	Sample 1	Sample 2	Total
Scores $\leq$ pooled median	$i_{1}$	$i_{2}$	$i_{1} + i_{2}$
Scores $\geq$ pooled median	$n_{1} - i_{1}$	$n_{2} - i_{2}$	$n - (i_{1} + i_{2})$
Total	$n_{1}$	$n_{2}$	$n$

Under the null hypothesis,

H_{0}

, we would expect about half of each group's scores to be above the pooled median and about half below, that is, we would expect

i_{1}

to be about

n_{1} / 2

and

i_{2}

to be about

n_{2} / 2

g08acc returns:

(a)the frequencies $i_{1}$ and $i_{2}$ ;
(b)the probability, $p$ , of observing a table at least as ‘extreme’ as that actually observed, given that $H_{0}$ is true. If $n < 40$ , $p$ is computed directly (‘Fisher's exact test’); otherwise a $χ_{1}^{2}$ approximation is used.

H_{0}

is rejected by a test of chosen size

α

p < α

4 References

Siegel S (1956) Non-parametric Statistics for the Behavioral Sciences McGraw–Hill

5 Arguments

1: $n1$ – Integer Input: On entry: the size of the first sample, $n_{1}$ .

Constraint: $n1 \geq 1$ .
2: $x [n1]$ – const double Input: On entry: the elements of x must be set to the data values in the first sample.
3: $n2$ – Integer Input: On entry: the size of the second sample, $n_{2}$ .

Constraint: $n2 \geq 1$ .
4: $y [n2]$ – const double Input: On entry: the elements of y must be set to the data values in the second sample.
5: $below$ – Integer * Output: On exit: the number of scores in the first sample which lie below the pooled median, $i_{1}$ .
6: $above$ – Integer * Output: On exit: the number of scores in the first sample which lie above the pooled median, $i_{2}$ .
7: $p$ – double * Output: On exit: the tail probability, $p$ , corresponding to the observed dichotomy of the two samples.
8: $fail$ – NagError * Input/Output: The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
NE_INT_ARG_LT: On entry, n1 must not be less than 1: $n1 = 〈value〉$ .

On entry, n2 must not be less than 1: $n2 = 〈value〉$ .

7 Accuracy

The probability returned should be accurate enough for practical use.

8 Parallelism and Performance

g08acc is not threaded in any implementation.

9 Further Comments

The time taken by g08acc is small, and increases with

n

10 Example

This example is taken from page 112 of Siegel (1956). The data relate to scores of ‘oral socialisation anxiety’ in 39 societies, which can be separated into groups of size 16 and 23 on the basis of their attitudes to illness.

g08ac: FL CL CPP AD

NAG CL Interfaceg08acc (test_​median)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG CL Interface
g08acc (test_median)