g02ba computes means and standard deviations of variables, sums of squares and cross-products of deviations from means, and Pearson product-moment correlation coefficients for a set of data.

Syntax

C#
public static void g02ba(
	int n,
	int m,
	double[,] x,
	double[] xbar,
	double[] std,
	double[,] ssp,
	double[,] r,
	out int ifail
)
Visual Basic
Public Shared Sub g02ba ( _
	n As Integer, _
	m As Integer, _
	x As Double(,), _
	xbar As Double(), _
	std As Double(), _
	ssp As Double(,), _
	r As Double(,), _
	<OutAttribute> ByRef ifail As Integer _
)
Visual C++
public:
static void g02ba(
	int n, 
	int m, 
	array<double,2>^ x, 
	array<double>^ xbar, 
	array<double>^ std, 
	array<double,2>^ ssp, 
	array<double,2>^ r, 
	[OutAttribute] int% ifail
)
F#
static member g02ba : 
        n : int * 
        m : int * 
        x : float[,] * 
        xbar : float[] * 
        std : float[] * 
        ssp : float[,] * 
        r : float[,] * 
        ifail : int byref -> unit 

Parameters

n
Type: System..::..Int32
On entry: n, the number of observations or cases.
Constraint: n2.
m
Type: System..::..Int32
On entry: m, the number of variables.
Constraint: m2.
x
Type: array<System..::..Double,2>[,](,)[,][,]
An array of size [dim1, m]
Note: dim1 must satisfy the constraint: dim1n
On entry: x[i-1,j-1] must be set to xij, the ith observation on the jth variable, for i=1,2,,n and j=1,2,,m.
xbar
Type: array<System..::..Double>[]()[][]
An array of size [m]
On exit: the mean value, x-j, of the jth variable, for j=1,2,,m.
std
Type: array<System..::..Double>[]()[][]
An array of size [m]
On exit: the standard deviation, sj, of the jth variable, for j=1,2,,m.
ssp
Type: array<System..::..Double,2>[,](,)[,][,]
An array of size [dim1, m]
Note: dim1 must satisfy the constraint: dim1m
On exit: ssp[j-1,k-1] is the cross-product of deviations Sjk, for j=1,2,,m and k=1,2,,m.
r
Type: array<System..::..Double,2>[,](,)[,][,]
An array of size [dim1, m]
Note: dim1 must satisfy the constraint: dim1m
On exit: r[j-1,k-1] is the product-moment correlation coefficient Rjk between the jth and kth variables, for j=1,2,,m and k=1,2,,m.
ifail
Type: System..::..Int32%
On exit: ifail=0 unless the method detects an error or a warning has been flagged (see [Error Indicators and Warnings]).

Description

The input data consist of n observations for each of m variables, given as an array
xij,  i=1,2,,nn2,j=1,2,,mm2,
where xij is the ith observation on the jth variable.
The quantities calculated are:
(a) Means:
x-j=1ni=1nxij,  j=1,2,,m.
(b) Standard deviations:
sj=1n-1i=1nxij-x-j2,  j=1,2,,m.
(c) Sums of squares and cross-products of deviations from means:
Sjk=i=1nxij-x-jxik-x-k,  j,k=1,2,,m.
(d) Pearson product-moment correlation coefficients:
Rjk=SjkSjjSkk,  j,k=1,2,,m.
If Sjj or Skk is zero, Rjk is set to zero.

References

None.

Error Indicators and Warnings

Errors or warnings detected by the method:
Some error messages may refer to parameters that are dropped from this interface (LDX, LDSSP, LDR) In these cases, an error in another parameter has usually caused an incorrect value to be inferred.
ifail=1
On entry,n<2.
ifail=2
On entry,m<2.
ifail=-9000
An error occured, see message report.
ifail=-6000
Invalid Parameters value
ifail=-4000
Invalid dimension for array value
ifail=-8000
Negative dimension for array value
ifail=-6000
Invalid Parameters value

Accuracy

g02ba does not use additional precision arithmetic for the accumulation of scalar products, so there may be a loss of significant figures for large n.

Parallelism and Performance

None.

Further Comments

The time taken by g02ba depends on n and m.
The method uses a two-pass algorithm.

Example

This example reads in a set of data consisting of five observations on each of three variables. The means, standard deviations, sums of squares and cross-products of deviations from means, and Pearson product-moment correlation coefficients for all three variables are then calculated and printed.

Example program (C#): g02bae.cs

Example program data: g02bae.d

Example program results: g02bae.r

See Also