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98 CHAPTER 4 Statistical analysis

Table 4.28 Sample Data for Wilcoxon Signed-Rank Test Continued
Participants Alphanumeric Image-Based
Participant 4 5 5
Participant 5 2 7
Participant 6 3 4
Participant 7 4 6
Participant 8 6 5
Participant 9 4 3
Participant 10 3 4

In cases when three or more sets of data are compared and the parametric analysis
assumptions are not met, the Kruskal-Wallis one-way ANOVA by ranks (an exten-
sion of the Mann-Whitney U test) may be considered when the samples are inde-
pendent. When the data sets are dependent on each other, you can consider using
Friedman's two-way ANOVA test.
In the authentication study discussed previously, suppose you would like to
evaluate a drawing-based password technique in additional to the alphanumeric
technique and the image-based technique, the study will include three conditions.
If you recruit three groups of participants and let each group use one authentication
technique during the study, the data will be collected from independent samples
and the frustration rating can be analyzed through the Kruskal-Wallis one-way
ANOVA by ranks. Sample data for the test is demonstrated in Table 4.29. The mean
score for the alphanumeric password is 3.25. The mean score for the image-based
password is 4.63. The mean score for the drawing-based password is 5.63.
The result of the Kruskal-Wallis test is an H value. In this example, H(2) = 11.897,
p < 0.05. Therefore, the null hypothesis is rejected. The result suggests that there is
significant difference in the perceived level of frustration between the three authen-
tication techniques.

Table 4.29 Sample Data for Kruskal-Wallis One-Way Analysis of Variance by
Ranks
Group Participants Rating Coding

Alphanumeric Participant 1 5 0
Alphanumeric Participant 2 3 0
Alphanumeric Participant 3 4 0
Alphanumeric Participant 4 4 0
Alphanumeric Participant 5 2 0
Alphanumeric Participant 6 3 0
Alphanumeric Participant 7 3 0
Alphanumeric Participant 8 2 0
Image-based Participant 9 3 1
Image-based Participant 10 5 1
Image-based Participant 11 6 1