This sounds like a really basic question, but I am looking for some informed feedback from fellow scientists with knowledge of statistics. Recently I had a debate with reviewers of a manuscript over the choice of statistical analysis for comparing two sets of ordinal data. These data are from psychological clinical scales and are similar to a Likert scale (in this case, a rating from 1-7).
An obvious choice for comparing scale results from two populations of patients would be a singed ranks test like Mann-Whitney U (or a t-test [?!] according to the reviewers), however the scoring distributions are non-normal, which I argued invalidate interpretation of any Mann-Whitney U test results. I opted, instead, to build contingency tables and analyze the groups with a Pearson's Chi Squared test. They did not like that.
In a world of computer statistics packages, it seems to me that many people are quick to dismiss simple statistical tests, despite their being robust and the question asked being simple. Do any of you have opinions regarding a better approach to analyzing ordinal data?
The dataset in question consisted of Likert scale-like assessments, rated 1-7. There were up to 30 questions/observational assessments per scale. I chose to compare each question separately between patient groups. Some questions are arranged in clusters of based on symptom type (for example, in PANSS there are clusters for positive [7], negative [7], and general [16] psychopathology symptoms), but these are general groupings and each assessment still stands on its own to rate a particular issue. For example, in PANSS positive symptom set, there is a rating for delusions and one for grandiosity, both of which are positive symptoms and interact but are distinct behavioral features.
So, what is the best way to analyze these types of data? Thanks.
Dear Michael: If you do not clarify more it is difficult to answer, because I do not know if such a test is of "central tendency" (for which the MEDIUM is the choice), of "deviation" (AVERAGE DEVIATION), of "correlation" (the CORRELATION COEFFICIENT OR "RO" OF SPEARMAN), of "inference" at a given confidence level (CHI SQUARE), of "location of data with respect to a given group" (CENTILES, PERCENTILE, QUARTILES, DELICES ...) and a long etcetera, although I hope that what is offered is somehow useful
Doing a contingency table for a 7-point scale wouldn't be my first idea, just like reviewers you mentioned :)
What again are your contraindications for using a U test? As far as I know, it does not require a normal distribution. I think because of that it's often used instead of a t-test when the data distribution is other than normal. I checked Wikipedia (;)) note on Mann-Whitney U and there is a note of an assumption of equal distributions and test checking for differences in distribution.
Both the test is non-parametric, and again it is quite unclear whether the independent variable is dichotomous or have more than two categories. Chi-square is a good choice if variables have more category, even the Kruskal Wallis Test is good to use in your case. Since you haven't cleared how many categories your independent variables have, it is difficult to determine the most appropriate test in your case Sir.
I recomend using the Brunner-Munzel test. It is my go to test when I am dealing with ordered categorical data. Here are some references:
Article A nonparametric test for proving noninferiority in clinical ...
https://www.jclinepi.com/article/S0895-4356(09)00309-6/abstract
Thank you all for your replies. Noting many of your comments, I realized that you need more detail to make a proper assessment. Apparently, I did a poor job at describing the dataset, so I will fill in some specifics.
There are two (2) sets of schizophrenia patients with differing symptom sets to which psychiatric scales have been applied. These are combination patient response and clinician assessment ratings that run from 1 to 7 ordinally, so there are up to 7 categories (less if they are combined to meet the criteria for a proper contingency table). Depending on the test, there are between 8 and 30 questions. To compare the two populations for a given test, I constructed contingency tables and did a simple chi square analysis to compare the distributions.
I decided against a ranks test such as Mann-Whitney since the results cannot be interpreted unless all assumed criteria are met, one of those being distribution curve shape. Both datasets must have the same shape. This is based on recommendations by Harvey Motulsky. I read over criteria regarding Mann-Whitney by Jarrold Zar and did not find this particular restriction, however I trust Motulsky's judgement.
In the case of the data I examined, one patient set presented with bell-shaped distribution, whereas the other looked like a ski slope. According to Motulsky, this invalidates the use of a Mann-Whitney test since even significant results cannot be properly understood. Noting the number of patients in each group (100 each), however, I did read that with those numbers, even for ordinal integer data, parametric methods such as t-test with a Welch correction yield similar results to Mann-Whitney and are appropriate to use.
I also intend to look into the Brunner-Munzel test as I am unfamiliar with it, but willing to give it a go.
What are your thoughts? By doing a chi square analysis did I completely miss the boat?
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