# F-Test

F- test is generally known as the arcane ratio test and it is used mostly in  context of analysis of variance. This technique was developed by Prof.Fisher. Prof. Fisher developed this test on the basis of agricultural experiment.

For test of hypothesis of equality among several sample means. The F-test is considered to be more appropriate. Moreover in the case of F-Test there is no assumption of equality of variances as it was in the case of t-test for testing the equality of the means of two samples.

F-test initially was used to verify the hypothesis of equality between two variances. In fact F-Test is the test of significance concerning two sample variances. It is based on F-Test.

Assumptions :

• Population should be normal.
• Observations are independent.
• There is no measurement error.
• Number of observations must be less then 30.

F- Ratio is calculated with the help of following formula :

$$F\; \left( \mbox{C}al \right)\; =\; \frac{L\arg e\; Variance}{\mbox{S}mall\; Variance}$$

$$F\; \left( \mbox{C}al \right)\; =\; \frac{\mbox{S}_{1}^{2}}{\mbox{S}_{2}^{2}}$$

Where S12 is large variance

Where S22 is large variance

$$\mbox{S}_{1}^{2}=\; \frac{\sum_{}^{}{x_{i}^{2}}}{n_{1}-\; 1}$$   and   $$\mbox{S}_{2}^{2}=\; \frac{\sum_{}^{}{x_{i}^{2}}}{n_{2}-\; 1}$$

If F (Tab) > F (Cal) then variance are equal and If F (Tab) < F (Cal) then variance are unequal.

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