NAG Library Routine Document

G01ABF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     N – INTEGERInput

On entry: $n$, the number of pairs of observations.

Constraint: $\mathbf{N}\ge 1$.

2:     X1(N) – REAL (KIND=nag_wp) arrayInput

On entry: the observations from the first sample, $x_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,n$.

3:     X2(N) – REAL (KIND=nag_wp) arrayInput

On entry: the observations from the second sample, $y_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,n$.

4:     IWT – INTEGERInput/Output

On entry: indicates whether user-supplied weights are provided by you:

$\mathbf{IWT}=1$ 

• Indicates that user-supplied weights are given in the array WT.

$\mathbf{IWT}\ne 0$ 

• Indicates that user-supplied weights are not given. In this case the routine assigns the value $1.0$ to each element of the weight array, WT.

On exit: is used to indicate the number of valid observations, $m$; see Section 3(g), above.

5:     WT(N) – REAL (KIND=nag_wp) arrayInput/Output

On entry: if weights are being supplied then the elements of WT must contain the weights associated with the observations, $w_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,n$.

Constraint: if $\mathbf{IWT}=1$, $\mathbf{WT}\left(\mathit{i}\right)\ge 0.0$, for $\mathit{i}=1,2,\dots ,\mathbf{N}$.

On exit: if $\mathbf{IWT}=1$, the elements of WT are unchanged, otherwise each element of WT will be assigned the value $1.0$.

6:     RES($13$) – REAL (KIND=nag_wp) arrayOutput

On exit: the elements of RES contain the following results:

$\mathbf{RES}\left(1\right)$	mean of the first sample, $\stackrel{-}{x}$;
$\mathbf{RES}\left(2\right)$	mean of the second sample, $\stackrel{-}{y}$;
$\mathbf{RES}\left(3\right)$	standard deviation of the first sample, $s_1$;
$\mathbf{RES}\left(4\right)$	standard deviation of the second sample, $s_2$;
$\mathbf{RES}\left(5\right)$	corrected sum of squares of the first sample, $c_{11}$;
$\mathbf{RES}\left(6\right)$	corrected sum of products of the two samples, $c_{12}$;
$\mathbf{RES}\left(7\right)$	corrected sum of squares of the second sample, $c_{22}$;
$\mathbf{RES}\left(8\right)$	product-moment correlation coefficient, $R$;
$\mathbf{RES}\left(9\right)$	minimum of the first sample;
$\mathbf{RES}\left(10\right)$	maximum of the first sample;
$\mathbf{RES}\left(11\right)$	minimum of the second sample;
$\mathbf{RES}\left(12\right)$	maximum of the second sample;
$\mathbf{RES}\left(13\right)$	sum of weights, ${\displaystyle \sum _{i=1}^n}{w}_i$ ($=\mathbf{N}$, if $\mathbf{IWT}=0$, on entry).

7:     IFAIL – INTEGERInput/Output

On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of IFAIL on exit.

On exit: $\mathbf{IFAIL}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6  Error Indicators and Warnings

$\mathbf{IFAIL}=1$

On entry,

$\mathbf{N}<1$.

$\mathbf{IFAIL}=2$

The number of valid cases, $m$, is $1$, hence the standard deviation, 3(d), and the product-moment correlation coefficient, 3(e), cannot be calculated.

$\mathbf{IFAIL}=3$

The number of valid cases, $m$, is $0$, or at least one of the weights is negative.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (g01abfe.f90)

9.2  Program Data

Program Data (g01abfe.d)

9.3  Program Results

Program Results (g01abfe.r)