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stat200ch12_winter10 - STAT 200 Chapter 12 Inference for...

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STAT 200 Chapter 12 Inference for One-Way Analysis of Variance One-Way Analysis of Variance (Section 12.1) Objective: to compare the means of three or more independent populations Examples: Comparison of mean annual income among 4 populations: university graduates who have a major in computer science, civil engineering, statistics and actuarial science. Comparison of the mean reduction in blood pressure in hypertensive patients randomized to three different treatment groups: antihypertensive drug A, B and C. Analysis of Variance (ANOVA) is a statistical method that tests the equality of three or more population means by analyzing sample variances or variation in the data. When there is only one characteristic that we can use to classify the populations, we fit the one-way ANOVA model. The one-way ANOVA model: X ij = μ i + ij , i = 1 , 2 , ..., I, j = 1 , 2 , ..., n i there are I populations within population i , there are n i individuals the population mean for population i is given by μ i X ij represents the measurement on the j th individual in the i th population X ij varies about the population mean μ i ; its value is expressed as the population mean μ i plus an error term ij the error term ij is a random variable Assumptions: For each fixed i
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