I have a dataset of the following form:
| System A Rating | System B Rating |
|---|---|
| 4.5 | 5 |
| 3 | 4 |
| 5 | 3 |
| etc. | etc. |
I have 155 such data points gathered using a survey. Which statistical test should I use to show statistical significance if one system has significantly better ratings than the other?
Thanks.
Topic hypothesis-testing difference dataset statistics
Category Data Science
You need to perform some tests to identify the appropriate statistical measure for comparing the two distributions accurately.
For each group/system, run a normality test to make sure that you are not dealing with an ultra exotic distribution to which central limit theorem does not apply (very unlikely).
Calculate the variance for each group, in order to see whether you can use tests that make the assumption of equal variances. To statistically test if the variances can be assumed to be equal, you can perform a Levene's test.
If variances are equal you can move ahead with independent unpaired t-test, otherwise you should trust Welch's test. You can perform these tests online as well, e.g. here https://www.graphpad.com/quickcalcs/ttest1.cfm
Mann Whitney U Test (Wilcoxon Rank Sum Test) shall enable us to compare the ratings on System A and system B. This test compares the shape of each population and tells whether the two samples differ. If the shape is same, the null hypothesis is accepted. If the shape of one of distribution is different from the another distribution, the two systems have a significant difference in observed ratings.
Geeks Mental is a community that publishes articles and tutorials about Web, Android, Data Science, new techniques and Linux security.