Analysis of variance, how to do it?

Answer: How to do variance analysis:

(1) Find the sum of squares

There are three ways to calculate the sum of squares: one is to use the "sum of squares" Define the formula, that is, formula 9-3.9-4. One is to use the original data formula or use sample statistics to calculate.

1. Total sum of squares

The total sum of squares is the sum of squares of the deviations of all observations from the overall mean. To calculate the total sum of squares using the original data, use Equation 9-10. The total sum of squares of the data in Table 9-1 is equal to: SS,=∑∑X nk(∑∑X)°

2. The sum of squares between groups

The sum of squares between groups is The sum of the squared deviations of the group means from the grand mean. Calculate the sum of squares between groups using the original data using formula 911. The sum of squares between groups of the data in Table 9-1 is equal to SS, -∑(∑X)_(∑∑X)

The sum of squares within the group is the difference between the value of each subject and the group mean The sum of squared deviations. The formula for calculating the sum of squares within a group is 9-12. The sum of squares within the group of the data in Table 9-1 is equal to: ss? =∑∑x-∑(∑X)°

(2) Calculate the degrees of freedom

Calculate the degrees of freedom The formula is shown in Formula 9-8. In Table 9-1, *** there are 3 groups, each group has 4 subjects, so

the total degrees of freedom are dfr=N-1=12-1=11 degrees of freedom df between groups. =k-1=3-1=2

Degrees of freedom within the group dfw=k(n-1)=3x(4-1)=9

(3) Calculate the average Square

MS of mean square between groups. The within-group mean square MSw is calculated as the between-group sum of squares divided by the between-group degrees of freedom, and the within-group mean square MSw is calculated as the within-group sum of squares divided by the within-group degrees of freedom.

(4) Calculate the F value

(5) Check the F value table to conduct the F test and make a decision

If the force value of the null hypothesis is rejected (p -value) is set as p=0.05. If the calculated value is much greater than the critical value of the determined significance level, indicating that the probability of occurrence of the F value is less than 0.05, the null hypothesis can be rejected. It can be said that the average of different groups is between Statistically speaking, at least one pair with significant differences is the most appropriate experimental control, and it can also be concluded that the independent variable has a significant effect on the dependent variable.

(6) Display variance analysis table

The calculation results of the above steps can be summarized into a variance analysis table.