Lab11_Nested design and Random Block

Lab11_Nested design and Random Block - EXST 7015...

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EXST 7015 - Statistical Inference II, Fall 2011 Lab 11: Randomized Block Design and Nested Design OBJECTIVES: The objective of an experimental design is to provide the maximum amount of reliable information at the minimum cost. In statistical terms, the reliability of information is measured by the standard error of estimates (that is directly related with the population variance, inversely related to sample size). Properly applied experimental design may effectively reduce the population variance, and/or could structure data collection to reduce the magnitude of the experimental error. Usually data resulting from the implementation of experimental designs are described by linear model and analyzed by the analysis of variance as was introduced last week. Random block design is one of the simplest and probably the most popular experimental design. In this design the sample of experimental units is divided into groups or blocks and then treatments are randomly assigned to units in each block. In some experiments blocks may be of sufficient size to allow several units to be assigned to each treatment in a block. Such replication of treatments is referred to as randomized blocks with sampling. The linear model for data from such an experiment is y ijk = μ + τ i + β j + τβ ij + ε ijk ( i = 1, 2, …,t; j = 1, 2, …, b; k =1, 2, …, k) Where y ijk is the observed value of the response variable in the k th replicate of the treatment i in block j ; μ is the overall mean; τ i is the fixed effect of treatment i; β j is the effect of block j , a random variable with mean zero and variance σ 2 β ; τβ ij is the experimental error, a random variable with mean zero and variance σ 2 τβ ; and ε ijk is the sampling error, which is the measure of variation among units treated alike within a block, a random variable with mean zero and variance σ 2 . As you might be aware that in the above model, if the block effect is fixed, the interaction is also fixed so that it becomes a two-factor factorial design and F ratios for all the tests using the sampling error in the denominator. Nested design refers to some experimental situations where experimental units may
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This note was uploaded on 12/29/2011 for the course EXST 7015 taught by Professor Wang,j during the Fall '08 term at LSU.

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Lab11_Nested design and Random Block - EXST 7015...

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