Question

What is an F- test?

Answer 1

Hint: For solving this question you should know about F-test. An “F- test” is a catch all term of any test that uses the F- distribution. It is generally used as a comparison of two variances. And this test is also used in regression analysis, and how test and scheffe test.

Complete step-by-step solution:
According to our question it is asked to explain about the F- test.
To calculate the F- value of F- test we use the formula
F Value = \[\dfrac{\text{Larger sample Variance}}{\text{Smaller Sample Variance}}=\dfrac{\sigma _{1}^{2}}{\sigma _{2}^{2}}\]
The F- test is a test which uses F-distribution. F- value is a value on the F-distribution. Various statistical tests generate a F-value. And this F-Value can be used to determine whether the test is statistically significant.
In order to compare two variances, one has to calculate the ratio of the two variances, which is known as F-Value.
If we perform the F-test then we have to follow these steps: -
Step 1: Firstly, frame the null and alternate hypothesis. The null hypothesis assumes that the variances are equal. \[{{H}_{0}}:\sigma _{1}^{2}=\sigma _{2}^{2}\]. And the alternate hypothesis states that the variances are unequal. \[{{H}_{1}}:\sigma _{1}^{2}\ne \sigma _{2}^{2}\]. Here, \[\sigma _{1}^{2}\] & \[\sigma _{2}^{2}\] are symbols of variances.
Step 2: Calculate the test statistic (F - distribution), i.e. \[\sigma _{1}^{2}/\sigma _{2}^{2}\] where \[\sigma _{1}^{2}\] assume to be larger and \[\sigma _{2}^{2}\] assume to be larger and \[\sigma _{2}^{2}\] to be smaller sample variance.
Step 3: Calculate the degrees of freedom. Degree of freedom \[\left( d{{f}_{2}} \right)={{n}_{2}}-1\], where \[{{n}_{1}}\] and \[{{n}_{2}}\] are sample sizes.
Step 4: Look at the F-value in the F-table. For finding the right critical value divide alpha by 2. Thus, the F-value is found.
In the table \[D{{F}_{1}}\] is read across in the top row. \[D{{F}_{2}}\] read down the first column.
Step 5 : Compare the F-static obtained in step 2 with the critical value which we obtained in step 4. If the F-static is greater than the critical value at the required level of significance. We reject the null hypothesis. And if the F-statistic is less than the critical value then we can’t reject the null hypothesis.

Note: The F-test is an easy process but we have to do it step by step and always do it in the same manner because all steps are dependent on each other. So, we can’t leave at any step. And if all steps are covered then compare and get your answer.