Lab10_ANOVA and Post-ANOVA Tests

Lab10_ANOVA and Post-ANOVA Tests - EXST 7015 - Statistical...

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EXST 7015 - Statistical Inference II, Fall 2011 Lab 10: ANOVA and Post ANOVA Test OBJECTIVES: Analysis of variance (ANOVA) is the most commonly used technique for comparing the means of groups of measurement data. There are lots of different experimental designs that can be analyzed with different kinds of ANOVA. For this week’s lab, the most basic type of ANOVA, one-way ANOVA will be introduced. In a one-way ANOVA, there is one continuous variable (Response Variable) and one categorical variable (Treatment). Multiple observations of the response variable are made for each level of the treatment. One-way ANOVA corresponds to the completely randomized designed experiment (CRD) with one fixed treatment effect, with its linear model as the following: Y ij = μ + τ i + ε ij = μ i + ε ij ( i = 1, 2, …, t; j = 1, 2, …, n) Where μ is the overall mean; τ i are the treatment level effects, and ε ij is the random error. μ i is the mean of the i th level of treatment. The null hypothesis test of one-way ANOVA is that the means of the response variable are the same for the different levels of treatment (H 0 : μ 1 = μ 2 =…= μ t ) ; the alternative hypothesis is that they are not all the same. There are three assumptions need to be considered for ANOVA: the treatments are independently sampled; residuals or deviation of observations within groups should be normally distributed (evaluated by residual plot, normality test); and the variance from each level of treatment is the same (i.e. homogenous variance, Bartlett test is preferred method to evaluate the homogeneity of variance). ANOVA usually proceeds with an F-test of the MSTreatment (d.f.= t-1) over MSError (d.f. = t(n-1)). The MSError estimates a variance σ 2 ε , and MSTreatment estimates the same σ 2 ε plus the difference between the levels of treatment ( σ 2 ε + n σ 2 τ ). So the F-test can be written as the following: F= MSTreatment/MSError = ( σ 2 ε + n σ 2 τ )/ σ 2 ε It is One Tailed F-test since the variance of treatment is expected to be large if the null hypothesis is rejected. Once the null hypothesis of ANOVA is rejected, i.e., the significant difference among the levels of
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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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Lab10_ANOVA and Post-ANOVA Tests - EXST 7015 - Statistical...

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