Chapter 5: Using pspp
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5.3 Hypothesis Testing One of the most fundamental purposes of statistical analysis is hypothesis testing. Researchers commonly need to test hypotheses about a set of data. For example, she might want to test whether one set of data comes from the same distribution as another, or whether the mean of a dataset significantly differs from a particular value. This section presents just some of the possible tests that pspp offers. The researcher starts by making a null hypothesis. Often this is a hypothesis which he suspects to be false. For example, if he suspects that A is greater than B he will state the null hypothesis as A = B.2 The p-value is a recurring concept in hypothesis testing. It is the highest acceptable probability that the evidence implying a null hypothesis is false, could have been obtained when the null hypothesis is in fact true. Note that this is not the same as “the probability of making an error” nor is it the same as “the probability of rejecting a hypothesis when it is true”.
5.3.1 Testing for differences of means 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: • 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. 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. 2
This example assumes that it is already proven that B is not greater than A.