Introduction to Probability and Statistics for Engineers and Scientists
444 Chapter 10:Analysis of Variance Definition The statistic SSW= ∑m i= 1 ∑n j= 1 (Xij−Xi.)^2 is called thewithin samples sum of ...
10.3One-Way Analysis of Variance 445 will be a chi-square random variable withm−1 degrees of freedom. That is, if we define SSbb ...
446 Chapter 10:Analysis of Variance TABLE 10.1 Values of Fr,s,.05 r= Degrees of Freedom s= Degrees of for the Numerator Freedom ...
10.3One-Way Analysis of Variance 447 p-Values in a One-way ANOVA Start Quit 1 2 3 4 5 Sample 1 220 251 226 246 260 244 235 232 2 ...
448 Chapter 10:Analysis of Variance When computing by hand, the quantitySSbdefined by SSb=n ∑m i= 1 (Xi.−X..)^2 should be comput ...
10.3One-Way Analysis of Variance 449 The value of the test statistic is thus TS= 863.3335/2 1991.5785/12 =2.60 Now, from Table A ...
450 Chapter 10:Analysis of Variance =(m−1)σ^2 /n+ ∑m i= 1 (μi−μ.)^2 + 2 ∑m i= 1 (μi−μ.)E[Yi−Y.] =(m−1)σ^2 /n+ ∑m i= 1 (μi−μ.)^2 ...
10.3One-Way Analysis of Variance 451 where W= 1 √ n C(m,nm−m,α) √ SSW/(nm−m) and where the values ofC(m,nm−m,α) are given, forα= ...
452 Chapter 10:Analysis of Variance Hence, with 95 percent confidence, we can conclude that the mean grade point average of firs ...
10.3One-Way Analysis of Variance 453 is chi-square withmdegrees of freedom; therefore, replacingμin the preceding by its estimat ...
454 Chapter 10:Analysis of Variance 10.4 TWO-FACTOR ANALYSIS OF VARIANCE: INTRODUCTION AND PARAMETER ESTIMATION Whereas the mode ...
10.4Two-Factor Analysis of Variance: Introduction and Parameter Estimation 455 However, if we letμdenote the average value of th ...
456 Chapter 10:Analysis of Variance where ∑m i= 1 αi= ∑n j= 1 βj= 0 The valueμis called thegrand mean,αiis thedeviation from the ...
10.4Two-Factor Analysis of Variance: Introduction and Parameter Estimation 457 we see that unbiased estimators ofμ,αi,βj— call t ...
458 Chapter 10:Analysis of Variance 10.5 Two-Factor Analysis of Variance: Testing Hypotheses Consider the two-factor model in wh ...
10.5Two-Factor Analysis of Variance: Testing Hypotheses 459 ∑m i= 1 αi= ∑n j= 1 βj=0. Since the sum of all theαiis equal to 0, i ...
460 Chapter 10:Analysis of Variance To obtain a second estimator ofσ^2 , consider the row averagesXi.,i=1,...,m. Note that, when ...
10.5Two-Factor Analysis of Variance: Testing Hypotheses 461 We base our test of the null hypothesisH 0 that there is no row effe ...
462 Chapter 10:Analysis of Variance Station Year 123456 1970 53 35 31 37 40 43 1971 36 34 17 21 30 18 1972 47 37 17 31 45 26 197 ...
10.6Two-Way Analysis of Variance with Interaction 463 10.6 Two-Way Analysis of Variance with Interaction In Sections 10.4 and 10 ...
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