## Stata 15 help for ranksum

```
[R] ranksum -- Equality tests on unmatched data

Syntax

Wilcoxon rank-sum test

ranksum varname [if] [in], by(groupvar) [porder]

Nonparametric equality-of-medians test

median varname [if] [in] [weight] , by(groupvar) [median_options]

ranksum_options        Description
-------------------------------------------------------------------------
Main
* by(groupvar)         grouping variable
porder               probability that variable for first group is
larger than variable for second group
-------------------------------------------------------------------------

median_options         Description
-------------------------------------------------------------------------
Main
* by(groupvar)         grouping variable
exact                performs Fisher's exact test
medianties(below)    assign values equal to the median to below group
medianties(above)    assign values equal to the median to above group
medianties(drop)     drop values equal to the median from the analysis
medianties(split)    split values equal to the median equally between
the two groups
-------------------------------------------------------------------------
* by(groupvar) is required.
by is allowed with ranksum and median; see [D] by.
fweights are allowed with median; see weight.

ranksum

Statistics > Nonparametric analysis > Tests of hypotheses > Wilcoxon
rank-sum test

median

Statistics > Nonparametric analysis > Tests of hypotheses > K-sample
equality-of-medians test

Description

ranksum tests the hypothesis that two independent samples (that is,
unmatched data) are from populations with the same distribution by using
the Wilcoxon rank-sum test, which is also known as the Mann-Whitney
two-sample statistic (Wilcoxon 1945; Mann and Whitney 1947).

median performs a nonparametric K-sample test on the equality of medians.
It tests the null hypothesis that the K samples were drawn from
populations with the same median.  For two samples, the chi-squared test
statistic is computed both with and without a continuity correction.

ranksum and median are for use with unmatched data.  For equality tests
on matched data, see [R] signrank.

Options for ranksum

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

by(groupvar) is required.  It specifies the name of the grouping
variable.

porder displays an estimate of the probability that a random draw from
the first population is larger than a random draw from the second
population.

Options for median

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

by(groupvar) is required.  It specifies the name of the grouping
variable.

exact displays the significance calculated by Fisher's exact test.  For
two samples, both one- and two-sided probabilities are displayed.

medianties(below|above|drop|split) specifies how values equal to the
overall median are to be handled.  The median test computes the
median for varname by using all observations and then divides the
observations into those falling above the median and those falling
below the median.  When values for an observation are equal to the
sample median, they can be dropped from the analysis by specifying
medianties(drop); added to the group above or below the median by
specifying medianties(above) or medianties(below), respectively; or
if there is more than 1 observation with values equal to the median,
they can be equally divided into the two groups by specifying
medianties(split).  If this option is not specified,
medianties(below) is assumed.

Examples

---------------------------------------------------------------------------
Setup
. webuse fuel2

Perform rank-sum test on mpg by using the two groups defined by treat
. ranksum mpg, by(treat)

Same as above, but include estimate of probability that the value of mpg
for an observation with treat = 0 is greater than the value of mpg for an
observation with treat = 1
. ranksum mpg, by(treat) porder

Perform Pearson chi-squared test of the equality of the medians of mpg
between the two groups defined by treat
. median mpg, by(treat)

Perform Fisher's exact test of the equality of the medians of mpg between
the two groups defined by treat
. median mpg, by(treat) exact

---------------------------------------------------------------------------
Setup
. webuse medianxmpl

Perform Pearson chi-squared test of the equality of the medians of age
between the two groups defined by gender
. median age, by(gender)

Same as above command
. median age, by(gender) medianties(below)

Same as above command, but for observations with values of age equal to
the median, put them in the group above the median
. median age, by(gender) medianties(above)

Same as above command, but drop observations with values of age equal to
the median
. median age, by(gender) medianties(drop)

Same as above command, but for observations with values of age equal to
the median, divide them equally between the two groups
. median age, by(gender) medianties(split)
---------------------------------------------------------------------------

Stored results

ranksum stores the following in r():

Scalars
r(N_1)         sample size n_1
r(N_2)         sample size n_2
r(z)           z statistic
r(group1)      value of variable for first group
r(sum_obs)     actual sum of ranks for first group
r(sum_exp)     expected sum of ranks for first group
r(porder)      probability that draw from first population is larger
than draw from second population

median stores the following in r():

Scalars
r(N)           sample size
r(chi2)        Pearson's chi-squared test
r(p)           p-value for Pearson's chi-squared test
r(p_exact)     Fisher's exact p
r(groups)      number of groups compared
r(chi2_cc)     continuity-corrected Pearson's chi-squared
r(p_cc)        continuity-corrected p-value
r(p1_exact)    one-sided Fisher's exact p

References

Mann, H. B., and D. R. Whitney. 1947. On a test whether one of two random
variables is stochastically larger than the other.  Annals of
Mathematical Statistics 18: 50-60.

Wilcoxon, F. 1945. Individual comparisons by ranking methods.  Biometrics
1: 80-83.

```