Chapter 10
Module 2For self study: Running Tests in SPSS
Assignment 10.4Assignment 4
Open the file Moviezone.sav. Say we suspect that male and female subjects respond differently to their arts and culture education program (CAE is the Dutch abbreviation). One of the tests that we could run is an independent sample t-test. Read up on what this test does, and when to apply it in Chapter 10. Select the test from the Analyze-menu in SPSS, select gender as grouping variable, and the variables related to appreciation of CAE (cae1, cae2, cae3, and cae4). Interpret the results by first looking at the Levene test: check whether to look at “equal variances assumed” or “equal variances not assumed”. In your report on this test, include the means for cae1 through cae4 for male and female subjects separately, the relevant data of the t-tests (t-value, degrees of freedom, and the significance level).
In the data set we have information about the interest for several cultural activities. We want to know whether there are significant differences between subjects’ appreciation for visiting a museum (museum2), going to a theatre (theater2), a dance performance (dans2), a pop concert (pop2), or going to the movies (film2). A paired sample t-test can only test the differences between mean scores on these variables in pairs. As you can imagine, with four variables this amounts to a lot of comparisons (six). Since the study is concerned with the popularity of art house movies, maybe it is interesting to look at the attraction of going to the movies relative to the other activities. Select the paired sample t-test from the Analyze menu. Make the following pairs: film2— museum2, film2— theater2, film2— dans2, film2— pop2. Report and interpret the result: what does it tell you about an evening at the movies and its competitors?
Run a Kolmogorov Smirnov test on the variables film2, museum2, theater2 and dans2, and on cae1 through cae4. Interpret the results. What does this tell you about what we did in Exercises 1 and 2?
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Run the same comparisons as under Exercise 1, using the Mann-Whitney test. Do the results differ from those found before?
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Make the same comparisons as under Exercise 2, but this time with the Wilcoxon test. How do the test results relate to those we found before?
We use the independent sample test when subjects can be part of no more than one group. And in this case they can’t. The participants are either male or female. You have run the test for the four variables, all at once, and this is the result:
| Group Statistics | |||||
|---|---|---|---|---|---|
| Gender | N | Mean | Std. Deviation | Std. Error Mean | |
| cae1 | male | 310 | 3.0097 | 1.20540 | .06846 |
| female | 352 | 3.5170 | 1.14715 | .06114 | |
| cae2 | male | 310 | 2.4194 | 1.08756 | .06177 |
| female | 346 | 2.7225 | 1.07051 | .05755 | |
| cae3 | male | 310 | 2.7129 | 1.15952 | .06586 |
| female | 347 | 3.1037 | 1.09157 | .05860 | |
| cae4 | male | 311 | 2.3087 | 1.15614 | .06556 |
| female | 346 | 2.5838 | 1.09818 | .05904 | |
This first table already tells you something about what the data look like: on all variables you see that female participants scored higher than the males. The information about the means (and the SD’s of course) may be useful, later, when you write up your report.
Look now at the rest of the output. As you remember, using the t-test means that you have to check the results of the Levene test first.
| Independent Samples Test | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Levene’s Test for Equality of Variances | t-test for Equality of Means | |||||||||
| F | Sig. | t | df | Sig. (2-tailed) | Mean Difference | Std. Error Difference | 95% Confidence Interval of the Difference | |||
| Lower | Upper | |||||||||
| cae1 | Equal variances assumed | .001 | .974 | −5.545 | 660 | .000 | −.50737 | .09150 | −.68704 | −.32770 |
| Equal variances not assumed | −5.527 | 640.044 | .000 | −.50737 | .09179 | −.68762 | −.32712 | |||
| cae2 | Equal variances assumed | .516 | .473 | −3.594 | 654 | .000 | −.30319 | .08435 | −.46882 | −.13756 |
| Equal variances not assumed | −3.591 | 643.802 | .000 | −.30319 | .08442 | −.46897 | −.13741 | |||
| cae3 | Equal variances assumed | 4.873 | .028 | −4.449 | 655 | .000 | −.39084 | .08785 | −.56335 | −.21834 |
| Equal variances not assumed | −4.434 | 635.965 | .000 | −.39084 | .08815 | −.56395 | −.21774 | |||
| cae4 | Equal variances assumed | 1.654 | .199 | −3.127 | 655 | .002 | −.27513 | .08798 | −.44790 | −.10237 |
| Equal variances not assumed | −3.119 | 639.039 | .002 | −.27513 | .08822 | −.44838 | −.10189 | |||
When the results on this test are significant we have to reject the null hypothesis that variances of the two groups are equal. Here however, there is just one instance where variances are unequal: in the case of cae3. So here we have to check the second row (for “Equal variance not assumed”); for the other three we can check the row labeled “Equal variance assumed”. You will also see that there is not much difference, whether we look at variance assumed or not assumed; but remember, sometimes it is a matter of having to reject your hypotheses, or not. What we see is that in all cases the t-value is negative. That is irrelevant here: they would have been positive if we would have entered the groups in the reversed order (that is first 2 then 1, when defining the groups). What is relevant is that all the results of the t-test are significant. This means that next time that you would take a random sample from the same population you have a good chance that you again find t-values as large as here, or even larger. In other words: there are significant differences between the male and female students as to their appreciation for the art education program. The differences are small but significant.
