STA 6166 UNIT 5
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# Design of Experiments

 Topics Covered What makes a good experiment? This is the question that will drive this last unit. We will first try to make a distinction between different types of studies - observational versus experimental. Both types of studies have their own strengths and weaknesses. Often, both are called experiments. Good science is equated with good experiments. Good experiments have a number of characteristics in common. First, they have a very detailed plan that identifies the experimental objectives, the responses being measured, the factors (treatments) being evaluated and the efforts used to control extraneous sources of variation (noise). What can't be controlled directly may be controlled via randomization. Finally the variability that is left over (the residual variation) must be estimated. Designed experiments may be very simple (as with the completely randomized design) to quite complex (as with fractional factorial experiments). In this unit we will explore the simplest class of experimental designs, the balanced block experiments. Part of any experiment is clearly defining the treatments to be applied to the experimental units. Treatments may be quite simple (a list of baking ovens we want to compare) to complex (combinations of ovens, baking temperatures, and times). Treatments are typically made up of combinations of one or more factors, each factor being evaluated at two or more levels. We will see that there are efficiencies to be gained by doing experiments on factorial treatments. Of course, it is useless to do an experiment unless we have a means of analyzing the resulting data. We will show how the general linear model and the analysis of variance table can be used to analyze and test hypotheses specific to the different experimental designs. Finally we will explore how combining regression concepts with experimental design concepts in the analysis of covariance provides a very power tool for experimental studies. Objectives To introduce some of the basic experimental designs. To understand the importance and use of randomization, replication and blocking in the design and analysis of experiments. To see how the General Linear Model is used to analyze experimental designs. To learn how to incorporate ancillary measurements into an experimental design and especially into the analysis of the resulting data. Sections 1 Design Concepts for Experiments and Studies 2 Analysis of Variance for Standard Designs 3 Analysis of Covariance Unit Test Link to Unit Test