文档介绍：Chapter 4
analysis of variance (ANOVA)
Section 1
the basic idea and condition of application
Objective: deduce pare several (or two ) population means .
Method: analysis of Variance (ANOVA), ie F test paring several sample means .
Basic idea : according to the type of design, the sum of squares of deviation from means (SS) and degree of freedom (df) were divided into two or several sections . Except the chance error, the variation of every section can be explained by a certain or some factors.
Condition of Application :
population : normal distribution and homogeneity of variance.
Sample: independent and random
Types of design :
The ANOVA pletely random design;
The ANOVA of randomized block design;
The ANOVA of Latin square design;
The ANOVA of cross-over design ;
The basic idea of ANOVA pletely random design
partition of variation
sum of squares of deviations from mean,SS :
1. total variation : the degree of variation of all variable values , the formula as follows
amend factor:
2. between- group variation: the sum of squares of deviations from mean between groups means and grand mean show the effects of treatment and random error, the formula :
-group Variation : differences among values within each group .The formula as follows:
the relation of three variation