Understanding ANOVA Table and F-Statistics in CFA
This is about the definition of F-statistics, F-value, or F-test statistics - you can hear all kinds of expressions about the same idea, so don't get too confused by it. This quiz is about the relationship between ANOVA table, how to calculate F-value, and how to check the F-value table.
Let me quickly give you a review of what an ANOVA table is. If this is an ANOVA table, of course, you will get degrees of freedom. You always need to consider degrees of freedom in the field of statistics, or you will get the wrong answer or some biased answer rather than the correct answer.
When you have the ANOVA table, you will have mainly three subjects to consider: one is the regression, the other is residual, and of course, you have the total, which is the sum of regression and residual. You add all that up to get the total.
Normally, you have the degrees of freedom and the SS (Sum of Squares). As the name suggests, you need to add all that up and square it. This is just an intermediate result, not the final result. What we need is the Mean Sum of Squares, which means you take the sum of squares and divide it by the number of subjects you are dealing with to get the mean.
Once we add different subjects, we get different means of the squares: Mean Sum of Square of Regression (MSR) and Mean Sum of Square of Residual (MSE), sometimes called residual error, which is the data we can't get.
Once you calculate the MSR and MSE, you can calculate F-Statistics directly. From the definition point of view, F-value equals the larger number divided by the smaller number. The larger number we deal with is the Mean Sum of Regression because you're doing a regression analysis, and regression will be a big part, while residual, as suggested, is a very small part of it.
If you're not given MSR and MSE directly, you can calculate them. For MSR, when it comes to regression, the important variable we need to consider is K (number of variables). We divide SSR by K. For residual, if there is a total degree of freedom n, we subtract K because we already used K in regression, and we minus 1 - that's how we get the MSE.
Once you get the F-value, you will check that against the F-value table to find the critical value. You find your denominator degrees of freedom and numerator degrees of freedom and locate the exact critical value (CV). If the F-value is bigger than the critical value, you can know that F is significant. This is how we do the significance test of whether this whole regression is as significant as it claims to be, just like we do the normal test but using the significance of F and t-test.