	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

nag_median_test (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: $n1$ – IntegerInput: On entry: the size of the first sample, $n_{1}$ .

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

Constraint: $n2 \geq 1$ .
4: $y [n2]$ – const doubleInput: 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 3.7 in How to Use the NAG Library and its Documentation).

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

nag_median_test (g08acc) is not threaded in any implementation.

9

Further Comments

The time taken by nag_median_test (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.

NAG Library Function Document

nag_median_test (g08acc)

▸▿ 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

1

Purpose

2

Specification

3

Description