This dialog is activated by selecting the **Chi-square Test for Variance...** command from the Statistics -> Hypothesis Testing -> menu.
A chi-squared test is any statistical hypothesis test where the sampling distribution of the test statistic is a chi-squared distribution when the null hypothesis is true.
Please visit the Wikipedia article on the Chi-squared test for more details about this statistical test.

The chi-square compares the variance (V) of a population to a V_{test} value specified in the null hypothesis.
By default QtiPlot performs a two-tailed test, the default alternate hypothesis being that the variance of the population and the
V_{test} values are different (V <> V_{test}). It is also possible to perform an upper-tailed test by choosing the alternate hypothesis
that V > V_{test} or a lower-tailed test (V < V_{test}).

This test uses the *Chi-Square* statistic, χ^{2} = (N-1)V/V_{test}, where N is the size of the population.

The test statistic is used to compute a probability (*P value*).
For a lower-tailed test the probability is calculated using the formula p = chi2cdf(χ^{2}, DoF),
where the chi2cdf function calculates the lower tail of the cumulative distribution function for the
chi-squared distribution with *DoF = N-1*
degrees of freedom. For an upper-tailed test, the probability is calculated using the formula p = 1-chi2cdf(χ^{2}, DoF).
For a two-tailed test the probability is calculated using the formulas p = chi2cdf(χ^{2}, DoF)
if chi2cdf(χ^{2}, DoF) < 0.5 and p = 2[1-chi2cdf(χ^{2}, DoF)] otherwise.

The null hypothesis is rejected if the calculated probability is lower than the value of the *Significance Level*.

If the *Confidence Interval(s)* box is checked QtiPlot also computes a confidence interval (*Lower Limit* and
*Upper Limit*) for each user defined level.