Theme 14 Ranking tests

Transcription

1 Slide 14.1 Theme 14 Ranking tests

2 Slide 14.2 Overview The tests which we have considered so far assumed that the data on our variables is normally distributed What do we do if this assumption has been violated and the data does not have a bellshaped distribution? In such cases we use non-parametric tests Non-parametric tests make fewer assumptions about the population from which the sample has been drawn and involve ranking data

3 Slide 14.3 Equivalent Tests Non-parametric tests often have an equivalent parametric test The Mann-Whitney U test is equivalent to the unrelated t-test and can be applied to exactly the same data i.e. data is obtained from two independent groups The Wilcoxon matched pairs test is equivalent to the related t-test and can be applied to exactly the same data i.e. data obtained from the same sample at two points in time or from two matched samples

4 Slide 14.4 Key Steps Figure 18.1 Key steps in non-parametric statistics

5 Slide 14.5 Example of a Wilcoxon Test Let us return to the example that we used when looking at the related t-test A researcher is interested in investigating whether the eye contact between a baby and his/her mother increases over time The frequency of eye contact is recorded when the babies are aged 6 and 9 months The researcher now wishes to determine whether or not there is a statistically significant difference between the means of the two sets of scores

6 Slide 14.6 Frequencies of Eye Contacts Baby 6 months 9 months Clara 3 7 Martin 5 6 Sally 5 3 Angie 4 8 Trevor 3 5 Sam 7 9 Bobby 8 7 Sid 7 9

7 Slide 14.7 Entering the Data

8 Slide 14.8 Conducting a Wilcoxon Test Select Analyze, Nonparametric Tests, Legacy Dialogs and 2-Related Samples... Move the appropriate pair of variables to the Test Pairs: Move the dependent variable to the Test Variables List: box and the grouping (independent) variable to the Grouping Variable: box Select Define Groups..., define the two groups, select Continue and then OK Check to see if the p value is significant at.05 or less If it is, determine the direction of the difference

9 Slide 14.9 Output for a Wilcoxon Test

10 Slide Interpretation We could report these results as follows: There was no significant difference in the amount of eye-contact by babies between 6 and 9 months, Wilcoxon, z(n = 8) = -1.71, twotailed p =.088. The researcher thus concludes that the frequency of eye contacts over this time period has not increased significantly

11 Slide Example of a Mann-Whitney U Test Let us return to the example we used when considering the unrelated t-test A researcher collects the emotionality scores from 2 groups of children Group 1 = children from two-parent families Group 2 = children from lone-parent families The researcher now wishes to determine whether or not there is a statistically significant difference between the means of these two sets of scores

12 Slide Emotionality Scores Two-Parent Lone-Parent Mean = Mean = 9.50

13 Slide Entering the Data

14 Slide Entering the Data (Continued)

15 Slide Conducting the Mann-Whitney U test

16 Slide Conducting the Mann-Whitney U test (Continued)

17 Slide Output

18 Slide Interpretation The researcher therefore concludes that there is a statistically significant difference between the two groups We could report the results of this analysis as follows: The Mann Whitney U test found that the emotionality scores of children from twoparent families were significantly higher than those of children in lone-parent families, U(n1 = 10, n2 = 12) = 23.5, two-tailed p =

19 Slide Working with Three or More Groups So far we have focused on testing for differences between two groups Sometimes you may wish to know whether the means of three or more different sets of scores are significantly different from each other but the data is not normally distributed Friedman test: For use with related data (this is the equivalent of the related ANOVA) Kruskal Wallis test: For use with unrelated data (this is the equivalent of the unrelated ANOVA)

20 Slide Conclusion Non-parametric tests can be used when working with data which is not normally distributed They are sometimes referred to as ranking tests as they involve ranking data We have considered the use of the Wilcoxon test and the Mann-Whitney U test You should understand when these tests are used and what their parametric equivalent tests are