Chi-Square Test Calculator for Variance

one varaince test tutorial

Target: To check if the assumed σ20 is statistically correct, based on a sample varaince S2

Example1: A farmer calculated last year the varaince of the apples' weight in his apple orchard σ20 equals 2 kg2, based on big sample
Current year he checked a small sample of apples and the sample varaince S2 equals 3 kg2
Was the variance of the apple's weight changed this year?


Normal DistributionThe population's distribution is Normal
standard deviationYou assume you know the population variance ( σ220)

Required Sample Data

varianceSample variance of the population
sample sizeSample size of the population

Enter input data and then press "Calculate test" button to get the results


H0: σ2 ≥ σ20H0: σ2 = σ20H0: σ2 ≤ σ20
H1: σ2 < σ20H1: σ2 ≠ σ20H1: σ2 > σ20

Test statistic

Chi2 statistic

χ² distribution

Normal distribution left tailed Normal distribution two tailed Normal distribution right tailed

Test calculation

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

tails: the default is right tailed test (usually you worried only if the standard deviation is bigger then the expected one)

Statistic Data

α:Significant level (0-1), maximum chance allowed rejecting H0 while H0 is correct (Type1 Error)
Outliers:It is not recommended to exclude outliers unless you know the reasons
or or enter summarized data (x, n, σ, S) in Group form

Enter sample data

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

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

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 column includes the header, and paste below.

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


n:Sample size
σ0:Standard deviation
S:Sample Standard deviation
Normality pval:Shapiro Wilk test
Outlierscount: ,based on the Tukey's fences method, k=1.5

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