I have two very large independent groups (n=30,000 and 12,000). Each data point is an individual’s UK Deprivation Index decile (the Deprivation Index itself is a ranking from 1 to 32,844 of an area’s relative deprivation where 1 is most deprived). My hypothesis is that one group is more deprived than the other, i.e. has more people in the lower deciles.

The distributions look like this: enter image description here

What would be the appropriate test for my hypothesis? Mann-Whitney?


  • $\begingroup$ I would have thought that your samples are large enough, that a simple z-test would suffice. In reality though, I probably wouldn't do anything fancy/analytic here, I would take the brute-force (Monte Carlo) route. Construct a pool of all individuals in the UK along with their deprivation index, and many times over draw random samples of n=30k and n=12k, and compute the difference in mean deprivation levels. Doing this over and over will allow you to create a sampling distribution of this test statistic, and then you can see where your value falls in this distribution. $\endgroup$
    – gazza89
    May 26 at 14:30
  • $\begingroup$ Thank you. Does a ‘mean’ decile have any statistical meaning for ordinal data, given that the deprivation ranks are not equally spaced. What is the meaning of e.g. the 4.76th decile. Also, I’m not sure about sampling a pool of the whole UK given that my samples are from a specific region. $\endgroup$
    – Tom
    May 26 at 15:03
  • $\begingroup$ on the latter, I think in the UK you can get the decile of each area (LSOA is the area they are reported at I believe) and you can also get the population of each LSOA, so you could create a "bag of deprivation indices", which essentially mimics the entire UK population and can be sampled from (technically without replacement) $\endgroup$
    – gazza89
    May 26 at 16:36
  • $\begingroup$ On the former, I'm not sure that's a stats question. If you have 2 groups of 2 people each, and group 1 has 1 person from decile 1 and one person from decile 3, and the second group has two people from decile 2, statistical significance aside, which group is "more deprived" ? I can't think of a more meaningful comparison than comparing the mean, but this is where domain knowledge needs to come in. If instead instead you want to change the question to "are the distributions of deprivation statistically significantly different between groups", I would suggest a different method(s) $\endgroup$
    – gazza89
    May 26 at 16:37


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