Estimation of the parameters in the balanced incomplete block design

ABSTRACT In this study, the methods which are used for estimating the treatment effects in the balanced incomplete block design and the estimated values of the treatment effects obtained by using these methods have been compared. When it is impossible to make the required number of treatments, which are needed for each block in the randomized complete block design, the experiment is designed in the balanced incomplete block design. In the balanced incomplete block design, it is suggested that other methods should be used rather than the least squares estimators to estimate the treatment effects. Therefore, in order to estimate the treatment effects in the balanced incomplete block design, the intrablock, the interblock and the combined estimates methods are introduced in literature. In this study, the simulation studies were made by using the programs written in statistical software Minitab. The intrablock, the interblock and the combined estimates for the balanced incomplete block design and the least squares estimates for the randomized complete block design of the treatment effects were calculated 2500 times by simulation. The results were compared and the most appropriate estimator of the treatment effects for the balanced incomplete block design was investigated. The means and the standard deviations of the estimates were considered as the criteria of this comparison. After the evaluation of the results, it was observed that each of the three methods gave unbiased results when the block effects were insignificant for the balanced incomplete block design. When the block effects were significant, it was seen that the results of the means of the intrablock and the combined estimates were unbiased. The interblock estimates results were observed as inappropriate. In both of the situations in which the block effects were significant and insignificant, the standardVI deviation of the intrablock estimates is lower than the standard deviations of the interblock and the combined estimates.