Experimental Design ConceptsBlocking(Chapters 14 amp; 15).ppt

STA 6166 Experimental Design Concepts:Blocking(Chapters 14 15) Experimental Design Basics. Completely randomized design revisited. Accounting for more than one factor. Blocking (and randomized block designs) to remove confounding. Why Experimental Design? Experimental design (for an experimental study): the manner in which the experimental units are arranged or grouped, and how the treatments are assigned to them. To call in the statistician after the experiment is done may be no more than asking him to perform a post-mortem examination: he may be able to say what the experiment died of. Sir R.A. Fisher (1938) Fisher compared a dataset to a sample of gold ore. The finest analysis could only extract the proportion of gold contained in the ore. But a good design could yield a sample with more gold! [data = ore; information = gold.] Experimental Error Experimental error is the variation in the responses among experimental units (e.u.’s) which are assigned the same treatment, and are observed under the same experimental conditions. It is measured by SSE (or MSE). Ideally, we would like experimental error to be zero! This is impossible because of (at least) one or more of the following reasons: There are inherent differences in the e.u.’s before they receive treatments. There is variation in the devices that record the measurements. There is variation in applying or setting the treatments. There are extraneous factors other than the treatments which affect the response. Experimental Error Control Control over the magnitude of experimental error can be achieved by: Careful choice of e.u.’s. Homogeneity of e.u.’s decreases MSE. Taking care with experimental procedures and recording of measurements. Smaller errors result in smaller MSE. Blocking of e.u.’s. Blocking decreases MSE. Choice of experimental design used. Designs with more factors generally lead to smaller MSE. Using explanatory variables or covariates (variables that are thought to affect th