The
TM_TEST
function computes the
Student's T-statistic and the probability that two sample populations *
X*
and *
Y*
have significantly different means. *
X*
and *
Y*
may be of different lengths. The result is a two-element vector containing the T-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 means. The default assumption is that the data is drawn from populations with the same true variance. This type of test is often referred to as the
t-means
test.

The T-statistic 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 ```
tm_test.pro
```

in the ```
lib
```

subdirectory of the IDL distribution.

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 Student's t-statistic and its significance assuming that *
X*
and *
Y*
belong to populations with the same true variance.

The result indicates that *
X*
and *
Y*
have significantly different means.