I am trying to analyze the following data set. I have 4 treatments and 15 time points. My data are categorical (clinical score) and I have 5 animals per treatment. I am trying to run this analysis of prism but have not been able to fit a non-parametric post-hoc option so far because I am simply not offered one. I thought about doing a chi-square test for overall analysis of score prevalence. I do understand my test options but I am stuck with the software technicalities. Any help?
There is no sensible way to do an ANOVA with categorical data.
The fact that categorical data (e.g. "scores") are often written as numbers does not mean that they can be interpreted like numbers. I suggest to avoid the numerical coding of categorical data. Instead of scores 1-5, say, take the values "insufficient", "bad", "just ok", "good", "excellent". Now consider you have a sample like {"bad","bad","just ok", "good", "bad"}: what is the mean and the standard deviation of these values? Here it is obvious that these questions are utter nonsense. Coding these values as {2;2;3;4;2} does not change their meaning, and the average 2.4 is not interpretable (e.g. as "between 'bad' and 'just ok', with a little tendency towards 'bad'). Particularily, the confidence interval (1.49...3.71) will not mean that 95% of such intervals will include athe population parameter (because there is no such population parameter). Therefore, the results obtained by ANOVA on such "numbers" is not interpretable.
A work-around is to use the ranks of the data. In the above example this would be {2,2,4,5,2} for the sample. Here the mean would not be informative by itself but in comparison to another sample (when the ranks are determined from the whole set of data). The variance gives some information about the dispersion of the ranks (although the Gini-index would be a far better and more sensible measure here!). The ranks of two(or more) groups might thus be compared by ANOVA (given you don't have some very strabnge rank-distribution, the ANOVA is robust enough to give not-too-wrong answers). But it must be clear that you are not anymore analyzing scores but score-ranks.
A note on transformations (since it was mentioned by Mario): Generally it is a practicable solution, often leading to scientifically even more sensible interpretations - but only when the data is in fact numerical/metric! There is no transformation possible for categorical data! How will you calculate the logarithm of "just ok", or the square root of "good"? These are no numbers! (Proprtions, as mentioned, are numbers - but then it would mean to analyze proportions of categories and not mean categories, what is actually done in an ordered logistic regression)
Can you please share research objective?
In above scenario, survival analysis seems to be appropriate.
FIrstly, you have ordinal data. This calls for an ordered logistic regression model. Secondly, if you measured each mouse at severeal (or all) time-points, you have a reapeated-measures design, that should be appropriately modelled.
I have no clue how to do this in Prism. I know Prism a little bit and I doubt that this will provide a reasonable solution. I'd recommende two things: (1) go to a local statistician and ask for help (the analysis of ordinal data is a little tricky, and if you don't need this more often it might save time and nerves just to sooperate with someone who has solid experience in analyzing such data) and/or (2) use R (http://www.r-project.org) what can handle such data also for repeated measurements and then even for "mouse" as a random effect.
There will surely be some ways to analyze the data with other methods, and these methods might be frequently applied by many physicians, but they won't be correct. The best of these suboptimum methods might be a rank-analysis, but here also you might abolutely need to model the repeated-measures structure (if it is there). There is no (known) way to simply get confidence intervals of p-values for effects there, so you will have to employ some bootstrapping. Not a big deal in R, but when you do not know all this it save you months of work and desparation when you go to a statistician.
Your chi-squared test can not handle the reapeated-measures structure. Also, this test throws aways the information fo the order of the score-values. The "repeated-measures alternative" for the Chi-squared test is the McNemar-test, but I do not know if there is a derivate for n x m tables (with n>2 and m>2) and if this is at all sensible for your data.
Reading suggestion: Alan Agresti (1990). Categorical data analysis. New York: Wiley.
Dear, I hope that my comments not late, anyhow as you interest in Prism you can analyze you data by following steps using Prism: from the first page of prism select column then create. Enter your data then select analyze then one way ANOVA, then OK. A new dialog will appear, select repeated measure test and from post hoc select Bonferrori then ok.
There is no sensible way to do an ANOVA with categorical data.
The fact that categorical data (e.g. "scores") are often written as numbers does not mean that they can be interpreted like numbers. I suggest to avoid the numerical coding of categorical data. Instead of scores 1-5, say, take the values "insufficient", "bad", "just ok", "good", "excellent". Now consider you have a sample like {"bad","bad","just ok", "good", "bad"}: what is the mean and the standard deviation of these values? Here it is obvious that these questions are utter nonsense. Coding these values as {2;2;3;4;2} does not change their meaning, and the average 2.4 is not interpretable (e.g. as "between 'bad' and 'just ok', with a little tendency towards 'bad'). Particularily, the confidence interval (1.49...3.71) will not mean that 95% of such intervals will include athe population parameter (because there is no such population parameter). Therefore, the results obtained by ANOVA on such "numbers" is not interpretable.
A work-around is to use the ranks of the data. In the above example this would be {2,2,4,5,2} for the sample. Here the mean would not be informative by itself but in comparison to another sample (when the ranks are determined from the whole set of data). The variance gives some information about the dispersion of the ranks (although the Gini-index would be a far better and more sensible measure here!). The ranks of two(or more) groups might thus be compared by ANOVA (given you don't have some very strabnge rank-distribution, the ANOVA is robust enough to give not-too-wrong answers). But it must be clear that you are not anymore analyzing scores but score-ranks.
A note on transformations (since it was mentioned by Mario): Generally it is a practicable solution, often leading to scientifically even more sensible interpretations - but only when the data is in fact numerical/metric! There is no transformation possible for categorical data! How will you calculate the logarithm of "just ok", or the square root of "good"? These are no numbers! (Proprtions, as mentioned, are numbers - but then it would mean to analyze proportions of categories and not mean categories, what is actually done in an ordered logistic regression)
I believe neither chi-square test nor ANOVA can handle the repeated-measures design. In SPSS, the solution is in the repeated-measures statistic.
Mahfuz, ANOVA can, when the time points for all measurements are the same and no measuremenets are missing. You can model the subject as one factor, what will account for the between-subject variance. When the time-points are different and/or mesaurements are missing, the subject needs to be modeled as random factor. Although tusually not names as such, the statistical significance of the fixed effects in these models is actually still obtained by an ANOVA.
Firstly, I am Prof. Roshini Sooriyarachchi and not Ms. A.A. Sunethra. Ms. A.A. Sunethra is a research student of mine. Now to get to the problem. You can use Proc Genmod in SAS with the GEE option and specify multinomial distribution for fixed totals or Poisson distribution for random totals. If you need more help regarding the programming get in touch with me.
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