There is a 2X2 experimental design. One factor is the group: patients vs controls. The other factor is the within-subject condition: pain ratings for self vs for others. The pain rating is acquired on a 7-point numerical scale. Of note, there are 10 trials in each condition, i.e., participants are required to rate their pain intensity for 10 pain-related images. Therefore, each participant completed 20 trials.
For data analysis, most of the papers using a similar experimental design applied a repeated-measures ANOVA. Firstly, the mean pain value of the 10 trials was calculated for each condition per subject. Then this mean value was treated as the DV and the repeated-measures ANOVA was conducted with the group (patients vs controls) as the between-subject factor and the condition (ratings for self vs others) as the within-subject factor.
My questions:
1. Is such a parametric ANOVA appropriate for the above experimental design if the sphericity assumption is satisfied?
2. Is it reasonable to calculate the mean of the pain ratings in each condition? Indeed, pain ratings on numerical scales are ordinal, and therefore nonparametric tests should be applied for such variables.
3. If non-parametric tests are applied for such a dataset, how to do? The median is calculated for each condition first and then how?
Many thanks and welcome for clarification and discussion.
Hello Cuizhen Liu. The short answer is that it depends on who you ask. As you noted, it is not uncommon for people in psychology and related areas to treat the mean (or sum) of several Likert-type items as if it has interval scale properties, and to use ANOVA models. But some other folks object very strongly to that practice, and would urge you to use methods that treat the data as ordinal. See this article, for example:
Liddell, T. M., & Kruschke, J. K. (2018). Analyzing ordinal data with metric models: What could possibly go wrong?. Journal of Experimental Social Psychology, 79, 328-348.
You have not said what software you use. If you are using SPSS (which is quite popular in psychology), and if you want to use a model that treats the data as ordinal, you could use the GENLINMIXED command to estimate a multilevel (or mixed) ordinal logistic regression (or logit) model, with the 10 images clustered within participants. To get an ordinal logit model, you would need the following for the TARGET_OPTIONS sub-command:
/TARGET_OPTIONS DISTRIBUTION=MULTINOMIAL LINK=CLOGLOG
You can find more info and examples here:
- https://www.ibm.com/docs/en/spss-statistics/28.0.0?topic=genlinmixed-overview-command
The book by Heck, Thomas, and Tabata would be helpful too, I think:
- https://www.routledge.com/Multilevel-Modeling-of-Categorical-Outcomes-Using-IBM-SPSS/Heck-Thomas-Tabata/p/book/9781848729568
HTH.
Given there are likely difference between the photos, it may be useful to takes these into account. It is often more useful to predict the actual responses, rather than some aggregate value of them (here the mean). The choice on how to treat them depends on what your research questions are. If looking for linear effects, the lmer function in lme4 (in R) could work with random effects for person and trial. Is there a reason that you are using the means?
Interesting, before the choice could be better to select the pain spectrum lived for patients and control.
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