MAT-Repo

Design of Experiment Repo

Introduction

Statistical studies can be categorized into two main types, observational studies and experimental studies

• Observational studies are conducted to get an understanding on the prevailing situation.

• Experimental studies are conducted to explore causal relationships. In an observational study the researchers passively observe the subjects in the population without imposing anything on them. On the other hand in experimental studies treatments are imposed on the subjects and their responses are observed.

Experiments are performed by investigators in all fields of inquiry, usually to discover something about a particular process or system. An experiment is a test or series of runs in which purposeful changes are made to the input variables of a process or system so that we may observe and identify the reasons for changes that may be observed in the output response. All experiments are designed experiments, some are poorly designed, some are well-designed

Basic Principles of Design of Experiments

The Basic Principles of Design of Experiments are randomization, replication and blocking.

Terms and Concepts in Design of Experiments

Treatments

Treatments are the different procedures we want to compare. These could be different kinds or amounts of fertilizer in agronomy, different long rate structures in marketing, or different temperatures in a reactor vessel in chemical engineering.

Experimental Units

Experimental units are the things to which we apply the treatments. These could be plots of land receiving fertilizer, groups of customers receiving different rate structures, or batches of feedstock processing at different temperatures.

Responses

Responses are outcomes that we observe after applying a treatment to an experimental unit. That is, the response is what we measure to judge what happened in the experiment; we often have more than one response. Responses for the above examples might be nitrogen content or biomass of corn plants, profit by customer group, or yield and quality of the product per ton of raw material.

Randomization

Randomization is the use of a known, understood probabilistic mechanism for the assignment of treatments to units.

Experimental Error

Experimental Error is the random variation present in all experimental results. Different experimental units will give different responses to the same treatment, and it is often true that applying the same treatment over and over again to the same unit will result in different responses in different trials. Experimental error does not refer to conducting the wrong experiment or dropping test tubes.

Measurement Units

Measurement units (or response units) are the actual objects on which the response is measured. These may differ from the experimental units.

Control

Control has several different uses in design. First, an experiment is controlled because we as experimenters assign treatments to experimental units. Otherwise, we would have an observational study. Second, a control treatment is a standard treatment that is used as a baseline or basis of comparison for the other treatments. This control treatment might bethe treatment in common use, or it might be a null treatment (no treatment at all). For example, a study of new pain killing drugs could use a standard pain killer as a control treatment.

Placebo

Placebo is a null treatment that is used. Placebos are often used with human subjects, because people often respond to any treatment: for example, reduction in headache pain when given a sugar pill.

Factors

Factors combine to form treatments. For example, the baking treatment for a cake involves a given time at a given temperature. The treatment is the combination of time and temperature, but we can vary the time and temperature separately. Thus we speak of a time factor and a temperature factor. Individual settings for each factor are called levels of the factor.

Confounding

Confounding occurs when the effect of one factor or treatment can’t be distinguished from that of another factor or treatment. The two factors or treatments are said to be confounded. Except in very special circumstances, confounding should be avoided.

TOPICS COVERED

• Single Factor Experiments : Checking the model assumptions, Treatment Contrasts, Multiple Comparisons, Randomized Block Designs, Latin Squares Designs, Balanced Incomplete Block Designs.

• Factorial Designs: Fixed, Random, and Mixed Models.

• 2k Factorial designs: Blocking and Confounding in 2k Factorial Designs.

• Fractional Factorial Designs and Nested Designs.