Finding the best shift according to a customer review

Question

There are three different shifts and data (100 reviews) about customers review (1-5) for each of them.

The question is: Which of the shifts is the best and should get some reward?

Is it possible to use the chi-square test to find out if there are any differences between the shifts? If so, how do I find out which one should get the reward?

Answer 1

Pavline,

A Chi Square independence test is used to determine whether there is the relationship (or independence) between two or more categorical variables (are people who buy a SUV more likely to buy a black SUV?); a Chi Square GOF test is used to determine whether an observed distribution fits a given expected distribution; a Chi Square Variance test determines whether the variance of a population has changed. I am not sure any of these fit your problem.

The data set you have here is numerical and ordinal, meaning there is likely a higher value associated to a score of 5 than to a score of 1, and the difference between each score is likely constant. This is a Likert scale. You could obviously simply run the average of each shift and grant the prize to the higher scoring shift.

However, if you are trying to determine whether there is a statistical significance between these three shifts based on the scores, you may want to perform a non-parametric alternative to an ANOVA test.

One non-parametric test to substitute for ANOVA in the case of ordinal data is the Kruskal-Wallis test. The test is rather easy to perform in Excel; its test statistic follows a Chi-Square distribution for which the p-value can be calculated (but, just like ANOVA, it will not tell you which shift is significantly different from the other two, only if the three shifts appear to be different). This test does require however the distributions to be somewhat similar in shape, and is less sensitive than an ANOVA test (as you would expect from any non-parametric test).