This paper continues the work begun in [l] and examines the loss of power when using tests based on the assumption that the variable being sampled has a “complete” normal distribution, when in fact, sampling is from a symmetrically truncated distribution. The hypothesis considered here is the one - sided test for the variance of a normal distribution. Some tables have been computed and they show that appreciable losses in size occur. Some loss occurs in the power too, but this decreases with the alternative value of the variance and the degree of truncation.