A common statistical test involves hypotheses about means.
The `T-TEST`

command is used to find out whether or not two separate
subsets have the same mean.

t-test uses the file `physiology.sav` previously
encountered.
A researcher suspected that the heights and core body
temperature of persons might be different depending upon their sex.
To investigate this, he posed two null hypotheses:

- The mean heights of males and females in the population are equal.
- The mean body temperature of males and females in the population are equal.

In addition to the T-test, the `T-TEST`

command also performs the
Levene test for equal variances.
If the variances are equal, then a more powerful form of the T-test can be used.
However if it is unsafe to assume equal variances,
then an alternative calculation is necessary.
pspp performs both calculations.

For the `height` variable, the output shows the significance of the
Levene test to be 0.33 which means there is a
33% probability that the
Levene test produces this outcome when the variances are equal.
Had the significance been less than 0.05, then it would have been unsafe to assume that
the variances were equal.
However, because the value is higher than 0.05 the homogeneity of variances assumption
is safe and the “Equal Variances” row (the more powerful test) can be used.
Examining this row, the two tailed significance for the `height` t-test
is less than 0.05, so it is safe to reject the null hypothesis and conclude
that the mean heights of males and females are unequal.

For the `temperature` variable, the significance of the Levene test
is 0.58 so again, it is safe to use the row for equal variances.
The equal variances row indicates that the two tailed significance for
`temperature` is 0.20. Since this is greater than 0.05 we must reject
the null hypothesis and conclude that there is insufficient evidence to
suggest that the body temperature of male and female persons are different.

PSPP> get file='/usr/local/share/pspp/examples/physiology.sav'. PSPP> recode height (179 = SYSMIS). PSPP> t-test group=sex(0,1) /variables = height temperature. Output: 1.1 T-TEST. Group Statistics #==================#==#=======#==============#========# # sex | N| Mean |Std. Deviation|SE. Mean# #==================#==#=======#==============#========# #height Male |22|1796.49| 49.71| 10.60# # Female|17|1610.77| 25.43| 6.17# #temperature Male |22| 36.68| 1.95| .42# # Female|18| 37.43| 1.61| .38# #==================#==#=======#==============#========# 1.2 T-TEST. Independent Samples Test #===========================#=========#=============================== =# # # Levene's| t-test for Equality of Means # # #----+----+------+-----+------+---------+- -# # # | | | | | | # # # | | | |Sig. 2| | # # # F |Sig.| t | df |tailed|Mean Diff| # #===========================#====#====#======#=====#======#=========#= =# #height Equal variances# .97| .33| 14.02|37.00| .00| 185.72| ... # # Unequal variances# | | 15.15|32.71| .00| 185.72| ... # #temperature Equal variances# .31| .58| -1.31|38.00| .20| -.75| ... # # Unequal variances# | | -1.33|37.99| .19| -.75| ... # #===========================#====#====#======#=====#======#=========#= =# |

**Example 5.6: The T-TEST command tests for differences of means.
Here, the height variable's two tailed significance is less than
0.05, so the null hypothesis can be rejected.
Thus, the evidence suggests there is a difference between the heights of
male and female persons.
However the significance of the test for the temperature
variable is greater than 0.05 so the null hypothesis cannot be
rejected, and there is insufficient evidence to suggest a difference
in body temperature.**