
e(V) (co)variance estimates
e(sd) vector of standard deviation estimates
e( N) vector of numbers of nonmissing observations
e( N stdsum) number of nonmissing observations within the standard strata
e( p stdize) standardizing proportions
e(error) error code corresponding to e(b)
Functions
e(sample) marks estimation sample
In addition to the above, the following is stored in r():
Matrices
r(table) matrix containing the coefficients with their standard errors, test statistics, p-values,
and confidence intervals
Note that results stored in r() are updated when the command is replayed and will be replaced when
any r-class command is run after the estimation command.
10 mean — Estimate means
Methods and formulas
Methods and formulas are presented under the following headings:
The mean estimator
Survey data
The survey mean estimator
The standardized mean estimator
The poststratified mean estimator
The standardized poststratified mean estimator
Subpopulation estimation
The mean estimator
Let y be the variable on which we want to calculate the mean and y
j
an individual observation on
y, where j = 1, . . . , n and n is the sample size. Let w
j
be the weight, and if no weight is specified,
define w
j
= 1 for all j. For aweights, the w
j
are normalized to sum to n. See The survey mean
estimator for pweighted data.
Let W be the sum of the weights
W =
n
X
j=1
w
j
The mean is defined as
y =
1
W
n
X
j=1
w
j
y
j
The default variance estimator for the mean is
b
V (y) =
1
W (W − 1)
n
X
j=1
w
j
(y
j
− y)
2
The standard error of the mean is the square root of the variance.
If x, x
j
, and x are similarly defined for another variable (observed jointly with y), the covariance
estimator between x and y is
d
Cov(x, y) =
1
W (W − 1)
n
X
j=1
w
j
(x
j
− x)(y
j
− y)
Survey data
See [SVY] Variance estimation, [SVY] Direct standardization, and [SVY] Poststratification for
discussions that provide background information for the following formulas. The following formulas
are derived from the fact that the mean is a special case of the ratio estimator where the denominator
variable is one, x
j
= 1; see [R] ratio.
mean — Estimate means 11
The survey mean estimator
Let Y
j
be a survey item for the jth individual in the population, where j = 1, . . . , M and M
is the size of the population. The associated population mean for the item of interest is Y = Y/M
where
Y =
M
X
j=1
Y
j
Let y
j
be the survey item for the jth sampled individual from the population, where j = 1, . . . , m
and m is the number of observations in the sample.
The estimator for the mean is y =
b
Y /
c
M, where
b
Y =
m
X
j=1
w
j
y
j
and
c
M =
m
X
j=1
w
j
and w
j
is a sampling weight. The score variable for the mean estimator is
z
j
(y) =
y
j
− y
c
M
=
c
My
j
−
b
Y
c
M
2
The standardized mean estimator
Let D
g
denote the set of sampled observations that belong to the gth standard stratum and define
I
D
g
(j) to indicate if the jth observation is a member of the gth standard stratum; where g = 1, . . . ,
L
D
and L
D
is the number of standard strata. Also, let π
g
denote the fraction of the population that
belongs to the gth standard stratum, thus π
1
+ · · · + π
L
D
= 1. π
g
is derived from the stdweight()
option.
The estimator for the standardized mean is
y
D
=
L
D
X
g =1
π
g
b
Y
g
c
M
g
where
b
Y
g
=
m
X
j=1
I
D
g
(j) w
j
y
j
and
c
M
g
=
m
X
j=1
I
D
g
(j) w
j
The score variable for the standardized mean is
z
j
(y
D
) =
L
D
X
g =1
π
g
I
D
g
(j)
c
M
g
y
j
−
b
Y
g
c
M
2
g
12 mean — Estimate means
The poststratified mean estimator
Let P
k
denote the set of sampled observations that belong to poststratum k and define I
P
k
(j)
to indicate if the jth observation is a member of poststratum k; where k = 1, . . . , L
P
and L
P
is
the number of poststrata. Also let M
k
denote the population size for poststratum k. P
k
and M
k
are
identified by specifying the poststrata() and postweight() options on svyset; see [SVY] svyset.
The estimator for the poststratified mean is
y
P
=
b
Y
P
c
M
P
=
b
Y
P
M
where
b
Y
P
=
L
P
X
k=1
M
k
c
M
k
b
Y
k
=
L
P
X
k=1
M
k
c
M
k
m
X
j=1
I
P
k
(j) w
j
y
j
and
c
M
P
=
L
P
X
k=1
M
k
c
M
k
c
M
k
=
L
P
X
k=1
M
k
= M
The score variable for the poststratified mean is
z
j
(y
P
) =
z
j
(
b
Y
P
)
M
=
1
M
L
P
X
k=1
I
P
k
(j)
M
k
c
M
k
y
j
−
b
Y
k
c
M
k
!
The standardized poststratified mean estimator
The estimator for the standardized poststratified mean is
y
DP
=
L
D
X
g =1
π
g
b
Y
P
g
c
M
P
g
where
b
Y
P
g
=
L
p
X
k=1
M
k
c
M
k
b
Y
g ,k
=
L
p
X
k=1
M
k
c
M
k
m
X
j=1
I
D
g
(j)I
P
k
(j) w
j
y
j
and
c
M
P
g
=
L
p
X
k=1
M
k
c
M
k
c
M
g ,k
=
L
p
X
k=1
M
k
c
M
k
m
X
j=1
I
D
g
(j)I
P
k
(j) w
j
The score variable for the standardized poststratified mean is
z
j
(y
DP
) =
L
D
X
g =1
π
g
c
M
P
g
z
j
(
b
Y
P
g
) −
b
Y
P
g
z
j
(
c
M
P
g
)
(
c
M
P
g
)
2
where
z
j
(
b
Y
P
g
) =
L
P
X
k=1
I
P
k
(j)
M
k
c
M
k
(
I
D
g
(j)y
j
−
b
Y
g ,k
c
M
k
)
and
z
j
(
c
M
P
g
) =
L
P
X
k=1
I
P
k
(j)
M
k
c
M
k
(
I
D
g
(j) −
c
M
g ,k
c
M
k
)
mean — Estimate means 13
Subpopulation estimation
Let S denote the set of sampled observations that belong to the subpopulation of interest, and
define I
S
(j) to indicate if the jth observation falls within the subpopulation.
