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Likert scales and chi squared
Posted:
Feb 27, 1997 7:36 PM


 Forwarded message from Susan GouldLeighton 
I have some students who are doing surveys that use Likert (?) scales ie 15 agree / disagree answers. I realize theses are really not parametric, but can you consider the answers as part of a two way table, if you ask two samples that you think may have a difference and apply a chi square inference test or am I completely out to lunch ?
 End of forwarded message from Susan GouldLeighton 
I guess you could do it. What are you trying to find out? In real life no one performs a study unless they HAVE a real question they want an answer to (or are doing a dissertation). In teaching stats., our goal is generally student learning. This can leave us in an artificial situation in which we have activities and examples in which there IS no real research question.
The chisquared test will tell you whether the answer patterns differ somehow. The problem is not that you can't do the test, but that the test does not answer a very interesting question. More specific queries might be whether one group gives higher (or more variable) ratings than another.
There are two common problems with student surveys. One is failure to take a random sample. Though taking one can be a nuisance, it is probably much easier to do in a classroom setting than it is in real life. This may be an extreme position, but I feel that if your students do not take a random sample you should not ask them to use ANY inference techniques on the resulting data. Treat the data as merely descriptive of the people they DID survey. If you attempt inference, sample bias is likely to be large compared to any problems introduced e.g. by treating a Likert scale as measurement data. The other common bad practice in student surveys is multiple inference. In a classical hypothesis test situation you have ONE hypothesis formulated prior to the study. The formulas do not apply to multiple hypotheses or hypotheses formulated on the basis of sample data.
I remember fighting with the Sociology Dept. at an institution that shall remain nameless. Students took a Research Methods course in which they had a big project consisting of a fairly long survey. They then did tests to see if there was any relationship between answers to Question A and answers to Question B  for all possible values of A and B! For a 20item questionaire, this amounts to 190 pairs. Using an alpha of 0.05, you should not be surprised to find 9 or 10 "significant" results even if there are no real relationships at all. Unfortunately, the Dept. always interpreted these as signs they had found something real rather than as the expected number of false conclusions.
_   Robert W. Hayden   Department of Mathematics /  Plymouth State College MSC#29   Plymouth, New Hampshire 03264 USA  *  Rural Route 1, Box 10 /  Ashland, NH 032179702  ) (603) 9689914 (home) L_____/ hayden@oz.plymouth.edu fax (603) 5352943 (work)



