F Test for Variances Calculator

Two population variances comparison
H0: σ1 = σ2
H1: σ1 < > σ2
Test statistic
Z statistic
F distribution
F distribution left tailed F distribution two tailed F distribution right tailed
Test parameters

If you enter raw data, the tool will run the Shapiro-Wilk normality test and calculate outliers, as part of the test calculation.

The default is two tailed test.
Significance level (0-1), maximum chance allowed rejecting H0 while H0 is correct (Type1 Error)
It is not recommended to exclude outliers unless you know the reasons
or or enter summarized data ( n, S) below

Enter sample data

Header: You may change groups' name to the real names.
Data: When entering data, press Enter after each value.

The tool will not count empty cells or non-numeric cells.

Enter sample data

You may copy data from Excel, Google sheets or any tool that separate data with Tab and Line Feed.
Copy the data, one block of 2 consecutive columns includes the header, and paste below.

Copy the data,

It is okay to leave empty cells, empty cells or non numeric cells won't be counted

Sample data

The population's name.
Sample size.
Group1's sample standard deviation.
Shapiro Wilk test p-value
count: ,based on the Tukey's fences method, k=1.5
The population's name
Sample size
Group2's sample standard deviation.
Shapiro Wilk test p-value
count: ,based on the Tukey's fences method, k=1.5


Target: To check if the difference between the population's standard deviations of two groups is significance, using sample data
Example1: A man of average hight is expected to be 10cm taller than a woman of average hight (d=10)
Example2: The average weight of an apple grown in field 1 is expected to be equal in weight to the average apple grown in field 2 (d=0)


Normal DistributionNormal distribution - the F test for variances is very sensitive to the normality assumption.

Required Sample Data

standard deviationS1,S2 -Sample standard deviations of group1 and group2
sample sizen1,n2 - Sample size of group1 and group2

R Code

The following R code should produce the same results:

Currently, there is no direct R function for the two-sample z test.