Analysis of Variance ANOVA CH 13 ANOVA n

Analysis of Variance (ANOVA) CH 13 變異數分析

ANOVA 假設 n n n Ho: 1= 2= 3 or H o: j = k H 1: at least one population mean is different from the others. H 1: 不全等，至少有二個 不同， i不 全等 H 1: j ≠ k

Model underlying oneway ANOVA The model indicates that any person's score, comprised of three components , is the grand mean for everyone in the sample the treatment or group effect random error for a person, i. e. , the extent to which a person differs from the rest of the group

Variance between sample means n F= Variance expected by chance

difference between groups 組間變異 difference within group 組內變異 group 1 group 2 group 3

Calculating the F statistic which is the test statistic in ANOVA Mean Square 均方 where SS represents sums of squares, df represents degrees of freedom, MS represents mean squares

Treatment total Grand total

n dfbetween=k-1; k=# of treatment (level) n dfwithin =N-k; N=total sample size n dftotal =N-1

F table n n 如何查Fc? Fdfb, dfw , =0. 05 dfb , 在上方 dfw , 在左方

dfbetween (分子) dfwithin (分母)

Results