1. Home
2. PRCORRELATION procedure

# PRCORRELATION procedure

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 Saves cumulative lower probabilities Saves cumulative upper probabilities Saves probability densities 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 – r2))

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.

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
```
Updated on March 6, 2019