If I do ANOVA after calculating the MEAN (which will form my continuous dependent variable) of all 6 items ( MOT 1, MOT 2, MOT 3, MOT 4, MOT 5, MOT 6), then how can i find out difference between my three groups (independent categorical variable), on the basis of any specific motivation item out of these: ( MOT 1, MOT 2, MOT 3, MOT 4, MOT 5, MOT 6) ?
Please suggest the right way to do it. I know ANOVA can give me significant difference between the three groups with post hoc analysis, but how can I ascertain the difference on a specific item level, if I am transforming the 6items to a mean value? Is it better to do MANOVA or apply any other technique for this purpose??
How do you calculate the mean non-numerical values ("MOT 1" ..."MOT 6")?
At some stage you need to convert these values into numbers. With this you lose the direct connection to the original values, because there is no naturally correct way of doing this. The only rule you should obey is that the order is conserved, so if "MOT 1" is "lower" than "MOT 2", the number assigned to "MOT 1" should also be smaller than the number assigned to "MOT 2". This is very often achieves by simply assigning the rank numbers to the values ("MOT 1" is assigned 1, "MOT 2" is assigned 2, and so on). So what ANOVA does is to test differences in the mean ranks. This is not the same as mean differences in your original variable, for which a "mean" is not defined at all!
You can use ANOVA to test differences in mean ranks, as long as the variances in all groups are similar. This may not be the case when the mean rank in any group is close to one of its limits (in your case 1 or 6), that is, when the majority of values is "extreme" ("MOT 1" or "MOT 6").
Jochen Wilhelm asked: How do you calculate the mean non-numerical values ("MOT 1" ..."MOT 6")?
I understood MOT1 to MOT6 to be 6 Likert-type items with (whole number) values probably ranging from 1 to 5 or 1 to 7. Karan Berry, is that right?
You can analyze the items individually.
Probably the best approach for what you want is to construct a single ordinal regression model that includes terms for Question and for Group. And then the post-hoc analysis can tease out the differences among Questions or among Groups or among the interaction of these two. This gives you the differences among Groups for the questionnaire overall as well for individual items.
However, a simpler approach would be use a Kruskal-Wallis test and Dunn (1964) post-hoc test for each item to see the differences for that item among Groups.
I should also mention that when you combine the several items into a scale value (by using the mean value across items for a participant), usually you are treating the whole questionnaire as measuring a single thing. In this case, the differences among individual items aren't really of interest; it's the overall scale value that is of interest.
This doesn't mean that can't both look at the overall scale value for a participant and the responses to individual items. But I think it's fairly rare that both are of interest.
Thanks Dr Sal Mangiafico. You suggested kruskal wallis, but i am treating my likert items as interval data, so i plan to do one way anova. I understand that transforimng these 6 items to mean value and then using it as dependent variable in ANOVA with 3 groups, will give me overall difference between the three groups. But, I am more interested to find out the individual item level difference between the three groups, so shall i do 6 one way ANOVA'S, and analyze them separately or can I do MANOVA as well?? Please answer Professor.
Before you use MANOVA, please review the following articles.
Article Multivariate Analysis Versus Multiple Univariate Analyses
Article MANOVA: A Procedure Whose Time Has Passed?
See also this blog post by Thom Baguley:
- http://psychologicalstatistics.blogspot.com/2021/08/i-will-not-ever-never-run-manova.html
I wouldn't run anova on each item. I would use K-W. But, yes, I meant you could run a model (test) for each item.
The other option is the omnibus ordinal regression model I mentioned.
Karan Berry – Your data are not interval, and treating them as interval doesn't change this. Have a look at
Liddell TM, Kruschke JK. Analyzing ordinal data with metric models_ What could possibly go wrong? Journal of experimental social psychology. 2018 Nov 1;79(Journal of Marketing Research 29 May 1987):328–48.
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