terms of the function F = aTreatment/aError that is obtained directly from the ANOVA calculations. He named it F in honor of Fisher. Fisher's field of experimentation—agriculture— was a fortunate choice because results had immediate application with assessable economic value, because simplifying assumptions such as normality and independence of errors were usually tenable, and because the cost of conducting experiments was modest.

Three Principles of Good Experimental Design

The publication of Fisher's Statistical Methods for Research Workers and his 1935 The Design of Experiments gradually led to the acceptance of what today is considered to be the cornerstone of good experimental design: randomization. It is hard to imagine the hostility that greeted the suggestion that participants or experimental units should be randomly assigned to treatment levels. Before Fisher's work, most researchers used systematic schemes, not subject to the laws of chance, to assign participants. According to Fisher, random assignment has several purposes. It helps to distribute the idiosyncratic characteristics of participants over the treatment levels so that they do not selectively bias the outcome of the experiment. Also, random assignment permits the computation of an unbiased estimate of error effects—those effects not attributable to the manipulation of the independent variable—and it helps to ensure that the error effects are statistically independent.

Fisher popularized two other principles of good experimentation: replication and local control or blocking. Replication is the observation of two or more participants under identical experimental conditions. Fisher observed that replication enables a researcher to estimate error effects and obtain a more precise estimate of treatment effects. Blocking, on the other hand, is an experimental procedure for isolating variation attributable to a nuisance variable. As the name suggests, nuisance variables are undesired sources of variation that can affect the dependent variable. There are many sources of nuisance variation. Differences among participants comprise one source. Other sources include variation in the presentation of instructions to participants, changes in environmental conditions, and the effects of fatigue and learning when participants are observed several times. Three experimental approaches are used to deal with nuisance variables:

1. Holding the variable constant.

2. Assigning participants randomly to the treatment levels so that known and unsuspected sources of variation among the participants are distributed over the entire experiment and do not affect just one or a limited number of treatment levels.

3. Including the nuisance variable as one of the factors in the experiment.

The last experimental approach uses local control or blocking to isolate variation attributable to the nuisance variable so that it does not appear in estimates of treatment and error effects. A statistical approach also can be used to deal with nuisance variables. The approach is called analysis of covari-ance and is described in the last section of this chapter. The three principles that Fisher vigorously championed— randomization, replication, and local control—remain the cornerstones of good experimental design.

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