4
3quality in Japanese industry are legendary, distinguishes between two approaches to statistical analysis: enumerative and analytic. From Deming (1975):
Enumerative. "The action to be taken on the frame depends purely on estimates or
complete counts of one or more specific populations of the frame. The aim of the statistical study in an enumerative problem is descriptive.' Virtually all classical statistical procedures t-tests, Ftests, analysis of variance (ANOVA), standard confidence intervals are enumerative in nature.
Analytic. *In Which action will be taken on the process or cause-system that produced the frame studied, the aim being to improve the practice in the future.* Only statistical procedures which involve prediction rather than estimation or hypothesis testing are analytic in nature. 
Deming (19~75) puts it another way: *A 100 percent sample in an enumerative problem
provides the complete answer to the problem posed for an enumerative problem. . In contrast, a 100 percent sample of a group of patients, or of a section of land, or of last week's product, industrial or agricultural, is still inconclusive in an analytic problem. This point, though fundamental in statistical information for business, has escaped many writers."
Clearly, most on-farm trials have analytic rather than enumerative objectives. Thus, the literal application of enumerative statistical procedures, many of which form the core of statistical tradition in agricultural research, is not appropriate for most on-farm trials. For example, the analysis of variance (ANOVA) can be very useful for interpreting data from on-farm trials. However, traditional ANOVA places much emphasis on hypothesis testing and significance levels. These are important in enumerz.- ve studies, but essentially irrelevant to analytic studies, where the emphasis is on prediction and taking action.
Ad hoc statistical procedures are common in analytic studies. While many of these
procedures can be validly criticized using enumerative statistical arguments, these criticisms often miss the point. Analytic studies are usually conducted with less prior knowledge of and control over experimental conditions. The choice is frequently between no knowledge and useful, if imperfect knowledge; conditions of optimality characteristic of enumerative statistical procedures are simply not an option. Analytic studies typically sacrifice control over variability for a broadened research domain. This does not make them incorrect or invalid, it just means that the researcher must understand the trade-offs and choose statistical methods accordingly.
The complex variability in on-farm trials often troubles those trained in traditional statistical methods for agricultural research. In statistical jargon, these methods are examples of "ordinary least squares"; their main virtue is that they are easy (relativelyl) to do without a computer, which was a vital consideration in the 1 920s, and 1 930s. when they were developed. Their main drawbacks are the rigid structure and narrow, frequently unrealistic assumptions required of the data to permit legitimate interpretation. Since on-farm trials rarely satisfy these assumptions, many have concluded falsely that they are somehow "statistically improper." In truth, traditional methods simply cannot accommodate the complexity of on-farm trials.
*Ordinary least squares* theory has long since been supplanted by more versatile methods, mixed linear model methods (or "mixed model methods* as they will be referred to here) being of particular importance to on-farm trials. The virtue of mixed model methods is their flexibility; their drawback is that they generally require a computer. Thus. while mixed model theory has been around for nearly a half century, it did not become practical to use until the 1 970s in developed countries and the 1 980s, in most developing countries.. By then, more traditional methods were so deeply entrenched in statistics courses, on experiment stations, and in agricultural research journals that substantial re-education has either been required or, more correctly, is still required.