anova(英文版)(編輯修改稿)
2025-01-28 17:17 本頁面
【文章內(nèi)容簡介】 e observations are mutually independent. ? Stat ? Nonparametrics ? Runs Test ? The k groups exhibit homogeneity of variance. . ?1178。 = ?2178。 = ? = ?k178。 ? Stat ? ANOVA ? Test for Equal Variances ? The residuals are normally distributed. . e ~ NID(0,?178。) ? Stat ? Basic Statistics ? Normality Test 16 ANOVA Assumptions 543210 1 2 3 4543210R e s i d u a lFrequencyH i s t o g r a m o f R e s i d u a l s2 52 01 51 0501 00 1 0O b s e r v a t i o n N u m b e rResidualI C h a r t o f R e s i d u a l sM e a n = 7 . 4 0 E 1 6U C L = 8 . 1 1 4L C L = 8 . 1 1 42 01 51 0543210 1 2 3 4F i tResidualR e s i d u a l s v s . F i t s210 1 2543210 1 2 3 4N o r m a l P l o t o f R e s i d u a l sN o r m a l S c o r eResidualR e s i d u a l A n a l y s i s o n A N O V A M o d e l17 ANOVA Models Fixed Effects (ANOVA I) Model ? factor levels in the experiment are specifically chosen ? the conclusion is relevant only for the chosen levels and may not be extended to similar treatments that were not considered Random Effects (ANOVA II) Model ? factor levels are randomly drawn from a large population of treatments ? the conclusion is valid for the entire population of treatments Mixed Effects (ANOVA III) Model ? one or more factors are fixed factors while others are random factors 18 ANOVA Models A k–Way ANOVA model involves the study of k factors. k–Way ANOVA I : k factors。 all factors of fixed effect k–Way ANOVA II : k factors。 all factors of random effect (Will not be discussed in GB course) k–Way ANOVA III : k factors。 some factors of fixed effect (Will not be discussed in GB course) others of random effect 19 OneWay ANOVAI Model where Yij is the value of the response variable in the jth trial for the ith factor level or treatment ?. is the overall mean for all observations ?i=?i–?. is the effect of the ith treatment . ?ij is the random error ponent . The hypothesis may now be rephrased: H0 : ?1 = ?2 = ? = ?r = 0 Ha : no
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