In this chapter, we discuss hypothesis tests concerning regression parameters when X is measured with error. In Section 3.3.1 we argued, in the context of some special cases, that naive tests for the regression coefficients of Z are not valid in general when X is measured with error and X is correlated with Z. In particular, we illustrated this in Figure 3.5, where we graphically illustrated a two-group, unbalanced analysis of covariance, showing that if X has a different distribution in the two groups, then the treatment effect test is invalid in the naive test, where W is simply substituted for X. In this chapter, we give a more detailed and thorough account of testing when X is measured with error.