The FV_TEST function computes the F-statistic and the probability that two sample populations *X* and *Y* have significantly different variances. *X* and *Y* may be of different lengths. The F-statistic formula for sample populations *x* and *y* with means x and y is defined as:

where *x* = (*x*_{0}, *x*_{1}, *x*_{2}, ..., *x*_{N-1}) and *y* = (*y*_{0}, *y*_{1}, *y*_{2} ..., *y*_{M-1})

This routine is written in the IDL language. Its source code can be found in the file fv_test.pro in the lib subdirectory of the IDL distribution.

## Examples

; Define two n-element sample populations:

X = [257, 208, 296, 324, 240, 246, 267, 311, 324, 323, 263, $

305, 270, 260, 251, 275, 288, 242, 304, 267]

Y = [201, 56, 185, 221, 165, 161, 182, 239, 278, 243, 197, $

271, 214, 216, 175, 192, 208, 150, 281, 196]

; Compute the F-statistic (of X and Y) and its significance:

PRINT, FV_TEST(X, Y)

IDL prints:

2.48578 0.0540116

The result indicates that X and Y have significantly different variances.

## Syntax

*Result* = FV_TEST(*X*,* Y*)

## Return Value

The result is a two-element vector containing the F-statistic and its significance. The significance is a value in the interval [0.0, 1.0]; a small value (0.05 or 0.01) indicates that *X* and *Y* have significantly different variances. This type of test is often referred to as the F-variance test.

## Arguments

### X

An *n*-element integer, single- or double-precision floating-point vector.

### Y

An *m*-element integer, single- or double-precision floating-point vector.

## Keywords

None.

## Version History

4.0 |
Introduced |