11. The next step is to calculate the degrees of freedom. This is calculated

as follows:

df N

A

N

B

2. In our case this is 20 2. Therefore, the df 18.

12. Now you are ready to see if your results are statistically significant. In

order to this, consult Table A1 in Appendix A. As we did not make any

predictions about which group would find the information on train

times quicker than the other, we are interested in the critical t values

for a two-tailed test. If we had made a prediction that females would

find the train departure information quicker than males, we would be

looking at columns related to one-tailed values.

13. Once you have your tails sorted out, look for the column where it says

df 18. If your value of t is larger than the figure listed in that column

we can say that you have found a significant difference in search times

between females and males at the 5 per cent level (p 0.05). If it is

lower, we did not find a significant difference in search times between

males and females in your study. The final thing to mention here is how

to report this finding in your written report. Conventionally you would

report this finding as follows: t 0.89, df 18, two-tailed ns (where

ns stands for not significant). This could be written out more formally

as the mean time taken for females to find train departure information

(M 225.1 secs) using the PDA application is not significantly quicker

than the average time taken by male users (M 210.1 secs), t 0.89,

df 18, two-tailed ns.

Wilcoxon signed-ranks test

This test should be used if you have a two condition related design, using

the same participants (or matched participants) to participate in both con-

ditions. The aim of this test is to compare participants’ performance in the

two conditions to find out whether or not there is any difference between

the scores obtained. This test is the non-parametric equivalent of the

related t-test. The example we will use here will be data from a group of

participants who used two different methods of interaction to carry out a

web search using a PDA device. The first condition required participants

to use a stylus to interact with the application and the second condition

required them to use keypad entry. After using each version of the appli-

cation participants were asked to rate the usability of the device using a

Likert-type questionnaire. Let’s look at Technical Tip 3 to work through

how to calculate this statistic.

152 Understanding Mobile Human–Computer Interaction

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Data analysis 153

Technical Tip 3

Calculating a Wilcoxon singed-ranks test

The data obtained from this study comes from the attitude score obtained

from each participant on the Likert usability scale described above. The

scale was based on a 7-point scale. The higher the overall usability score,

the more positively the participant rated the PDA application. Table 8.7

provides information on what the initial data table may look like:

1. The first step in working out this formula is to calculate the difference

between each pair of scores, assigning plus or minus signs where

appropriate.

2. The next step is to rank the differences between the scores obtained

for the two conditions (ignoring the plus or minus signs this time).

3. After that, rank the plus difference and rank the minus differences.

4. Your data table should now look something like Table 8.8.

5. The next step is to take the smaller of the totals obtained for the plus

and minus rank differences. This gives us the value of a statistic called

W (remember this is called the Wilcoxon test) and this will be used to

look up the appropriate table for statistical significance.

6. The next step is to calculate the number of pairs of participants that do

not have tied scores. From the example above we can see that there

are no tied pairs of scores, therefore in this case N 10. However, if

Participant Stylus Input Attitude Score Keypad Entry Attitude Score

125 38

224 39

332 37

429 36

538 34

631 30

727 31

839 40

921 35

10 22 33

Table 8.7 Participant Attitude Scores for Stylus Input and Keypad Entry

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