Efficiencies of Friedman's χ2rtest are studied when observations within blocks are independent and when they are exchangeably dependent. At local alternatives the limiting power is found to increase monotonically with (a) the canonical correlations of distributions having expansions in canonical form, (b) the stochastically decreasing character of the mixing distributions in certain exchangeable sequences, and (c) an index of peakedness in a class of distributions containing exchangeable Cauchy and Gaussian laws.