1.14:
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.
1.14:
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.