Question

The F distribution differs from the t distribution is all of these ways except ?

Answer 1

• The t distribution differs from the F distribution :

BASIS FOR COMPARISON	T-TEST	F-TEST
Meaning	T-test is a univariate hypothesis test, that is applied when standard deviation is not known and the sample size is small.	F-test is statistical test, that determines the equality of the variances of the two normal populations.
Test statistic	T-statistic follows Student t-distribution, under null hypothesis.	F-statistic follows Snedecor f-distribution, under null hypothesis.
Application	Comparing the means of two populations.	Comparing two population variances

• Key Differences Between T-test and F-test

The difference between t-test and f-test can be drawn clearly on the following grounds:

1. A univariate hypothesis test that is applied when the standard deviation is not known and the sample size is small is t-test. On the other hand, a statistical test, which determines the equality of the variances of the two normal data sets, is known as f-test.
2. The t-test is based on T-statistic follows Student t-distribution, under the null hypothesis. Conversely, the basis of the f-test is F-statistic follows Snedecor f-distribution, under the null hypothesis.
3. The t-test is used to compare the means of two populations. In contrast, f-test is used to compare two population variances.

The p-value for the t-test is the probability of recording a t-value as far from zero, and this equals the probability of getting as large an F-ratio as the one evaluated from the data.