A Further Note on Missing Data

whereas Nelder has (rt 1) in the numerator. It should prove helpful to some to point out that inspection suffices to show that Nelder's formula is incorrect. Remembering the mathematical model, it is obvious that the general mean, the constant for the affected block and that for the affected treatment can all be estimated with any desired accuracy, simply by increasing the numbers of blocks and of treatments. Hence so can their sum, which is the estimate of the missing value. Nelder's formula is not conformable with this observation, having a lower limit of o2 as r and t become large. OIn the other hand, his formula for the r X r Latin square is correct, and is of the order of 3o-2/r as the square becomes large. In referring to Query 96, which raised a question about "impossible" estimated values, another error has occurred in Nelder's paper. The missing value, estimated to be -6.64, has a sampling error of 8.23 on 32 degrees of freedom. The 95% confidence interval is therefore -6.64 ? 16.76 (rather than Nelder's value of 8.10), thus giving no appreciable indication whether the estimated value is based oIn an erroneous model. There is some interest in the fact that not only missing values may have "impossible" estimated values. In the example of Query 96 the model leads to estimates of -3.23 and -1.48 for bait A for replications 4 and 11, respectively, but these are small compared with the sampling error of 8.23. While tests of "possibility" of estimated values may occasionally prove useful, it is probably always better to test for additivity, as discussed for this example by Tukey (1954).