To perform an F-test, we typically use statistical software such as R, Python, Excel, SPSS, etc.
The following examples show how to use each method in practice to compare the standard deviations between the following two datasets that show the exam scores received by students who used two different study methods to prepare for the exam:
One way to compare the standard deviations between the two datasets is to first calculate the variance of each dataset:
Next, we can calculate the ratio of the larger variance to the smaller variance:
Ratio of Variances: 103.41 / 24.21 = 4.27
Since this ratio is greater than 4, we would assume that the variances are not equal.
Thus, we would assume that the standard deviations between the two datasets are not equal.
Another way to compare the standard deviations between the two datasets is to perform an F-test.
Most statistical software is able to perform an F-test, but we will use the following code in R to do so:
#enter exam scores for both groups of students method1 #perform an F-test to determine if the variances are equal var.test(method1, method2) F test to compare two variances data: method1 and method2 F = 4.2714, num df = 14, denom df = 14, p-value = 0.01031 alternative hypothesis: true ratio of variances is not equal to 1 95 percent confidence interval: 1.434049 12.722857 sample estimates: ratio of variances 4.27144
The F-test returns the following results:
Recall that the F-test uses the following hypotheses:
Since the p-value of our test (.01031) is less than .05, we have sufficient evidence to reject the null hypothesis.
We would conclude that the variances are not equal.
Thus, we would conclude that the standard deviations between the two datasets are not equal.
Bonus: You can also use the Statology F-Test for Equal Variances Calculator to perform this F-test.
The following tutorials provide additional information about using standard deviations in statistics:
Hey there. My name is Zach Bobbitt. I have a Masters of Science degree in Applied Statistics and I’ve worked on machine learning algorithms for professional businesses in both healthcare and retail. I’m passionate about statistics, machine learning, and data visualization and I created Statology to be a resource for both students and teachers alike. My goal with this site is to help you learn statistics through using simple terms, plenty of real-world examples, and helpful illustrations.
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