# Simple Analysis of Likert Result with Mode and Median

So I made a questionnaire using Likert Scale. Let's say that I want to know "user's satisfaction of new web interface", where I used 5 questions with Likert Scale to answer that one question. The amount of sample is 40 and the example of the item is like this:

1) I'm comfortable with the new interface. [1 - 2 - 3 - 4 - 5]
scale meaning: [ 1 strongly disagree - - - 5 strongly agree ]

Because I have not much time and my knowledge in Statistics is very low, I thought of using the simple and most basic one to analyze the data. I read here and there, and my understanding is that since Likert is ordinal, don't use mean, use mode and median.

Now what I'm confused is, what those mode and median means? All the source said something about use mode or mean or median of frequency etc, but what is it that they represents?

For example, say the mode of question above is 4, and the median is 3. So what it is that they say? Something like, for mode = 4 : "4 means agree, so most of the user agree it's comfortable". But then how to relate this to other question result? And also, if frequency for 4 is 15 and frequency for 3 is 12, there's a lil difference between them, not sure I can say "most" user agrees...

Is the conclusion something I make myself or is there is there any example/guide on analyze Likert like this? When I couldn't find it, I've tried searching for chi-square and t-test, but not just I don't really understand why one use one, I can't find any example either.

First thing: If you are going to somehow average or combine responses to multiple questions, you are assuming that answers to all questions all measure the same underlying latent (underlying) variable (e.g., in this case, potentially "user's satisfaction of new web interface"). If these answers to these questions are not all related (e.g., does a person's answer to one question predict their answer to the other questions?), then you cannot combine them.

Typically when people create a new questionnaire, they examine whether the new questionniare is indeed useful (reliability, consistency, validity, etc). For example, check out:

http://www.brighamandwomens.org/medical_professionals/career/cfdd/mentoring%20resources/surveydesign.pdf

For questionnaires using the likert scale that have passed these measures, I have published papers in academic journals using the sum of the answers or mean (with statistics such as regression performed on these values). If we assume that your questionnaire has been designed correctly and that all the items measure some latent factor about "user's satisfaction of new web interface", then a mean of, say, 4.5 (halfway between 'strongly agree' and 'somewhat agree') suggests that the person falls somewhere between 'strongly agree' and 'somewhat agree' in being "satisfied with the new web interface."

In other words, the mean of all the scales is the value of the latent variable "user's satisfaction with the new web interface" for that person. If certain assumptions are met (e.g., see below), the central limit theorem allows the latent variable to be on a continuous scale instead of an ordinal one.

Don't use the mode or median.

p.s. snippet from wikipedia:

"Responses to several Likert questions may be summed providing that all questions use the same Likert scale and that the scale is a defensible approximation to an interval scale, in which case the Central Limit Theorem allows treatment of the data as interval data measuring a latent variable.[citation needed] If the summed responses fulfill these assumptions, parametric statistical tests such as the analysis of variance can be applied. Typical cutoffs for thinking that this approximation will be acceptable is a minimum of 4 and preferably 8 items in the sum.[12][13]"