Design of Experiments.

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Presentation transcript:

Design of Experiments

Principles of Experimental Design Control the effects of lurking variables on the response, most simply by comparing two or more treatments Randomize Replicate

Randomization The use of chance to divide experimental units into groups is called randomization. Comparison of effects of several treatments is valid only when all treatments are applied to similar groups of experimental units.

How to randomize? Flip a coin or draw numbers out of a hat Use a random number table; Table B in your book Use a statistical software package or program Minitab www.whfreeman.com/ips

Statistical Significance An observed effect so large that it would rarely occur by chance us called statistically significant.

Complete Randomized Design (CRD) The CRD is the simplest of all designs. It is equivalent to a t-test when only two treatments are examined. Replications of treatments are assigned completely at random to independent experimental subjects. Adjacent subjects could potentially have the same treatment.

CRD Sample layout: There are 4 (A – D) treatments with 3 replications (1 – 3) each. A1 B1 C1 A2 D1 A3 D2 C2 B2 D3 C3 B3

Randomized Complete Block Design (RCB) The RCB is the standard design for ‘agricultural’ experiments. The field is divided into units to account for any variation in the field. Treatments are then assigned at random to the subjects in the blocks-once in each block.

RCB Treatments are assigned at random within blocks of adjacent subjects, each treatment once per block. The number of blocks is the number of replications. Any treatment can be adjacent to any other treatment, but not to the same treatment within the block. Used to control variation in an experiment by accounting for spatial effects.

RCB Sample Layout: Each horizontal row represents a block. There are 4 blocks (I-IV) and 4 treatments (A-D) in this example. Block I A B C D Block II D A B C Block III B D C A Block IV C A B D

Always consider… Lack of realism is a major weakness of experiments. Is it possible to duplicate the conditions that we want?

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