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Likert Scale and Statistics

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[Converstion digested from the ScholarAlumni listserv, 3/19/2013]

Issue: I have been working the past year with a student on a project involving a Likert scale survey.  We have a pre- and post survey.  Is there a proper statistical tool to use to determine whether the disagree/strongly disagree group is statistically different from the agree/strongly agree group for one of the tests?  And is there a proper statistical tool to analyze whether these answers in the post are significantly different from the pre-test.


Suggestions from listserv participants:

Google search “statistical analysis of Likert pre post” for posts and scholarly articles. In general it looks like you get the means and do paired t-test.  There is an on-line stats book (lots of online calculators) that I used last semester in the master’s program in medical education: 


I've heard tell that with this kind of data (ie, rankings, not numerical data), that comparing means is inappropriate.  Instead, the correct statistical test is a  Wilcoxon Signed Rank test.  This is a non-parametirc, paired samples test, and can be used to compare the distribution of individuals' pre and post for each item.  I'm not a stats expert, but this approach was recommended to me recently for this exact same kind of data by somebody who is.  I have found the book "Discovering Statistics Using SPSS" by Andy Field to be very well done, and funny too.


The data from a Likert scale are not continuous so the 'normal' statistics like T-tests are not supposed to be used.  That does not mean that people don't use them but if you want to be sure your analyses are yielding results you can believe it is better to use an alternative like Chi-square.  Chi-square assumes a discrete distribution of data rather than continuous.


I think you can also use chi-squared contingency tables to essentially compare the distributions of responses... although I think that depends on how "evenly" your cells are populated in the table.  


I co-authored a paper on a cell biology lab module and we utilized a Stat professor to help with the analysis of pre and post knowledge surveys.  You may read what she did in the original paper: CBE-Life Sciences Education Vol 8, 140-146, 2009.  The paper should be available free online, or I can send you a PDF on request.

We compared student knowledge on pre and post tests that compared percent correct answers rather than a likert scale, however, I think were were a few likert scaled questions.

A quick look shows we did something called Multivariate Hotelling T(squared) test (Hotelling, 1931).  From our paper "Hotelling's T-squared is a multivariate extension of the Student's t test. In a t test, differences in the mean response between two normally distributed populations are studied. T(squared) is used when there are two or more response variables with multivariate normality assumption..."
You can read more from the paper and see what our stat colleague, Dr. Hyun-Joo Kim, recommended and did for us.
If anyone is interested in getting this type of stat help, our school offers stat help for a fee at:

Recently read about Rasch Analysis of LIkert results- Applying the Rasch Model- Bond and Fox---very readable.

I'm not sure if you are using a "true" likert scale, which is a seven point continuum with markers on each end:
Strongly Disagree                   Disagree

1 -----2------3------4-------5------6------7

Or, are you using a five point scale with "markers'?

Strongly Agree=5
Strongly Disagree=1

I've read much debate about each of these methods because the types of data could be considered continuous (the former) or discrete/categorical (the latter). Also, I've found a nice "primer" chapter on statistics, FYI. I've attached and included the link to reference:

My instinct says that the most appropriate test would a Chi-square or G-test.   Since you are dealing with categorical data and what you really want to compare is whether  the distribution in responses is different pre and post.   The Chi-square could be set up as a 2x2 format (pre and post) x (agree and disagree).  You would also have the option of setting up a 2 x 4 test (pre and post) x (strong agree, agree, disagree, strong disagree).  This would let you us the raw data without pooling categories, if that is helpful.   One thing that I know you do have to be aware of with Chi-square is cases where you might have a count of zero for a particular cell in the table (ie no one answered strongly disagree), so that is where your pooling approach can be helpful.

As others mentioned, I don't think that tests that compare means (t-test, even signed rank?) would be appropriate here.   Unless, you wanted to compare pre and post scores for individual students and then averaged across the respondents, that would be a different matter.

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