I have a data set from a study where I took responses to touch sensation, pricking sensation and cold sensation from both sides of the body. The response to these sensations can be either that it was more on one side, same on both sides or less on one side. Therefore I end up with a 3x3 table of repeated tests. Since McNemar test in SPSS is only valid for 2x2 tables, what are my options in such a scenario? Is there any test that can be performed in these situations?
More Same Less
Touch
Pricking
Cold
Harold, please look at Salvatore's second post in this thread and my first post.
HTH.
A McNemar test does something different than chi-square test. Chi- Square test is for test of independence and McNemar is not testing for independence, but consistency in responses across two variables.
SPSS may not have this option of analyzing 3x3 contingency table. RR, Stata and SAS does.
https://www.stata.com/stb/stb7/sbe6/mcc3i.hlp
Repeated Measures will work in your situation.
The McNemar test is often extended to square tables larger than 2x2. As @GayatriVishwakarma suggests, your best solution may be to use a different software package.
The R function mcnemar.test conducts the test easily, although it can fail if there are zeros in certain spots in the table.
For another approach, a 2 x 2 McNemar test can be performed as an exact binominal test. Likewise, McNemar tests on larger tables can be performed with multinomial tests. An example of this is given at the following webpage in the section "Optional analyses: conducting exact tests for symmetry": http://rcompanion.org/handbook/H_05.html .
The way you have your table set up, you cannot use McNemar test. (!!!!)
Essentially, with McNemar test, you need to have the same categories on the side of the table as on the top of the table. You can see the examples here, or elsewhere: http://rcompanion.org/handbook/H_05.html
I'm trying to think of how to advise you to analyze you data... Will respond later...
I agree with Salvatore's last post: The 3x3 table you show in the original question is not suitable for analysis via extensions of McNemar's test.
Nevertheless, for the benefit of someone who finds this thread later while searching for how to perform (an extension of) McNemar's test for (square) tables larger than 2x2, see this Tech Note on the NcNemar-Bowker test:
http://www-01.ibm.com/support/docview.wss?uid=swg21477019
HTH.
Thinking over your study... The good news is that you have different options to analyze your data. The bad news is that you have to decide how you want to analyze your data. With different options, the following may sound a bit confusing.
Your dependent variable is "Sidedness" (Left-more / Same / Right-more). You could treat this as a categorical variable or an ordinal variable. I think I would recommend considering it an ordinal variable.
You have the option to treat each Stimulus (Touch, Pricking, and Cold) as separate experiments. If so, you will not be able to directly compare among them. But it would simplify the analysis. If this case you would be interested to see if there is a significant "sidedness" for each stimulus. You might then consider One-sample Wilcoxon Signed-rank Test* (DV is ordinal), or chi-square goodness-of-fit (DV is categorical)**. ***
If you want to be able to compare the "sidedness" of each Stimulus, you want to be able to put all of them into the same model. This way you can test the hypotheses that one stimulus is more "sided" than another, as well as report if each stimulus is "sided".
I think the best way to do this would be to use ordinal regression. You would treat your DV as ordinal and you use Stimulus as the independent variable. You also need to include Subject as a blocking variable, preferably as a random effect. I'm not an SPSS user, but if memory serves, there have been discussions on this site on how to conduct ordinal regression with SPSS.
A simplified version of this approach would be to use Friedman (or Quade) test****, with Stimulus as the treatment and Subject as the blocks. A post-hoc would be Conover test or other appropriate post-hoc test.
All this being said, probably the best way to investigate and present this data is with simple descriptive statistics and plots. For example, you can present the proportion for each Stimulus for each Sidedness category. This can also be shown as a bar plot.
___________
* With only three categories in the ordinal variable, perhaps the one-sample sign test would be a better choice for a test, though less powerful.
** I think the null proportions for a chi-square goodness-of-fit test would be (0.25, 0.50, 0.25), but I'm not sure.
*** To give you some sense of the power here, for either of the one-sample Wilcoxon, one-sample sign, or chi-square GOF, counts of (10, 20, 2) will result in significantly "sidedness".
**** Again, with only three categories in the ordinal variable, I'm not sure how well these tests will behave.
My suggestion is that since SPSS software does not provision for 3x3 McNemar analysis, an alternative software package should be used. This is because adaptation of SPSS software for this study may not guarantee reliable output.
Harold, please look at Salvatore's second post in this thread and my first post.
HTH.
McNemar Bowker test is present in SPSS for 3X3 tables (same sample but in two occasions).
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