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 is greater than or equal to 4, the test differs from Page's and is often more efficient. As k arrow right Infinity the Pitman asymptotic relative efficiency of the normal scores test compared to Page's test tends to Infinity for uniform and exponential populations. For normal, uniform and exponential populations, this efficiency exceeds 1 for k is greater than or equal to 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. [ABSTRACT FROM AUTHOR]