The Importance of Lay-out in Determining Error Variance in Field Experiments

Abstract

S U M M A R YExamples are taken from three biometrical texts, two unpublished experiments and Yates (1937) to illustrate quantitatively how the lay-out of the plots can affect the estimate of error variance in field experiments and how confounding of treatment and positional effects can arise. In two examples in which the plots did not run the whole length or width of the block, the estimates of error were reduced by one half and one quarter respectively by allowing for sub-blocks within blocks or for rows and columns. In split-plot experiments where the main plots were split breadthwise, the sub-plot error was about the same size as the main-plot error or larger whereas it is expected to be at most one third that of the main plots when these are split lengthwise. Serious bias can arise in the estimate of treatment effects due to confounding with positional effects; this is illustrated. Christidis (1931) clearly showed the importance of long narrow plots (strips) each running the full length of the block in overcoming the effects of soil heterogeneity. The shape of plots and blocks in field trials was discussed by Fisher in Design of Experiments (1935, Section 29), but this book is rarely read by biometricians now, let alone by research workers. Except in the books by Dyke (1976, Chapter 2) and by Panse and Sukhatme (revised by Sukhatme and Amble, 1978, Chapters 8 and 15) which cover field experimentation very well, little advice is given on lay-out in modern statistical texts. In fact, some of the designs that appear in texts and papers directed to agricultural research are likely to be unsatisfactory, e.g. the lay-outs in Fig. 1. Even if the experimental area were homogeneous, such designs would be less efficient than ones using strips, and the presence of heterogeneity would lead to increased variance and possibly confounding of treatment and positional effects.Fisher stressed that each plot must sample the whole area of the block in which it is placed but conceded that agricultural convenience and labour costs must also be considered in deciding on a lay-out. Baker in the discussion of Mead and Riley (1981) stressed that ease of conducting an experiment must play a big part in designs to be put in the field by unskilled and mostly illiterate labour. Randomized blocks and split-plot designs are popular for this reason.Yates and Finney (1955, page 19) commented on the excessive use of splitplot designs. More recently Mead and Stern (1980) and Mead and Riley (1981) have questioned the use of split-plots, particularly for experiments on intercropping, mainly because different treatment comparisons have different pre-0014-4797/85/0000-0972 $05.00

Nonlinear Regression Modelling and Time Dependent Covarlates in Repeated Measures Experiments

“…The field layout and treatment allocation is conformal with a split plot layout, however the plot shape and longitudinal subdivision of the rows make the design inappropriate for this d y s i s (Roberts, 1985). This is further complicated by the effect of an irrigation watering gradient from the head ditch to the tail ditch.…”