The Variance Ratio Test – F – Test

The objects of the F-test is to discover whether the two independent estimates of population variance differ significantly, or whether the two samples may be regarded as drawn from the normal population having the same variance. For carrying out the test of significance. We calculate the ratio F. F is defined as:


n1 and n2 refer to the number of observations of the sample I and sample II respectively.
If the calculated value F exceeds F0.005 for (n1 – 1), (n2 – 1) d.f., we say that the ratio is significant at 5 % level. If F < F0.05 we say that the same could have come from two normal populations with the same variance.
It should be noted that the numerator is always the greater variance.
At the end of the text two tables are given – one giving the 5 % points of F and another giving the 1% points F for υ1 and υ2. υ1 is the number of degrees of freedom of the variance in the denominator.
The tables give the values of F which could be obtained in random sampling from a normal population at the stated probability levels and degrees of freedom. The test is applicable even when the distribution of population departs considerably from the normal type.   

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