If you followed the instructions carefully, this is what you had on your screen:
Clicking on OK would have produced the following output:
| Paired Samples Statistics | |||||
|---|---|---|---|---|---|
| Mean | N | Std. Deviation | Std. Error Mean | ||
| Pair 1 | museum2 | 2.8157 | 651 | 1.17138 | .04591 |
| film2 | 3.9616 | 651 | 1.01681 | .03985 | |
| Pair 2 | theater2 | 3.2446 | 654 | 1.11982 | .04379 |
| film2 | 3.9679 | 654 | 1.00863 | .03944 | |
| Pair 3 | dance2 | 2.8155 | 656 | 1.36962 | .05347 |
| film2 | 3.9695 | 656 | 1.00790 | .03935 | |
| Pair 4 | pop2 | 3.7230 | 657 | 1.17752 | .04594 |
| film2 | 3.9665 | 657 | 1.01006 | .03941 | |
Using the first table you can already try to detect a pattern. In all cases you see that film scores are higher than the other activities. However, you can also see that its popularity hardly differs from that of a pop concert. The means and standard deviations can be useful for your report; also, in this case it may be advisable to make a graph. For the readers of your report, it will be easier to understand what the results are.
| Paired Samples Test | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Paired Differences | |||||||||
| Mean | Std. Deviation | Std. Error Mean | 95% Confidence Interval of the Difference | t | df | Sig. (2-tailed) | |||
| Lower | Upper | ||||||||
| Pair 1 | museum2 – film2 | −1.14593 | 1.49622 | .05864 | −1.26108 | −1.03078 | −19.541 | 650 | .000 |
| Pair 2 | theater2 – film2 | −.72324 | 1.23558 | .04831 | −.81811 | −.62837 | −14.969 | 653 | .000 |
| Pair 3 | dance2 – film2 | −1.15396 | 1.42574 | .05567 | −1.26327 | −1.04466 | −20.730 | 655 | .000 |
| Pair 4 | pop2 – film2 | −.24353 | 1.05853 | .04130 | −.32462 | −.16244 | −5.897 | 656 | .000 |
In the table above we see what the differences were exactly. The smallest difference is found in the last row: the comparison of popularity of film with that of pop concerts (−.24). However, for all of the four comparisons that we made, we see that the t-values are highly significant. In other words, participants appreciated film always over other activities and the differences are significant (all p’s < .000). In your report you include the t-values and the degrees of freedom.
The Kolmogorov Smirnov test leads to the following results.
| Tests of Normality | ||||||
|---|---|---|---|---|---|---|
| Kolmogorov-Smirnov a | Shapiro-Wilk | |||||
| Statistic | df | Sig. | Statistic | df | Sig. | |
| cae1 | .196 | 634 | .000 | .904 | 634 | .000 |
| cae2 | .192 | 634 | .000 | .906 | 634 | .000 |
| cae3 | .173 | 634 | .000 | .917 | 634 | .000 |
| cae4 | .182 | 634 | .000 | .893 | 634 | .000 |
| film2 | .227 | 634 | .000 | .840 | 634 | .000 |
| museum2 | .197 | 634 | .000 | .902 | 634 | .000 |
| theater2 | .183 | 634 | .000 | .910 | 634 | .000 |
| dance2 | .158 | 634 | .000 | .893 | 634 | .000 |
Lilliefors Significance Correction.
These results indicate that the variables are not normally distributed. This means that we are not allowed to conduct a t-test. We should have done this first, of course, but we wanted you to practice using the paired samples t-test. Now let us look at the alternatives.
We see the same results as we found for the t-tests. Again all differences are highly significant.
4b. We hope you entered the dialog box as follows:
And here are the results of your test:
| Test Statistics b | ||||
|---|---|---|---|---|
| film2 – museum2 | film2 – theater2 | film2 – dance2 | film2 – pop2 | |
| Z | −15.485 a | −13.068 a | −16.183 a | −5.819 a |
| Asymp. Sig. (2-tailed) | .000 | .000 | .000 | .000 |
Based on negative ranks.
b.Wilcoxon Signed Ranks Test.
Again, all the results are significant. Your conclusions do not have to be altered. Bear in mind though, that sometimes the test results of non-parametric tests will be different from the parametric ones! It is very important, therefore, in terms of statistical validity, that you always use the appropriate tests. Critics (including your teachers) may simply ignore your findings if you don’t.