Levene's Calculator

Equality Of Variances

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

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Enter sample data from excel


You may copy the data from Excel, Google sheets or any tool that separate the data with Tab and Line Feed. Copy the data, one block of consecutive columns includes the header, and paste. Click to see example: example from excel
Empty cells or non-numeric cells will be ignored


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R code.
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Tukey HSD / Tukey Kramer

Target: To check if the difference between the variances of two or more groups is significant, using a sample data
The Levene's tests perform an ANOVA test over the absolute deviations from each group's average or the absolute deviations from each group's median.

When performing ANOVA test, we try to determine if the difference between the averages of the absolute residuals reflects a real difference between the groups, or is due to the random noise inside each group. The F statistic represents the ratio of the variance between the groups and the variance inside the groups. Unlike many other statistic tests, the smaller the F statistic the more likely the averages are equal.

Right-tailed F test, for ANOVA test you can use only the right tail. Why?
Hypotheses
H0: σ1 = .. = σk
H1: not(σ1 = .. = σk)
Test statistic
anova statistic
F distribution
F distribution right tailed

Assumptions

IndependentIndependent samples.
Normal DistributionNormal population distribution or symmetrical distribution.

Required Sample Data

averageSample data from all compared groups.

Parameters

k - Number of groups.
ni - Sample side of group i.
n - Overall sample side, includes all the groups (Σni, i=1 to k).
xi - Average of group i.
x - Overall average (Σxi,j / n, i=1 to k, j=1 to ni).
Si - Standard deviation of group i.

Results calculations

SourceDegrees of FreedomSum of SquaresMean SquareF statisticp-value
Groups
(between groups)
k - 1averageMSG = SSG / (k - 1)F = MSG / MSEP(x > F)
Error
(within groups)
n - kaverageMSE = SSE / (n - k)
Totaln - 1SS(total) = SSG + SSESample Variance = SS(total) / (n - 1)

R Code

The following R code should produce the same results