TESTING ORDERED-ALTERNATIVES IN THE PRESENCE OF INCOMPLETE DATA

In testing the Dull hypothesis of no treatment effects in a randomized block experiment, a researcher may restrict attention to an ordered a lternative and thereby increase the power of his test. Jonckheere and later Page proposed such test statistics based on the Kendall and Spea rman correlation coefficients. Motivated by notions of distance betwee n permutations, we generalize Jonckheere's and Page's tests to the sit uation in which one or more observations are missing from one or more blocks. Conditional on the pattern of missing observations, the result ing statistics are shown to be asymptotically normal. For a particular pattern of missing observations, the asymptotic efficiency of the ext ended Page test is found, in many cases, to be not much lower than for the standard Page test.