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Multiple paired ordinal variables

Effect size

There are two effect sizes that could be of interest when analyzing multiple paired ordinal variables. An effect size to go along with the results of the post-hoc test results, and an effect size for the the omnibus test (the Friedman test) itself.

With the post-hoc test we tested each possible pair of two ordinal variables, as such we can use the same effect size as discussed in the section 'paired - two ordinal' section. See the description there on which effect size to use and how to obtain these using SPSS, R or Excel.

As for the Friedman test one possible effect size recommended by Tomczak and Tomczak (2014) is Kendall's W (as described by Kendall and Smith (1939)). This is actually a measure of agreement among the respondents, where 0 would represent no agreement at all, and 1 being complete agreement.

For values between 0 and 1 the interpretation will depend on the field you work in. One such interpretation is for example from Cafiso, Di Graziano, and Pappalardo (2013, p. 257):

0.00 =W = 0.30 - Weak agreement
0.30 < W = 0.50 - Moderate agreement
0.50 < W = 0.70 - Good agreement
0.70 < W = 1.00 - Strong agreement

In the example Kendall W is 0.16 which would be considered weak. We can add this to our report:

The Friedman test indicated that there are differences between the average ranks among the seven different questions about the teacher, χ²(6, N = 52) = 49.79, p < .001. However a Kendall W of .16 indicates a weak level of agreement (according to the classification by Cafiso, Di Graziano, and Pappalardo (2013, p. 257)).
A post-hoc Dunn test with Bonferroni adjustment showed that 'the teacher was able to answer questions about the course' scored significant higher than his/her stimulation to participate in online activities (z = 3.27, p = .023), his/her stimulation to use discussion boards (z = 3.25, p = .025), and also his/her ability to motivate students (z = -3.81, p = .003). It also showed that the teacher ability to motivate students scored significant lower than his/her competence (z = -3.56, p = .008).

3+ Ordinal variables

Introduction

Impression

Visualisation

Omnibus test

Post-hoc test

Effect size

Reporting

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