Identifying Statistically Significant Differences: The F-Test

The F-test checks if the difference between two variances is too large to be explained by an indeterminate error. It compares the variance of a sample and that of a population or the variances of two samples.

The F-test is based on the null hypothesis, which states that the two variances compared are equal.

The test statistic F is evaluated as the quotient of variances, where the variance is expressed as the square of the standard deviation.

The variance with a larger value is placed in the numerator, making F greater than or equal to one always.

The F value should be one for the null hypothesis to be true. It becomes greater than one due to indeterminate and determinate errors.

For a one-tailed test, the obtained F value is compared to the tabulated F value at a chosen confidence level and degree of freedom. The null hypothesis is rejected when the obtained F value is lower than the tabulated F value in a lower-one-tailed test or greater in an upper-one-tailed test.