﻿ g02bb Method
g02bb 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 omitting completely any cases with a missing observation for any variable.

# Syntax

C#
```public static void g02bb(
int n,
int m,
double[,] x,
int[] miss,
double[] xmiss,
double[] xbar,
double[] std,
double[,] ssp,
double[,] r,
out int ncases,
out int ifail
)```
Visual Basic
```Public Shared Sub g02bb ( _
n As Integer, _
m As Integer, _
x As Double(,), _
miss As Integer(), _
xmiss As Double(), _
xbar As Double(), _
std As Double(), _
ssp As Double(,), _
r As Double(,), _
<OutAttribute> ByRef ncases As Integer, _
<OutAttribute> ByRef ifail As Integer _
)```
Visual C++
```public:
static void g02bb(
int n,
int m,
array<double,2>^ x,
array<int>^ miss,
array<double>^ xmiss,
array<double>^ xbar,
array<double>^ std,
array<double,2>^ ssp,
array<double,2>^ r,
[OutAttribute] int% ncases,
[OutAttribute] int% ifail
)```
F#
```static member g02bb :
n : int *
m : int *
x : float[,] *
miss : int[] *
xmiss : float[] *
xbar : float[] *
std : float[] *
ssp : float[,] *
r : float[,] *
ncases : int byref *
ifail : int byref -> unit
```

#### Parameters

n
Type: System..::..Int32
On entry: $n$, the number of observations or cases.
Constraint: ${\mathbf{n}}\ge 2$.
m
Type: System..::..Int32
On entry: $m$, the number of variables.
Constraint: ${\mathbf{m}}\ge 2$.
x
Type: array<System..::..Double,2>[,](,)[,][,]
An array of size [dim1, m]
Note: dim1 must satisfy the constraint: $\mathrm{dim1}\ge {\mathbf{n}}$
On entry: ${\mathbf{x}}\left[\mathit{i}-1,\mathit{j}-1\right]$ must be set to ${x}_{\mathit{i}\mathit{j}}$, the value of the $\mathit{i}$th observation on the $\mathit{j}$th variable, for $\mathit{i}=1,2,\dots ,n$ and $\mathit{j}=1,2,\dots ,m$.
miss
Type: array<System..::..Int32>[]()[][]
An array of size [m]
On entry: ${\mathbf{miss}}\left[j-1\right]$ must be set equal to $1$ if a missing value, $x{m}_{j}$, is to be specified for the $j$th variable in the array x, or set equal to $0$ otherwise. Values of miss must be given for all $m$ variables in the array x.
On exit: the array miss is overwritten by the method, and the information it contained on entry is lost.
xmiss
Type: array<System..::..Double>[]()[][]
An array of size [m]
On entry: ${\mathbf{xmiss}}\left[j-1\right]$ must be set to the missing value, $x{m}_{j}$, to be associated with the $j$th variable in the array x, for those variables for which missing values are specified by means of the array miss (see [Accuracy]).
On exit: the array xmiss is overwritten by the method, and the information it contained on entry is lost.
xbar
Type: array<System..::..Double>[]()[][]
An array of size [m]
On exit: the mean value, ${\stackrel{-}{x}}_{\mathit{j}}$, of the $\mathit{j}$th variable, for $\mathit{j}=1,2,\dots ,m$.
std
Type: array<System..::..Double>[]()[][]
An array of size [m]
On exit: the standard deviation, ${s}_{\mathit{j}}$, of the $\mathit{j}$th variable, for $\mathit{j}=1,2,\dots ,m$.
ssp
Type: array<System..::..Double,2>[,](,)[,][,]
An array of size [dim1, m]
Note: dim1 must satisfy the constraint: $\mathrm{dim1}\ge {\mathbf{m}}$
On exit: ${\mathbf{ssp}}\left[\mathit{j}-1,\mathit{k}-1\right]$ is the cross-product of deviations ${S}_{\mathit{j}\mathit{k}}$, for $\mathit{j}=1,2,\dots ,m$ and $\mathit{k}=1,2,\dots ,m$.
