**[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
__e__**xact** performs Fisher's exact test
__med__**ianties(below)** assign values equal to the median to below group
__med__**ianties(above)** assign values equal to the median to above group
__med__**ianties(drop)** drop values equal to the median from the analysis
__med__**ianties(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**.
**fweight**s are allowed with **median**; see weight.

__Menu__

__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(Var_a)** adjusted variance
**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.