Next: Linear Regression, Up: Hypothesis Testing [Contents][Index]
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.
Example 5.6 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:
For the purposes of the investigation the researcher decided to use a p-value of 0.05.
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| ... # #===========================#====#====#======#=====#======#=========#= =# |
Next: Linear Regression, Up: Hypothesis Testing [Contents][Index]