I'm a bit confused as to what assumptions my data needs to satisfy in order to use Mood's median test. Some resources state that you need the samples to come from population distributions with the same shape, while some sources, including wikipedia and the comments to this question:
seem not to mention any required assumptions at all. So my question is mainly this: What assumptions does Mood's Median test require (it would be great if some reliable references can be provided)? Does it require that the samples come from population distributions with the same shape?
If I have two sets of samples and I want to compare their group medians on some discrete scores, I can observe the sample distribution with a plot, but how does one check whether the population distributions of each sample have the same shape?
If the population distributions of each sample don't have the same shape and this is indeed required to use Mood's median test, then what statistical test is available to compare medians or means?
Any advice or help would be greatly appreciated!