How strong is the difference between the two groups on this item?

Question

To answer this question we need to do a cross tabulation, calculate a Chi Square significance test (SPSS will of course do this for us if we tell it to by clicking the right box) and a measure of effect size. The measure of effect size we will use is Phi.



Our output should look something like this:

Answer 1

In the table labelled ‘school is boring*gender crosstabulation’ we can find the expected values if there was no difference between boys and girls, and the actual values in the dataset. If there was no difference between boys and girls we would expect 60.5 boys and 60.5 girls (this number is of course a statistical artefact) to agree strongly that school is boring. In fact, 77 boys and 44 girls agreed strongly that school is boring. So boys are clearly more likely to agree strongly that school is boring than girls. However, girls are
somewhat more likely to agree that school is boring than would be expected if there was no difference between boys and girls, and girls are also more likely to disagree. Boys are
more likely to disagree strongly. Overall, then, boys appear to be more likely to give an extreme answer (strongly agree or strongly disagree) than girls.
Is this difference statistically significant, or, in other words, can we be reasonably confident that this difference reflects a difference in the population rather than random
sample fluctuation? To determine this we need to look at the Chi Square significance test.
In the third box we can see that the significance level of Pearson’s Chi Square is given as .001. This is a lot less than .05 and thus highly significant. We can therefore be reasonably confident that the difference in this sample represents a difference in the population.
Finally, we need to answer the question of how strong the difference is. To do that we use our effect size measure, Phi. This is .134, which suggests a modest difference between
boys and girls on this variable.