Validity of f-test in a randomized block design with missing data

✍ Scribed by S. P. Dash

• Publisher: John Wiley and Sons
• Year: 1980
• Tongue: English
• Weight: 396 KB
• Volume: 22
• Category: Article
• ISSN: 0323-3847
• DOI: 10.1002/bimj.4710220504

✦ Synopsis

Abstract

In this paper the first two moments of the test criterion (Treat. S.S.)/(Treat.S.S. + Error S.S.) have been derived assuming that one observation corresponding to the first plot of the first block which is under treatment ‘m’ (say), is missing in a randomized block design with ‘V’ treatments and ‘r’ blocks. To keep the analysis simple the case of one missing observation has been considered. It is concluded that in general the design is not unbiased in YATES (1951) sense and the usual F‐test is satisfactory iff /(vr ‐ r ‐ 1)=(S ‐ S~1~)/(v ‐ 1) (r‐1), the block errors are homogeneous and (vr ‐ r ‐ 1) is large. The analysis of three unifornity trial data indicates that the first condition is the most important for the F‐test to be satisfactory.

However, if one observation is missing at random from some plot of some block, the F‐test is unbiased. If the block errors are homogeneous and (vr ‐ r ‐ 1) GT96, the F‐test also provides a good approximation to the corresponding randomization test in this case.