Variance Analysis ANOVA

Source: http://blog.sciencenet.cn/blog-479412-391481.html

Variance analysis is to compare whether there are differences in the number of population samples. The method has ra.fisher first proposed, later by Gw.snedecor Perfect, in order to commemorate Fisher, so called variance analysis for F test.

Inter-group: between the =SS group between the MS Group/V Group, the SS represents the square sum of the mean difference, V represents the degree of freedom, the Inter-group variation includes the processing effect and the random error.

Within the group: within the =SS group within the MS Group/V Group, the differences within the group include random errors.

In the/ms group between F=ms Group, F was close to 1, indicating that there was little difference between groups.

The basic idea of variance analysis is to divide the total variance into inter-group and intra-group variation, and then calculate the F-value of both. The greater the F value, the greater the difference between the groups, the processing function, and vice versa, is caused by random errors.

Variance Analysis Application conditions: 1) sample independent, 2) from the normal population, 3) variance uniformity.

Variance analysis includes the analysis of the variance of the fully randomized design (completely random designs), also called the One-way (one-way) variance analysis and the random block Design (radomized), also called the two-way (two-way) variance analysis.

The variance analysis of completely random design is the method that randomly assigns the subjects to each treatment or control group, regardless of the influence of interference factors, the sample number of each group can be different.

Analysis of the variance of random block design the subjects are composed of Group B in the same or similar nature, and each group has G subjects, which are randomly assigned to G treatment Group, so that not only the number of samples is identical, but the biological characteristics are also more balanced.

Variance analysis rejects the H0, accepts the H1, only shows that the G-Total is not equal, if you want to know more about the two-group mean, you need to do 22 comparison or multiple comparisons, that is, Post-hoc test.

The relationship between Anova and T test:.

Variance Analysis ANOVA