F-Test

By economicslive Mathematical Economics and Econometrics No Comments

F- test is generally known as the variance 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. 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-distribution.

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 is ${\mbox{S}_{1}^{2}}$ large variance

Where ${\mbox{S}_{2}^{2}}$ 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.

Written by economicslive

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