A Distribution-Free Normal Scores Test for Ordered Alternatives in the Randomized Block Design

We introduce a normal scores test for ordered alternatives among k treatments in the randomized block design. For k = 2 or 3, the test is equivalent to a standard test due to Page [5]. For k ≥ 4, the test differs from Page's and is often more efficient. As k→ ∞, the Pitman asymptotic relative efficiency of the normal scores test compared to Page's test tends to ∞ for uniform and exponential populations. For normal, uniform and exponential populations, this efficiency exceeds 1 for k ≥ 4. We present a table of .01, .05, and .10 critical values for k = 4, n = 1(1)10 and k = 5, n = 1(1)5.