How to calculate mean square in anova table

Answer 1

To calculate mean square in the ANOVA table, you need to follow these steps:

1. First, calculate the sum of squares (SS) for each factor and the error term. The formula to calculate SS is:
- SS = Σ(xi - x̄)^2, where xi is the value of each observation and x̄ is the mean of all observations.

2. Next, determine the degrees of freedom (df) for each factor and the error term. The df for a factor is the number of levels of that factor minus one. The df for the error term is the total number of observations minus the total number of factors.

3. Calculate the mean square (MS) for each factor by dividing the SS by its respective df:
- MS = SS / df

4. Finally, compare the mean square values to determine whether a factor is statistically significant. To do this, divide the mean square of each factor by the mean square of the error term:
- F ratio = MS factor / MS error

If the F ratio is greater than the critical value at a given significance level, then the factor is considered statistically significant.