I am preparing to analyze some data and I have a question about how to go about it. It is a 39 question survey with 5-item Likert scale responses. I will be using the responses to separate the participants into the category that they score highest in for further analysis. The problem is that Category A corresponds to 14 questions, Category B has 11 questions, and Category C has 14 questions. What is the best way to go about determining which one the participant scores highest in, since the # of questions is not equal? Will it work to take their total possible points in each category and divide it by the number of points possible, then compare their percentages across the three categories to see which is the highest?
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I suppose your suggestion would be OK, but if all questions have 5 point response scales, why not just average the responses for each person over all the questions in each category? I wonder if you might be concerned about using the mean with ordinal data? That's a common concern, but I think it's generally overblown. With multiple questions, the subscale scores should be sufficiently equal-interval for your purposes. This topic has been discussed several times on CV; you might be interested in reading this question and especially the answer by @JeromyAnglim.
We can push past this strategy, however. I'm not sure you need to categorize your participants as being in either A, or B, or C. I'm typically against categorizing in this manner (for more on that, you might want to read this question and my answer there). They each certainly have some level of membership in each, and categorizing them amounts to throwing that information away. Moreover, even for those participants who are all more in A than elsewhere (for example), their level of A-ness will vary from participant to participant. Thus, simply calling each of them an 'A' throws away the information about their within-category variability. Why not keep those 3 scores for each participant, and use them as 3 covariates in a multiple regression model when it comes time to do your final analysis?
answered Jul 24, 2012 at 2:43
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$\begingroup$ Hi, thanks for the feedback. I was under the imrpession that calculating the means would not yield a result as precise as percentages, but I won't pretend to be good at statistics, so this information could be wrong :) As far as the categories,I will be conducting a 3-Way Anova using the primary motivation as one of the variables. So, its just one piece of the overall puzzle. $\endgroup$– LadyMCommented Jul 24, 2012 at 4:20
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$\begingroup$ @LadyM, I would say means are better than percentages in that sense. Also, what I'm suggesting is that you don't do a standard ANOVA, but use a multiple regression model instead (although ANOVA actually is an MR); it will be more appropriate given what you have & ultimately more informative. On a different note, if you find this answer helpful, you might consider upvoting by clicking the upward normal dist to the left of it, & if you think it answers your question, you could further accept it by clicking the check mark. No pressure, I just see you're new, & you might be unfamiliar w/ this. $\endgroup$ Commented Jul 24, 2012 at 13:30
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$\begingroup$ Thank you, yes I am new to this site, but I was certainly glad to find it. It has been several years since I have taken statistics and I will say that I struggled with it when I did. So any help is appreciated. I did click to vote for the post, but I received a message stating that I need 15 reputation first. I am going to go read about multiple regression ANOVAs now, thanks for the tip! $\endgroup$– LadyMCommented Jul 24, 2012 at 14:11
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$\begingroup$ @LadyM, sorry, I guess I forgot about the rep requirement; it's been a long time since I was <15. My answer in the question I link to in the 2nd paragraph has a little info about regression & ANOVA. There's probably more info somewhere. If you can't find enough for it to be clear to you, you can always ask another question on CV, just be sure to say what you've got so far & where you're still confused. (People here respond poorly to questions like 'What's the deal w/ regression & ANOVA?') However, the topic is to big for me to try to explain in comments. Good luck w/ your project. $\endgroup$ Commented Jul 24, 2012 at 14:22
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$\begingroup$ Thank you! I am sure that I will be posting here again, I am just getting started on the data analysis. I have been reading your post about regression and ANOVA. I am also reading about regression in my old stats books as well. If I understand it correctly, regression will capture interactions, right? That is what I am looking for. I have a 2X3X2 design and I am looking at the interactions between these IVs (male/female, motivation (3 types), and introvert/extrovert on the DV of specified time.I have a lot of other descriptive data as well. $\endgroup$– LadyMCommented Jul 24, 2012 at 15:48