# ANOVA

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### ????? :

????? ANOVA Analysis of Variance

### ????? :

????? ANOVA Analysis of variance. ?????????,?????????????????,????????,?????????????

### ANOVA :

ANOVA ??????? ?????=?????????? ???????????????,?????????????? ?????????????? ??F?????????????????????????,????????? ????????(????)???????????(F?),????????????????(t?Z?)

### ???? :

???? ????(experimental unit)=?????????????? ??(factor)=???????????? ??(level)=????????????? ??(treatment)=????????????

### Slide 5:

Example ???12?????????A?B?C??,??????????A??????B?,?????????C?,???????,??: ??????????experimental unit?????factor?????level????

### ?????????? :

?????????? 1.???????????????? 2.???????????? 3.?????????????????

### Slide 7:

????????(one factor ANOVA): ???????? ????????(two factor ANOVA): ?????????

### Slide 8:

k????????????????? ???=????+????(??) ????=?????+?????(?????) SST=SSB+SSW(SSE)

### SStotal=SSb+SSw :

SST:?????????????????????????,?????????? SSB:????????????????????? SSW:???????????,(????)??????????=SSE ???????????,?????(MS),????????? SStotal=SSb+SSw

### Slide 10:

?????????????ANOVA? F F=MSB / MSE

### Slide 11:

????????F?? reject H0

### Slide 12:

Example ???12?????????A?B?C??,??????????A??????B?,?????????C?,???????,??: 1.???ANOVA?????? 2.??ANOVA?? 3.???????????????a=0.05?? 4.???one factor ANOVA,or two factor ANOVA?

### Slide 13:

Example ??????4??????????????,??????: ?a?????????factor?????level???? ?b????one factor ANOVA,or two factor ANOVA? ?c???ANOVA?? ?d???4???????????a=0.05?[F0.05(3,18)=3.16]?

### Slide 14:

Example ????????????????,????????????,?????????,?????????,?????????????????????? ?a=0.05?

### ????(Priori comparison) :

????(Priori comparison) ??????????????????????,???????? ??????????,????????????????????????????? ??????t-test??: t?????????????????????????N-K,??D?

### ????(Posteriori comparison) :

????(Posteriori comparison) ????????????????????(follow-up test) ??????F???????????,??????(posteriori comparisons)

### Slide 17:

?????(experiment-wise error): ????????????????,????????????????(?HSD?)? ????,???????(????????)? ?????(comparison-wise error): ?????????????????????(?N-K?)? ?????,???????(???????)?

### Scheff’s methed :

Scheff’s methed ????,???n???????? ???????????????????????????,?????????(type I error)????????????????????????????????

### Scheff’s methed :

Scheff’s methed Cohen(1996)????Scheffe?????????F???? ????F?????,Scheffe??????? ????F??????,??Scheffe?????????????????????????

### ??????(randomized block design) :

??????(randomized block design) ?????????????,????????????????(treatment),??????????,????????????????? ??(block)?????????????,???,??,????????

### Slide 22:

???????????:????,????,???????? ANOVA?

### Slide 23:

Example ?A?B?C?????????????,????20???,??????,????????,???????????????