This dialog is activated by selecting the **One Sample t-Test...** command from the Statistics -> Hypothesis Testing -> menu.

A t-test is any statistical hypothesis test in which the test statistic follows a Student's t-distribution under the null hypothesis. It is assumed that the data is normally distributed. The Wikipedia article on the Student's t-test makes for excellent reading on this topic.

The one-sample form of a t-Test compares the mean (m) of a population to a m_{test} value specified in the null hypothesis.
By default QtiPlot performs a two-tailed test, the default alternate hypothesis being that the mean of the population and the
m_{test} values are different (m <> m_{test}). It is also possible to perform an upper-tailed test by choosing the alternate hypothesis
that m > m_{test} or a lower-tailed test (m < m_{test}).

This test uses the statistic t = N^{1/2}(m-m_{test})/SD, where N is the size of the population and
SD is the standard deviation, SD = [Σ(x_{i} - m)^{2}/(N-1)]^{1/2}.

The test statistic is used to compute a probability (*P value*).
For a lower-tailed test the probability is calculated using the formula *p = tcdf(t, DoF)*, where the *tcdf* function
calculates the lower tail of the cumulative distribution function for the
Student's t-distribution with *DoF = N-1*
degrees of freedom. For an upper-tailed test, the probability is calculated using the formula *p = 1-tcdf(t, DoF)*.
For a two-tailed test the probability is calculated using the formulas *p = 2tcdf(t, DoF)* if tcdf(t, DoF) < 0.5 and
*p = 2[1-tcdf(t, 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.