Question

Please explain the general concern that F (as reported for every regression) and t deal with, how they are similar, and how they are different.

Answer 1

Similarities:

Let us first understand the meaning of F ratio and t stat

F ratio is given as

Which is ratio of mean square between the sample and mean square with in sample

It is used to find out whether the variances in two independent samples are equal

Like t-values&  the F ratio has critical values that must be exceeded before we can reject our statistical null hypothesis.

T stat formula is given as below

Assumptions of t stastic is:

Random sampling

Normality of data distribution

Adequacy of sample size and equality of variance in standard deviation

It is also known as analysis of means

The F-distribution arises frequently as the null distribution of a test statistic, especially in likelihood-ratio tests,

perhaps most observable in the analysis of variance

It is also known as analysis of variance

Differences( between F test and T stat):

1)

T-test is a univariate hypothesis test, that is applied when standard deviation is not known and the sample size is smallT-test is a univariate hypothesis test, that is applied when standard deviation is not known and the sample size is small

while F-test is statistical test, that determines the equality of the variances of the two normal populations.

2)

t-test is used to compare two related samples, F-test is used to test the equality of two populations.

3)

T test is Comparing the means of two populations.

F Test Comparing two population variances