# Example 8: Wilcoxon Matched Pairs Test

The Wilcoxon matched pairs test is a nonparametric alternative to the t-test for dependent samples (see Basic Statistics and Tables). It will test the hypothesis that the scores for two variables were drawn from the same distribution. For a discussion of the logic and assumptions of this test, or for a comparison with the sign test, refer to the Nonparametric Statistics Notes - Wilcoxon Matched Pairs Test topic.

For this example, use the same data set (Synchron.sta), based on a study by Dodd (1979), that was used in the Example 2: Sign Test. When processing speech, one actually pays a lot of attention to visual cues as well; specifically, one can understand (encode) spoken words much more readily when the face of the person talking can be seen. In a sense, all people are "lip readers," at least to some extent. Dodd tried to find out whether infants as young as only 10 to 16 weeks old are already aware of the relationship between spoken words and the corresponding movements of the lips (of the speaker). For that purpose, Dodd placed the infants in a room so that they could watch a person behind a window reading normal speech. This speech was either delivered directly into the room (synchronous condition) or it was delayed by 400 milliseconds (asynchronous condition). The dependent variable was the amount of time that the infant watched the face behind the window. No hypotheses were formulated regarding the specific condition that should elicit the most attention (the asynchronous speech could be more interesting because it is novel, or it could draw attention away from the face because the face does not seem to be the source of the speech). File Synchron.sta contains the results of the study. Open this data file. Note that a two-letter identifier for each subject was entered as the case name.

Specifying the analysis. The Wilcoxon matched pairs test is a nonparametric alternative to the t-test for dependent samples. Since you have the same infants listening to speech under two different conditions, this test is appropriate. Select Nonparametrics from the Statistics menu to display the Nonparametric Statistics Startup Panel. Choose Comparing two dependent samples (variables) from the Quick tab and click the OK button to display the Comparing two variables dialog.

You can simultaneously perform this test on lists of variables (i.e., lists of pairs); however, there are only two variables of interest in this example. Thus, click the Variables button to display the standard variable selection dialog. From the First variable list, select In_Sync; from the Second variable list, select Out_Sync, and then click the OK button.

Reviewing the results. Now, click the Wilcoxon matched pairs test button in this dialog and the results spreadsheet is displayed.

The Wilcoxon test is significant at the .01 level (refer to Elementary Concepts for a discussion of "statistical significance"), which is more significant than the sign test was on the same data (see Nonparametric Statistics Notes - Wilcoxon Matched Pairs Test for a comparison of these tests). This reflects the fact that the sign test only uses information about the sign of the difference between the two variables, while the Wilcoxon test also takes the relative magnitude of those differences into account; thus, the Wilcoxon test is more sensitive than the sign test. From the results you can conclude that even at this age, infants can already discriminate between speech that is synchronized with the movement of the lips and unsynchronized speech; the term "read my lips" seems to capture a lot of truth about how one learns to understand language.

You can produce a box plot to visually display these results by clicking the Box & whisker plots for all variables button on the Comparing two variables dialog. Next, select both variables in the standard variable selection dialog and click the OK button. Then, select the type of statistics to be plotted in the Box-Whisker Type dialog. For this example, select the Mean/SE/SD option button, and then click the OK button to produce the following graph.

Apparently, the out-of-sync speech resulted in higher mean attention as well as greater variability on this variable.