Lecture9.chapt13 - Lecture 9, Chapter 13 Two-Way Analysis...

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Chapter 13 Two-Way Analysis of Variance: Two-way ANOVA compares the means of populations that are classified two ways or the mean responses in two-factor experiments. Examples: 1. The strength of concrete depends upon the formula used to prepare it. An experiment compares six different mixtures. Nine specimens of concrete are poured from each mixture. Three of these specimens are subjected to 0 cycles of freezing and thawing, three are subjected to 100 cycles, and three specimens are subjected to 500 cycles. The strength of each specimen is then measured. 2. Four methods for teaching sign language are to be compared. Sixteen students in special education and sixteen students majoring in other areas are the subjects for the study. Within each group they are randomly assigned to the methods. Scores on a final exam are compared. Why is it better to do a Two-Way ANOVA than to just do 2 separate One-Way ANOVAs: It is more efficient to study two factors simultaneously rather than separately. Your sample size does not have to be as large so experiments with several factors are an efficient use of resources. We can reduce the residual variation in a model by including a second factor thought to influence the response variable (lurking variable). We are reducing σ and increasing the power of the test. We can investigate the interactions between factors. Assumptions for Two-Way ANOVA: 1. We have two factors. We have I factor levels for the first factor (call it factor A) and J factor levels for the second factor (call it factor B). We have I x J combinations of individual factor levels. 2. We have independent SRSs of size ij n from each of I x J populations. 3. Each of the I x J populations are normally distributed. 4. Each of the I x J populations have the same standard deviation σ. Lecture 9, Chapter 13
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Lecture9.chapt13 - Lecture 9, Chapter 13 Two-Way Analysis...

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