Summary: Several method of permutation tests have been proposed for testing nullity of a partial regression coefficient in a linear model. These methods were compared in terms of empirical type I error and power. One striking result of the simulation based comparison is that the two emerging methods, while previously identified as equivalent formulations of the permutation strategy under the reduced model, did actually produce quite different results. And one of these methods have almost the best result. Some theoretical justification to the empirical findings is given. We compared estimators and variances of these two methods analytically in the double regression linear model. Our results give mathematical support to the observation obtained by simulations. Furthermore, for the first time we obtained the expected value of the estimators of the variance by the permutaional distribution and we found that one of these estimators is unbias