## FV_TEST

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 = (x0, x1, x2, ..., xN-1) and y = (y0, y1, y2 ..., yM-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.

### 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.

None.

### 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.

Introduced: 4.0