# Thread: Which tests to use in these examples? Wilcoxon etc.

1. ## Which tests to use in these examples? Wilcoxon etc.

I'm pretty clueless, but would appreciate any help very much. I have:

Group 1: went from nothing, to receiving surgery 1, and then later on received surgery 2.

-> A (before), B (after first surgery), C (after second surgery)

Group 2: went from nothing to receiving surgery 1

-> A (before), B (after first/only surgery)

These patients have answered questionnaires with several questions and outcomes, at each relevant moment in time (A, B, and C for group 1 only). These outcomes are different, most variables are discrete, one is binomial ("have this affected you positively: yes or no").

Mainly I want to compare outcomes in group 1; was the effect significant after first surgery vs before, or after second surgery vs after first surgery. The data is in most cases not normally distributed.

Question 1: for comparison in between the same group, since the data is not normally distributed, when comparing for example outcome X in time A vs time B, is it correct to use the Wilcoxon one sample test?

Question 2: if one outcome is normally distributed, and one outcome is not (for example outcome x in time A is normally distributed but outcome x in time B is not), do I still use the Wilcoxon one sample test?

Question 3: When comparing the two groups, for example outcome y at time A in group 1 vs the same in group 2, is it correct to use the Wilcoxon rank sum test (Mann-Whitney)? (if the data is not normally distributed)?

Question 4: When comparing the binomial outcome within groups and in between group 1 and group 2, is it the Chi^2 test in both cases, or in neither?

Question 5: Which is the most reliable/easiest method to evaluate whether the data is normally distributed in STATA?

2. ## Re: Which tests to use in these examples? Wilcoxon etc.

outcomes are different, most variables are discrete, one is binomial ("have this affected you positively: yes or no").
What do you mean by discrete outcome variables? Rating score?

The data is in most cases not normally distributed.
Well, distribution of the raw data is almost never of interest (for example. in pre-post-data, it is the difference which sometimes might be looked at), but in your case, normality or non-normality is no issue at all, from the beginning, since you do not have interval scaled data. How large are your sample sizes?
when comparing for example outcome X in time A vs time B, is it correct to use the Wilcoxon one sample test?
This test requires interval scaled data, which seemingly you do not have. For dichotomous items, you can use McNemar's test. If the discrete variables = rating scale items, then for these you can use the sign test.

Question 3: When comparing the two groups, for example outcome y at time A in group 1 vs the same in group 2, is it correct to use the Wilcoxon rank sum test (Mann-Whitney)? (if the data is not normally distributed)?
Again, no-one needs normally distributed data. In some cases the distribution within the respective groupos could be relevant. If you have n > 30 and interval scaled variables, you can use a t-test. If your data is ordinal, or sample size is small, then use the Mann-Whitney.

With kind regards

K.

3. ## The Following User Says Thank You to Karabiner For This Useful Post:

LasseNordenhem (05-08-2017)

4. ## Re: Which tests to use in these examples? Wilcoxon etc.

Sample size: Group 1 contains 46 patients, group 2 contains 212 patients.

Our variables are: scales from 0-100 (corresponding to how good or bad they experience a certain thing, e.g. headache), scales from 1-6 (corresponding to experiencing a certain thing all the time vs never), and finally a binary variable where they only could answer yes or no.

Originally we compared the situation before the first surgery with after the first surgery (A vs B) using t-tests, but then we heard that t-tests require normally distributed data (and our data is often skewed, for example, most of the patients experienced som degree of headache). We then learned that in order to compare A vs B in the same group of patients you had to use sign test, and A vs A between the two groups was compared by using Whitney mann/wilcoxon two-sample-test.

Does it make any sense at all?

5. ## Re: Which tests to use in these examples? Wilcoxon etc.

Our variables are: scales from 0-100 (corresponding to how good or bad they experience a certain thing, e.g. headache),
This could be treated as interval scaled, I suppose. As mentioned before, if normality were an issue, then only the normality of these scores within the respective groups or, in pre-post-tests, normality of the difference scores. But since your sample size is well > 30, you can use the dependent samples t-test and the independent samples t-test, respectively. The central limit theorem shows that the t-test is not much affected by non-normality if sample size is large enough.

scales from 1-6 (corresponding to experiencing a certain thing all the time vs never),
These are often considered as ordinal, therefeore sign test (pre-post) and U-test, respectively. Or, if you treat them as interval scaled, the respetive t-tests (see above).

We then learned that in order to compare A vs B in the same group of patients you had to use sign test, and A vs A between the two groups was compared by using Whitney mann/wilcoxon two-sample-test.
These are required for ordinal scaled variables or for small sample sizes. But it would not be a large mistake if you also used them for interval scaled & not-so-small samples. Mind that U-test/sign test do not compare means (not even medians).

With kind regards

Karabiner

6. ## The Following User Says Thank You to Karabiner For This Useful Post:

LasseNordenhem (05-08-2017)

7. ## Re: Which tests to use in these examples? Wilcoxon etc.

1) So for the variable ranging from 0-100, because it can be considered interval scaled, and there are > 30 sample size, its perfectly fine to use t-tests? We're thinking this variable could be a ratio? Since 0 corresponds to "no headache"?

2) Regarding the binomial variable, what test would be correct to use? McNemars? The question was regarding cutting down on work and could be answered yes/no. Again we want to compare pre/post, and between groups.

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