Moods median

Assuming your data meets the assumptions, Moods median will be fine.

Mood’s Median Test
overview how to example data see also
Stat > Nonparametrics > Mood’s Median Test

Mood’s median test can be used to test the equality of medians from two or more populations and, like the Kruskal-Wallis Test, provides an nonparametric alternative to the one-way analysis of variance. Mood’s median test is sometimes called a median test or sign scores test. Mood’s median test tests:

H0: the population medians are all equal versus H1: the medians are not all equal

An assumption of Mood’s median test is that the data from each population are independent random samples and the population distributions have the same shape. Mood’s median test is robust against outliers and errors in data and is particularly appropriate in the preliminary stages of analysis. Mood’s median test is more robust than is the Kruskal-Wallis test against outliers, but is less powerful for data from many distributions, including the normal.

Dialog box items
Response: Enter the column that contains the response data from all the samples.

Factor: Enter the column that contains the factor levels.

Store residuals: Check to store the residuals.

Store fits: Check to store the fitted values. These are the group medians.

I’d suggest several thing. First of all, is the difference in mean times big enough that you might care about? for instance, reducing an emergency room’s treat-and-release time from 240 to 230 minutes probably doesn’t interest anybody, whether or not it is statistically significant. If the difference has no customer impact, there’s no point in proceeding.

Assuming that you have a big enough difference to care about, the next step would be to plot the before and after data in a control chart. In Minitab, the Individuals-moving range chart may be worth considering. You would be looking for blatant signs of special cause variation. Special cause can distort the data to look like a different distribution from what you actually have.

If you have made it past those two tests (difference big enough to care about, and basically common cause variation), you might want to use Minitab’s distribution identification utility. It’s under quality, then reliability. Box-Cox is OK, too, but seeing the probability plot can give you insights that a Box-Cox table cannot.

If the data can be modeled using a log-normal distribution (the logarithms of the raw data are normally distributed), you could do a simple t-test on the transformed data.

If you need more info, reply to this forum and I’ll see it.