Calculates probabilities for product moment correlations (R.W. Payne).

### Option

`NOBSERVATIONS` = scalar |
Number of observations from which the correlation(s) were calculated |
---|

### Parameters

`DATA` = scalars, variates, tables, matrices, diagonal matrices or symmetric matrices |
Correlations for calculating probabilities or cumulative lower probabilities for calculating equivalent deviates |
---|---|

`CLPROBABILITY` = scalars, variates, tables, matrices, diagonal matrices or symmetric matrices |
Saves cumulative lower probabilities |

`CUPROBABILITY` = scalars, variates, tables, matrices, diagonal matrices or symmetric matrices |
Saves cumulative upper probabilities |

`PROBABILITY` = scalars, variates, tables, matrices, diagonal matrices or symmetric matrices |
Saves probability densities |

`CORRELATION` = scalars, variates, tables, matrices, diagonal matrices or symmetric matrices |
Saves correlations |

### Description

`PRCORRELATION`

calculates probabilities and equivalent deviates for the product moment correlation coefficient. The number of observations must be supplied by the `NOBSERVATIONS`

option, in a scalar. The `DATA`

parameter supplies the data values in any numerical data structure (scalar, variate, matrix, table, etc.). If these are correlations, you can save various probabilities using the parameters `CLPROBABILITY`

(cumulative lower), `CUPROBABILITY`

(cumulative upper) and `PROBABILITY`

(probability density). Alternatively, if `DATA`

contains probabilities, you can save equivalent correlation values using the `CORRELATION`

parameter.

Option: `NOBSERVATIONS`

.

Parameters: `DATA`

, `CLPROBABILITY`

, `CUPROBABILITY`

, `PROBABILITY`

, `CORRELATION`

.

### Method

`PRCORRELATION`

uses the fact that, for a correlation *r* based on *n* observations, the variable

*t* = *r* × √((*n* – 2) / (1 – *r*^{2}))

has a t distribution on *n*-2 degrees of freedom.

### Action with `RESTRICT`

If a `DATA`

variate is restricted, the calculations will be preformed only on the specified units.

### See also

Directive: `CORRELATE`

.

Procedures: `DCORRELATION`

, `FCORRELATION`

.

Commands for: Basic and nonparametric statistics.

### Example

CAPTION 'PRCORRELATION example'; STYLE=meta PRCORRELATION [NOBSERVATIONS=12] 0.5; CLPROBABILITY=clprob05;\ CUPROBABILITY=cuprob05; PROBABILITY=prob05; CORRELATION=corr05 PRINT clprob05,cuprob05,prob05,corr05; DECIMALS=5