Identifying Statistically Significant Differences: The F-Test

The F-test is used to compare two sample variances to each other or compare the sample variance to the population variance. It is used to decide whether an indeterminate error can explain the difference in their values. The underlying assumptions that allow the use of the F-test include the data set or sets are normally distributed, and the data sets are independent of each other. The test statistic F is calculated by dividing one variance by another. In other words, the square of one standard deviation by the square of the other. To obtain a value of one or greater than one as the result of the quotient, the larger value is always divided by the smaller value.

The null hypothesis of the F-test states that the ratio is equal to 1. After calculating the test statistic, it is compared to the tabulated critical F values at a chosen confidence level and the appropriate degree of freedom. The null hypothesis is rejected if the test statistic F is smaller than the tabulated F value. In that case, the difference from the desired value of unity–if any–is justified by an indeterminate error, and we state that the variations are not significantly different.