This paper defines the preliminary test estimator (PTE) of the univariate normal
mean under the original as well as the Edgeworth size corrected Wald (W), likelihood
ratio (LR) and Lagrange multiplier (LM) tests. The bias and mean squared
error (MSE) functions of the estimators are derived. The conflicts among the
biases and the MSEs of the PTEs under the three original and the size corrected
tests have been obtained. It is found that instead of the original W, LR and
LM tests, the use of the Edgeworth size corrected W, LR and LM tests in the
formation of the PTEs reduces the conflict among the biases and MSEs of the
estimators remarkably.