Randomization test of mean is compuationally inaccessible when the number of groups exceeds two

With the advent of fast computers, the randomization test of mean (also called the permutation test) received some attention in the recent years. Here we show that the randomization test is possible only for two-group design; comparing three groups requires a number of permutations so vast that even three groups of ten participants is beyond the current capabilities of modern computers. Further, we show that the rate of increase in the number of permutation is so large that simply adding one more participant per group to the data results in a computation time increased by at least one order of magnitude (in the three-group design) or more. Hence, the exhaustive randomization test may never be a viable alternative to ANOVAs.