P.Mean: Using ANOVA for a sum of Likert scaled variables (created 2008-10-09).
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I want to analyse data derived from a questionnaire. The range of possible values that my variable can take goes from 20 to 100. No evidence for rejecting the hypothesis of normality was found. I would therefore apply an ANOVA, but I still have some doubts whether this methods of analysis is valid, since the range of my dependent variable is not [- infinity;+ infinity]. Is the ANOVA a valid method of analysis or are there other approaches I can apply?
Reading between the lines, it sounds like you have 20 questions and each question gets a score of 1 to 5. I strongly suspect that your are using a Likert scale like strongly disagree=1, disagree=2, neutral=3, agree=4, strongly agree=5. Then you sum up these numbers to get a total score.
A sum of 20 items, none of which can possibly have extreme outliers, will almost always result in an approximately normally distribution for the sum. The Central Limit Theorem is your best friend here.
The limits only become a serious issue if you have lots of data piling up near 100 or lots of data piling up near 20. No variable in the real world has a range from -infinity to +infinity. It just doesn't happen. So the constraints on your variable are not a serious problem.
Some people will still encourage you to consider a nonparametric test instead, such as the Kruskal-Wallis test. I'm not one of those people. The Kruskal-Wallis test is a fine test, but it also has problems. For example, it is very difficult to produce confidence intervals associated with the Kruskal-Wallis test.
On the other hand, if you submit your data analysis in a peer-reviewed publication and a reviewer suggests changing to a nonparametric test, there's no reason to argue. In fact, if a reviewer brings up a finer point about data analysis, you should be glad, because he/she didn't say something like "this data set is so bad that no data analysis could salvage it."
If you have the time and energy, why not try the Kruskal-Wallis test and compare the results to the ANOVA model. I suspect that they will be very similar. And when that reviewer does come back with a request for this test, you can congratulate yourself for being so well prepared.
Just promise me, though, that you won't get into the habit of running two tests and choosing the one that produces the smaller p-value.
This work is licensed under a Creative Commons Attribution 3.0 United States License. This page was written by Steve Simon and was last modified on 2010-04-01. Need more information? I have a page with general help resources. You can also browse for pages similar to this one at Category: Analysis of variance.