Definition. This function returns the test statistics of an f-test. An f-test returns the one-tailed probability that the variances in array1 and array2 are not significantly different.
Arguments
array1 (required). The first array or range of data
array2 (required). The second array or range of data
Note
Arguments can be numbers, names, arrays, or references containing numbers.
If an array or reference argument contains text, logical values, or empty cells, those values are ignored. However, cells with the value 0 are included.
If the number of data points in array1 or array2 is less than 2 or if the variance of array1 or array2 is 0, F.TEST() returns the #DIV/0! error value.
Background. Use this function to determine whether two samples have different variances. For example, given test scores from public and private schools, you can test whether these schools have different levels of test score diversity. You want to know whether the variance of the test scores is different.
F.TEST() calculates the significance level that indicates whether two samples are identical. The question answered by F.TEST() is: Are the two variances of the given samples equal or not?
The calculation of the significance level uses the entire value range of the samples. The values of the first sample are array1, and the values of the second sample are array2. F.TEST() calculates the significance level based on array1 and array2 without calculating the sample variances first.
The calculated significance level is a percentage from 0 through 100. This value indicates the accuracy for statistical hypothesis tests. Often the accuracy is 90 or 95 percent
What does the result returned by F.TEST() mean? If the result for the significance level is 90 percent, the existing random numbers will match in only 100 minus 90 = 10 percent of the cases. This means that the probability that the data are 90 percent significant is 10 percent.
Therefore, a significance of 90 percent doesn’t indicate that the existing data with a probability of 10 percent is random and the probability that a certain fact is true is 90 percent.
Example. The compatibility of a medicine was examined in a clinical study. You have the test results as well as some explanations.
One test group took the normal daily dosage, and the other test group took an increased dosage at the beginning of the study. The goal was to determine whether the increased dosage accelerated the healing process. The duration of treatment was calculated in days.
The null hypothesis indicates that there is no difference in the two test groups regarding the success of treatment. The alternative hypothesis indicates that the second group recovered faster because this method of treatment is more efficient than the usual treatment.
You have to analyze the test results to determine whether the null hypothesis can be accepted or has to be rejected. Because you weren’t present during the test and don’t have all the background information, you want to calculate the probability that the variances of the two samples are equal by using the F.TEST() function. This means that you want to know the difference in the variances of the test results. What does the result of 0.89 returned by F. TEST(), seen in Figure 12-48, mean?
The result of 89 percent for the significance level means that the existing random numbers will match only in 100 minus 90 = 10 percent of the cases. This means that the probability that the data are 90 percent significant is 10 percent.
The calculation of the significance with F.TEST() indicates a probability of 89 percent that the variances of the two samples are not different. If you calculate the variance for both samples, this result is confirmed.
As you can see in Figure 12-49, the variances for both samples are only slightly different. The result returned by F.TEST() is confirmed with a significance of 89 percent.