The estimator for the subpopulation mean is y
S
=
b
Y
S
/
c
M
S
, where
b
Y
S
=
m
X
j=1
I
S
(j) w
j
y
j
and
c
M
S
=
m
X
j=1
I
S
(j) w
j
Its score variable is
z
j
(y
S
) = I
S
(j)
y
j
− y
S
c
M
S
= I
S
(j)
c
M
S
y
j
−
b
Y
S
(
c
M
S
)
2
The estimator for the standardized subpopulation mean is
y
DS
=
L
D
X
g =1
π
g
b
Y
S
g
c
M
S
g
where
b
Y
S
g
=
m
X
j=1
I
D
g
(j)I
S
(j) w
j
y
j
and
c
M
S
g
=
m
X
j=1
I
D
g
(j)I
S
(j) w
j
Its score variable is
z
j
(y
DS
) =
L
D
X
g=1
π
g
I
D
g
(j)I
S
(j)
c
M
S
g
y
j
−
b
Y
S
g
(
c
M
S
g
)
2
The estimator for the poststratified subpopulation mean is
y
P S
=
b
Y
P S
c
M
P S
where
b
Y
P S
=
L
P
X
k=1
M
k
c
M
k
b
Y
S
k
=
L
P
X
k=1
M
k
c
M
k
m
X
j=1
I
P
k
(j)I
S
(j) w
j
y
j
and
c
M
P S
=
L
P
X
k=1
M
k
c
M
k
c
M
S
k
=
L
P
X
k=1
M
k
c
M
k
m
X
j=1
I
P
k
(j)I
S
(j) w
j
Its score variable is
z
j
(y
P S
) =
c
M
P S
z
j
(
b
Y
P S
) −
b
Y
P S
z
j
(
c
M
P S
)
(
c
M
P S
)
2
where
z
j
(
b
Y
P S
) =
L
P
X
k=1
I
P
k
(j)
M
k
c
M
k
(
I
S
(j) y
j
−
b
Y
S
k
c
M
k
)
14 mean — Estimate means
and
z
j
(
c
M
P S
) =
L
P
X
k=1
I
P
k
(j)
M
k
c
M
k
(
I
S
(j) −
c
M
S
k
c
M
k
)
The estimator for the standardized poststratified subpopulation mean is
y
DP S
=
L
D
X
g =1
π
g
b
Y
P S
g
c
M
P S
g
where
b
Y
P S
g
=
L
p
X
k=1
M
k
c
M
k
b
Y
S
g ,k
=
L
p
X
k=1
M
k
c
M
k
m
X
j=1
I
D
g
(j)I
P
k
(j)I
S
(j) w
j
y
j
and
c
M
P S
g
=
L
p
X
k=1
M
k
c
M
k
c
M
S
g ,k
=
L
p
X
k=1
M
k
c
M
k
m
X
j=1
I
D
g
(j)I
P
k
(j)I
S
(j) w
j
Its score variable is
z
j
(y
DP S
) =
L
D
X
g =1
π
g
c
M
P S
g
z
j
(
b
Y
P S
g
) −
b
Y
P S
g
z
j
(
c
M
P S
g
)
(
c
M
P S
g
)
2
where
z
j
(
b
Y
P S
g
) =
L
P
X
k=1
I
P
k
(j)
M
k
c
M
k
(
I
D
g
(j)I
S
(j) y
j
−
b
Y
S
g ,k
c
M
k
)
and
z
j
(
c
M
P S
g
) =
L
P
X
k=1
I
P
k
(j)
M
k
c
M
k
(
I
D
g
(j)I
S
(j) −
c
M
S
g ,k
c
M
k
)
References
Bakker, A. 2003. The early history of average values and implications for education. Journal of Statistics Education
11(1). http://www.amstat.org/publications/jse/v11n1/bakker.html.
Cochran, W. G. 1977. Sampling Techniques. 3rd ed. New York: Wiley.
Manski, C. F., and M. Tabord-Meehan. 2017. Evaluating the maximum MSE of mean estimators with missing data.
Stata Journal 17: 723–735.
Stuart, A., and J. K. Ord. 1994. Kendall’s Advanced Theory of Statistics: Distribution Theory, Vol. 1. 6th ed. London:
Arnold.
mean — Estimate means 15
Also see
[R] mean postestimation — Postestimation tools for mean
[R] ameans — Arithmetic, geometric, and harmonic means
[R] proportion — Estimate proportions
[R] ratio — Estimate ratios
[R] summarize — Summary statistics
[R] total — Estimate totals
[MI] Estimation — Estimation commands for use with mi estimate
[SVY] Direct standardization — Direct standardization of means, proportions, and ratios
[SVY] Poststratification — Poststratification for survey data
[SVY] Subpopulation estimation — Subpopulation estimation for survey data
[SVY] svy estimation — Estimation commands for survey data
[SVY] Variance estimation — Variance estimation for survey data
[U] 20 Estimation and postestimation commands
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