Use this test to determine if there is a statistically significant difference between the medians of multiple data sets. The data sets do not have to fit any particular distribution, but the data itself should be continuous.

As an example, let’s consider a company that periodically surveys its customers to understand their level of satisfaction with the services that the company provides. Each quarter they send out a survey asking customers to rank those services on a scale of 0 – 10. From this they can calculate various metrics (for example, net promoter score). But as the company works to improve their customer service, they are interested to know if the median response value has changed. To test this, they first set up a template by clicking the “Compare data sets” button on the SuperEasyStats menu and selecting “Mood’s Median Test”

Choosing the Mood's Median test

When selecting this test, SuperEasyStats will ask how many data sets you want to compare. In this example, the company wants to compare data from the previous four surveys, so they choose four data sets:

Mood's Median test - choose how many data sets to compare

On the resulting data sheet, they start by choosing their alpha value. In this case, they want to be 95% sure the median has changed before they discard their default assumption that it has not changed, so they set the alpha value to 0.05 (which is the default). They then enter the response numbers from the previous four surveys and examine the results:

Mood's Median Test - example

In this case they see that the p-value is lower than their chosen alpha value. They have met their own threshold and are now able to say that the medians are actually different. To get a sense of where the major differences lie, they examine the summary columns on the left. Notice that the confidence intervals for Q1, Q2, and Q3 all overlap, but the confidence interval for Q4 does not overlap with the others. This is a strong indicator that the median for Q4 is statistically different from the others.