In this study, suitable number of permutations were tried to be determined empirically for permutation test, one of which lalternatively used in analysis of variance (ANOVA). Random numbers were generated from chi(2) (3). distribution by simulation technique, and type 1 error rates were calculated with their standard errors. For k=2, 3 and 4, data were dealt with what is commonly faced in practice. Number of observation (n) in each group were taken to be 5, 10 and 15 (except for k = 2). Number of permutation changes with respect to k and n. For k=2, 3 and 4, required number of permutation was determined to be 15,000, 25,000 and 30,000 respectively. In general, there is great advantage of not allowing number of permutation under 10,000, if permutation tests are to be used in testing significance of differences of means of groups.