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Topic: Likert scales and chi squared
Replies: 1   Last Post: Feb 28, 1997 12:01 AM

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Bob Hayden

Posts: 2,384
Registered: 12/6/04
Likert scales and chi squared
Posted: Feb 27, 1997 7:36 PM
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----- Forwarded message from Susan Gould-Leighton -----

I have some students who are doing surveys that use Likert (?) scales ie
1-5 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 Gould-Leighton -----

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 chi-squared 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 20-item 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

| | Robert W. Hayden
| | Department of Mathematics
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| | Plymouth, New Hampshire 03264 USA
| * | Rural Route 1, Box 10
/ | Ashland, NH 03217-9702
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