r
Type: array<System..::..Double,2>[,](,)[,][,]
An array of size [dim1, m]
Note: dim1 must satisfy the constraint: $\mathrm{dim1}\ge {\mathbf{m}}$
On exit: ${\mathbf{r}}\left[\mathit{j}-1,\mathit{k}-1\right]$ is the product-moment correlation coefficient ${R}_{\mathit{j}\mathit{k}}$ between the $\mathit{j}$th and $\mathit{k}$th variables, for $\mathit{j}=1,2,\dots ,m$ and $\mathit{k}=1,2,\dots ,m$.
ncases
Type: System..::..Int32%
On exit: the number of cases actually used in the calculations (when cases involving missing values have been eliminated).
ifail
Type: System..::..Int32%
On exit: ${\mathbf{ifail}}={0}$ 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
 $xij, i=1,2,…,nn≥2,j=1,2,…,mm≥2,$
where ${x}_{ij}$ is the $i$th observation on the $j$th variable. In addition, each of the $m$ variables may optionally have associated with it a value which is to be considered as representing a missing observation for that variable; the missing value for the $j$th variable is denoted by $x{m}_{j}$. Missing values need not be specified for all variables.
Let ${w}_{i}=0$ if observation $i$ contains a missing value for any of those variables for which missing values have been declared, i.e., if ${x}_{ij}=x{m}_{j}$ for any $j$ for which an $x{m}_{j}$ has been assigned (see also [Accuracy]); and ${w}_{i}=1$ otherwise, for $\mathit{i}=1,2,\dots ,n$.
The quantities calculated are:
(a) Means:
 $x-j=∑i=1nwixij∑i=1nwi, j=1,2,…,m.$
(b) Standard deviations:
 $sj=∑i=1nwixij-x-j2∑i=1nwi-1, j=1,2,…,m.$
(c) Sums of squares and cross-products of deviations from means:
 $Sjk=∑i=1nwixij-x-jxik-x-k, j,k=1,2,…,m.$
(d) Pearson product-moment correlation coefficients:
 $Rjk=SjkSjjSkk, j,k=1,2,…,m.$
If ${S}_{jj}$ or ${S}_{kk}$ is zero, ${R}_{jk}$ is set to zero.

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.
${\mathbf{ifail}}=1$
 On entry, ${\mathbf{n}}<2$.
${\mathbf{ifail}}=2$
 On entry, ${\mathbf{m}}<2$.
${\mathbf{ifail}}=4$
After observations with missing values were omitted, no cases remained.
${\mathbf{ifail}}=5$
After observations with missing values were omitted, only one case remained.
${\mathbf{ifail}}=-9000$
An error occured, see message report.
${\mathbf{ifail}}=-6000$
Invalid Parameters $〈\mathit{\text{value}}〉$
${\mathbf{ifail}}=-4000$
Invalid dimension for array $〈\mathit{\text{value}}〉$
${\mathbf{ifail}}=-8000$
Negative dimension for array $〈\mathit{\text{value}}〉$
${\mathbf{ifail}}=-6000$
Invalid Parameters $〈\mathit{\text{value}}〉$

# Accuracy

g02bb does not use additional precision arithmetic for the accumulation of scalar products, so there may be a loss of significant figures for large $n$.
You are warned of the need to exercise extreme care in your selection of missing values. g02bb treats all values in the inclusive range $\left(1±{0.1}^{\left({\mathbf{x02be}}-2\right)}\right)×{xm}_{j}$, where ${\mathit{xm}}_{j}$ is the missing value for variable $j$ specified in xmiss.
You must therefore ensure that the missing value chosen for each variable is sufficiently different from all valid values for that variable so that none of the valid values fall within the range indicated above.

# Parallelism and Performance

None.

The time taken by g02bb depends on $n$ and $m$, and the occurrence of missing values.
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. Missing values of $0.0$ are declared for the first and third variables; no missing value is specified for the second variable. 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, omitting completely all cases containing missing values; cases $3$ and $4$ are therefore eliminated, leaving only three cases in the calculations.

Example program (C#): g02bbe.cs

Example program data: g02bbe.d

Example program results: g02bbe.r