ANalysis Of VAriance ANOVA pnhsiehntu edu tw Group

變異數分析 ANalysis Of VAriance ANOVA 謝寶煖 台灣大學圖書資訊學系 pnhsieh@ntu. edu. tw

Group 1 Observation 2 Observation 3 Mean Sums of Squares (SS) 2 3 1 2 2 2 (2 -2) + (3 -2) + (1 -2) =2 6 7 5 2 2 Overall Mean Total Sums of Squares total SS (28) 可以分成 兩部份 一為組內變異(withingroup variability) (2+2=4) 二為平均數不同所造 成的變異 (28(2+2)=24). Group 2 (2 -4)2+ (3 -4)2+ (14)2+ (6 -4)2+ (7 -4)2+ (5 -4)2=28 6 2 4 28 MAIN EFFECT SS Effect Error 24. 0 df MS 1 4 24. 0 1. 0 F 24. 0 p. 008

SS Error and SS Effect • the within-group variability (SS) is usually referred to as Error variance. This term denotes the fact that we cannot readily explain or account for it in the current design. • the SS Effect we can explain. Namely, it is due to the differences in means between the groups. Put another way, group membership explains this variability because we know that it is due to the differences in means.

ANOVA p comparison of the variance n n between- groups variability (called Mean Square Effect, or MSeffect) within- group variability (called Mean Square Error, or Mserror) the null hypothesis：that there are no mean differences between groups in the population compare those two estimates of variance via the F test, which tests whether the ratio of the two variance estimates is significantly greater than 1.

T test vs. anova Experimental Group 1 Group 2 Males Mean Females Mean p total variance n 2 3 1 6 7 5 n 2 6 n 4 5 3 8 9 7 4 8 p p p error (within-group) variability due to experimental group membership variability due to gender T test: experiment or gender Anova: experiment x gender interaction

Main effects, two-way interaction Achievement oriented avoiders Challenging Test Easy Test 10 5 5 10 challenging tests make students work harder? p achievement-oriented students work harder than achievement- avoiders? Main Effects p challenging tests make only achievement-oriented students work harder, while easy tests make only achievement- avoiders work harder Interaction Effects p

Higher order interactions Females Challenging Test Easy Test Males Challenging Test Easy Test Achievementoriented 10 5 Achievementoriented 1 6 Achievementavoiders 5 10 Achievementavoiders 6 1

多變項共變分析 MANCOVA p Multivariate Analysis of Covariance

Example 1 p Independent variable n n n p Dependent variable n p Coworker program: 由同事上3天課，加上手冊 Consultant program：由外聘講師上3天課，加上手冊 Self-program：給手冊自學 3天 Job performance： 7點量表，由員 上司評分 每組各40名員

Example 2 p Independent variable n n n p p Coworker program: 由同事上3天課，加上手冊 Consultant program：由外聘上3天課，加上手冊 Self-program：給手冊自學 3天 每組各3000名員 Dependent variable： 7 n n n n Job performance： 7點量表，由員 上司評分 Organizational commitment Job satisfaction Turnover intention Job stress Role ambiguity

彙整 7項ANOVA 檢定 是”Play It Safe” table