The f-test is named in honour of the great statistician R.A. Fisher. The object of the f-test is to find out whether the two independent estimates of population variance differ significantly, or whether the two samples may be regarded as drawn from the normal populations having the same variance. For carrying out the test of significance, we calculate the ratio F. F is defined as:

The calculated value of F is compared with the table value for u₁ and u₂ at 5% or 1% level of significance. If calculated value of F is greater than the table value then the F ratio is considered significant and the null hypothesis is rejected. On the other hand, if the calculated value of F is less than the table value the null hypothesis is accepted and it is inferred that both the samples have come from the population having same variance.

Since F test is based on the ratio of two variances, it is also known as the variance ratio test. The ratio of two variances follows a distribution called the f distribution named after the famous statistician R.A. Fisher.

Assumptions in F-test: The F test is based on the following assumptions:

Normality, the values in each group are normally distributed,

Homogeneity, the variance within each group should be equal for all groups (σ₁² = σ₂² = ……..= σ_c²) this assumption is needed in order to combine or pool the variance within the groups into a single within groups source of variation.

Independence of error. It states that the error (variation of each value around its own group mean) should be independent for each value.

Some of its main topics are:

Variance analysis
Variance analysis-techniques
Irregular variations
f-test applications
Inverse interpolation
Extrapolation
Data coding
Semi averages method
Ratio-to-trend method
Trend origin shifting
Seasonal index-uses

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