Question

What do you think is the important factor for calculating the F statistic when analyzing data?​

Answer 1

F-Test

The F ratio is the ratio of Mean square column (MSC) to the Mean square error (MSE).

F test is used to find out the total variance comes from the variance between samples and variance within samples.

F=(Meansquarecolumn)or(SSC/Degreesoffreedom) / (MeanSquareerror) or(SSE/Degreesoffreedom)

The numerator degrees of freedom is k-1 i.e. samples -1

The numerator degrees of freedom is n-k i.e. observations –samples.

The larger the ratio, the more likely it is the groups have different means.

MSC

The Mean square column is the ratio of Variance between sample to the (k-1) degrees of freedom.

MSC = SSC / k−1

The Degrees of freedom is (k-1) i.e. Number of samples(k) -1.

MSE

The Mean square error is the ratio of variance within sample to the (n-k) degrees of freedom.

MSE = SSE / n−k

The Degrees of Freedom is (n-k) i.e. Total number of observations(n) –Number of Samples(k).

What is an F Statistic?

An F statistic is a value you get when you run an ANOVA test or a regression analysis to find out if the means between two populations are significantly different. It’s similar to a T statistic from a T-Test,A-T test will tell you if a single variable is statistically significant and an F test will tell you if a group of variables are jointly significant.

The F value in regression is the result of a test where the null hypothesis is that all of the regression coefficients are equal to zero. In other words, the model has no predictive capability. Basically, the f-test compares your model with zero predictor variables (the intercept only model), and decides whether your added coefficients improved the model. If you get a significant result, then whatever coefficients you included in your model improved the model’s fit.