Is the mean assets-to-liabilities ratio the same for healthy and failed companies?
This example describes a randomisation test.
The actual data are shown on the left. Randomisation uses the same values but randomly allocates them to the two groups. Click Randomise to randomly pick 33 of the the 101 values for the failed group.
The difference between the mean assets-to-liabilities ratios is the test statistic — it will be far from zero if H0 (no difference between healthy and failed companies) is false.
Click Accumulate and repeat the randomisation several more times. (Uncheck Animate to speed up the randomisation.)
A difference in means as far from zero as -0.902 is unlikely if the failed and healthy companies are really the same so there is strong evidence of a difference between the groups.
Emphasise the general concepts:
A study in Greece compared characteristics of 68 healthy companies with those of another 33 that had recently failed. The jittered dot plots on the left below show the ratio of current assets to current liabilities for each of the 101 companies.
The mean asset-to-liabilities ratio for the sample of failed companies is 0.902 lower than that for the healthy companies, but the distributions overlap. Might this difference be simply a result of randomness, or can we conclude that there is a difference in the underlying populations?