Likert Scale and T-Test Analysis

Question

I've been working on a research assessment for one of my units this semester which requires us to perform a basic statistical analysis of a survey which was distributed out. The assessment itself only requires descriptive statistics however, I did want to see if it was possible to do some simple inferential analysis given the data I have.

I've noted that one area of the survey uses a Likert scale for questions relating to a duty-free store e.g what is your overall impression of the variety of product items available, choice of brands, shop atmosphere etc. The responses range from Very poor (1), Poor (2), Neutral (3), Good (4) and Very Good (5).

In terms of these questions, I wanted to break down the results by comparing individuals who did make a purchase at the specific store, and those who did not. I've applied a T-Test for each question comparing the 2 groups and have found that there is a significant difference between the groups, however, I'm not sure the way I used the T-Test is correct for the type of data I have.

Given I have considered each question in isolation e.g impression of product variety between those who did complete a purchase and those who did not, would a T-Test be a suitable means of determining major differences between each group or is there an alternative analysis method I should be considering?

Answer 1

Since you are comparing each question, I would recommend using the Wilcoxon-Mann-Whitney and not the t-test. Results from a single Likert-type item probably will not meet the assumptions of the t-test well enough.

Some other approaches you might look into are the Cochran-Armitage test and ordinal regression.

EDIT: Be sure to understand the hypotheses tested by the t-test and WMW. They are different.

Answer 2

For a t-test, your data should follow a normal distribution. A Likert scale with 5 categories or more could follow a normal distribution (especially if you have a large enough sample).

I'd recommend you performing a normality test on your data (Kolmogorov Smirnov test, Shapiro Wilks test) and check that skewness and kurtosis for each variable is not greater than 2 or -2. If your data is normally distributed, you may use a t-test. If not, you can always use the Mann–Whitney U test (aka Wilcoxon test) which is the alternative to the t-test when assumptions are violated.