Chapter 10
Module 2For self study: Running Tests in SPSS
Assignment 10.1Assignment 1
In a study by Willemijn (Willemijn.sav) two groups of participants were assigned to one of two conditions. Each group saw one versions of a children’s movie called “Polleke”. In one version the order of scenes was randomized; the second was the original. Take a look at Willemijn’s questionnaire. One of the things she wanted to know is whether participants would remember facts from the movie better in the original version. She distinguished two types of information: incidental and central (that is, central to the story line). Let us see what happened. Conduct a t-test using group as independent variable, and incident and central as dependent variables. Interpret the results: (a) what does the Levene test tell us about the interpretation of the table SPSS produced? (b) How do you interpret the results of the t-tests?
First of all, (a) what is the use of this test? Run the appropriate test (reread Chapter 10 to remind you which test this is) to see whether you actually need it. (b) Report the results of your examination of the two variables incident and central and explain what this tells you about the previous assignment. (c) Now conduct the Mann-Whitney test using the same variables: “incident” and “central” as dependent variables and “group” as independent.
When you conducted the test correctly, you have the following output on your screen:
| Group Statistics | |||||
|---|---|---|---|---|---|
| Version participants saw | N | Mean | Std. Deviation | Std. Error Mean | |
| IncidenteleInfo | Original version | 25 | 1.7750 | .20729 | .04146 |
| Random version | 27 | 1.7870 | .15817 | .03044 | |
| CentraleInfo | Original version | 24 | 1.9417 | .11001 | .02246 |
| Random version | 27 | 1.8296 | .19771 | .03805 | |
This first table presents the descriptive statistics. As you know, these will help you to interpret the inferential statistics, in this case those of the t-test. Let us look at the data. What you see is that the mean results for both the incidental information and central information are almost the same in both groups. You do see, though, that the difference for “central information recall” in the group that saw the original version is slightly higher than in the group that saw the random version. The difference between these groups for “incidental information recall” is smaller still, if not hardly perceptible! We need to know more, however, before we can draw our conclusion. You need to realize that the small differences can be significant; that means that next time a researcher will conduct exactly the same procedure with participants randomly selected from the same population there is a good chance that she will find the same difference, or larger. Let us now look at the other results, those of the inference statistics.
| 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 | |||||||||
| IncidenteleInfo | Equal variances assumed | 2.494 | .121 | −.236 | 50 | .814 | −.01204 | .05090 | −.11428 | .09020 |
| Equal variances not assumed | −.234 | 44.826 | .816 | −.01204 | .05143 | −.11564 | .09157 | |||
| CentraleInfo | Equal variances assumed | 5.177 | .027 | 2.457 | 49 | .018 | .11204 | .04560 | .02040 | .20368 |
| Equal variances not assumed | 2.536 | 41.565 | .015 | .11204 | .04418 | .02285 | .20123 | |||
In the table above you first read the results for the Levene’s test. You see that the first (for incidental information recall) is not significant, while the second (for central information) is (p < .027). This means that in the upper part of the table we have to look at the row for “Equal variance assumed”. This leads us to a p-value of .814, which means that we cannot conclude that the manipulation had an effect on recall for incidental information. For the next variable, central, you need to use the results in the row for “Equal variance not assumed.” In this case, the t-test does show a significant effect (t = 2.54, df = 41.6, p < .015). This means that you can conclude that the groups did indeed score differently on this variable. The difference must have been caused by Willemijn’s manipulation. Distorting the order of the events caused participants to forget some of the elements in the film that were central to the narrative. It is peculiar (and interesting) that this effect only holds for the central information, and not for the incidental information, maybe casting light on the difference between central and peripheral motifs in story structure, as hypothesized by Tomashevsky at the time of Russian Formalism.
We already noted that the size of the effect was not spectacular. But are you sure? The assignment does not tell you on what scale the participants scored. In fact the scale was constructed using a combination of other variables. For this assignment it is not necessary to go into the particulars. What is important, however, is that you understand that interpreting the results of statistical tests requires you to know on what scale the participants scored. In this case it was between 0 and 2. You should interpret the mean difference of .11 in this perspective. What is more, it may be interesting to see what the range was for the data set: what were the lowest score and the highest scores? To do this, go to the menu Analyze, run the descriptive statistics, and you will find out that the range was rather small.
| Descriptive Statistics | |||||
|---|---|---|---|---|---|
| N | Minimum | Maximum | Mean | Std. Deviation | |
| IncidenteleInfo | 52 | 1.38 | 2.00 | 1.7813 | .18169 |
| CentraleInfo | 51 | 1.40 | 2.00 | 1.8824 | .17054 |
| Valid N (listwise) | 51 | ||||
You see that the scores varied between 1.40 and 2.00. So, of the 51 participants nobody scored lower than 1.40! In the light of this information the difference between the two mean group scores is still small, of course, but probably not as small as you first believed it was.
Chapter 10 describes the conditions for using the independent samples t-test. You always first need to check these conditions before running the tests. For this assignment you hopefully conducted a correct test, and ended up with the following output (if not, reread section 10.1).
| Tests of Normality | |||||||
|---|---|---|---|---|---|---|---|
| Version participants saw | Kolmogorov-Smirnov a | Shapiro-Wilk | |||||
| Statistic | df | Sig. | Statistic | df | Sig. | ||
| IncidenteleInfo | Original version | .263 | 24 | .000 | .850 | 24 | .002 |
| Random version | .229 | 27 | .001 | .905 | 27 | .017 | |
| CentraleInfo | Original version | .452 | 24 | .000 | .580 | 24 | .000 |
| Random version | .255 | 27 | .000 | .776 | 27 | .000 | |
Lilliefors Significance Correction.
What do these results tell you? What you can conclude from these numbers is that in both groups the distribution of both incidental information recall and central information recall is not normally distributed. This means that you are not allowed to use the t-test, but have to use a nonparametric equivalent! But, which test? Take a look at the chart in Figure 10.9 and you will know that it is Mann-Whitney’s test that is appropriate here.
Running this test will result in the following output:
| Ranks | ||||
|---|---|---|---|---|
| Version participants saw | N | Mean Rank | Sum of Ranks | |
| IncidenteleInfo | Original version | 25 | 26.82 | 670.50 |
| Random version | 27 | 26.20 | 707.50 | |
| Total | 52 | |||
| CentraleInfo | Original version | 24 | 30.50 | 732.00 |
| Random version | 27 | 22.00 | 594.00 | |
| Total | 51 | |||
| Test Statistics a | ||
|---|---|---|
| IncidenteleInfo | CentraleInfo | |
| Mann-Whitney U | 329.500 | 216.000 |
| Wilcoxon W | 707.500 | 594.000 |
| Z | −.151 | −2.321 |
| Asymp. Sig. (2-tailed) | .880 | .020 |
Grouping Variable: Version participants saw.
For the interpretation you focus on the results in the bottom row. For incident you there was no significant effect, but for central there was (p < .020). This means that you can conclude the difference between the group scores on recall of central information was indeed significant, when conducting the correct (nonparametric) test, i.e. the Mann-Whitney test.