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Examples for 08-27-2009 - STAT 420 Examples for Fall 2009...

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STAT 420 Examples for 08/27/2009 Fall 2009 ANOVA (Analysis of Variance) Population 1 Population 2 Population J mean μ 1 std. dev. σ mean μ 2 std. dev. σ mean μ J std. dev. σ y 1 1 , y 2 1 , … , y n 1 1 y 1 2 , y 2 2 , … , y n 2 2 y 1 J , y 2 J , … , y n J J 1 y , s 1 2 2 y , s 2 2 J y , s J 2 H 0 : μ 1 = μ 2 = … = μ J H 1 : not all of the μ j are equal. ( We want to test simultaneously for differences among the means of all J populations. ) Example : There is a great deal of interest in comparing the mileage rating of different makes of automobiles. Other things being equal, customers buy car that gets the best mileage. Suppose we wish to compare the mean fuel consumption for J = 3 different makes of automobile, Car 1, Car 2, and Car 3. Suppose 5 cars of each make are selected randomly and the gasoline mileage (in miles per gallon) is recorded for each car. Suppose that 1 y = 19.0, 2 y = 20.4, 3 y = 21.8. Is there enough evidence that the mean fuel consumption is not the same for Car 1, Car 2 and Car 3? Data Set A: Car 1 Car 2 Car 3 18.2 19.4 19.6 19.0 18.8 19.8 21.0 20.0 20.8 20.4 21.2 21.8 22.4 22.0 21.6 Sample mean 19.0 20.4 21.8 Sample std. dev. 0.5477 0.5099 0.4472 Sample variance 0.300 0.260 0.200
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Data Set B: Car 1 Car 2 Car 3 17.0 20.4 24.0 15.8 17.8 24.2 22.0 17.8 16.2 21.8 26.0 19.8 24.4 16.0 22.8 Sample mean 19.0 20.4 21.8 Sample std. dev. 3.26 3.29 3.97 Sample variance 10.66 10.84 15.76 The Analysis of Variance Idea: Analysis of Variance (ANOVA) compares the variation due to specific sources (between groups) with the variation among individuals who should be similar (within groups). In
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