Comparison of the means of two paired samples The z statistic follows a normal distribution. The user can enter this value or estimate it from the data (this is offered for teaching purposes only). T = (µ1 - µ2 -D) / (√s1²/n1 + s2²/n2) z-Testįor the z-test, the variance s² of the population is presumed to be known. If we consider that the variances are different, the statistic is given by: The t statistic follows a Student distribution with n1+n2-2 degrees of freedom. The test statistic is therefore given by:
Where s1 is the standard deviation of the first sample (group) and s2 is the standard deviation of the second sample. If we consider that the two samples have the same variance, the common variance is estimated by: XLSTAT gives the option of using Fisher's F test to test the null hypothesis of equality of the variances of the groups (samples) and to use the result of the test in the subsequent calculations. The use of Student's t test requires a decision to be taken beforehand on whether variances of the samples are to be considered equal or not. The z test if the true variance s² of the population is known.Student's t test if the true variance of the populations from which the samples are extracted is unknown.Let D be the assumed difference between the means (D is 0 when equality is assumed).Īs for the z and t tests on a sample, we use: Take a second sample S2, independent of S1 comprising n2 observations, of mean µ2 and variance s2². Take a sample S1 comprising n1 observations, of mean µ1 and variance s1². Comparison of the means of two independent samples The t and z tests are known as parametric because the assumption is made that the samples are normally distributed. A distinction is made between independent samples or paired samples. The calculation method differs according to the nature of the samples. These two tests are used to test the null hypothesis of equality of the means of two groups (samples).
Parametric t-tests and z-tests are used to compare the means of two samples. Display dominance diagrams to make a visual comparison of the samples.Use an F-test to test the equality of variances and help you choose between the t-test and the z-test.Choose the Monte-Carlo method or the asymptotic p-value method for the computation of the p-value.Choose between three different alternative hypotheses.Run a two-sample test for independent or paired samples.XLSTAT provides a complete and flexible two-sample t-tests and z-tests feature that proposes several standard and advanced options that will let you gain a deep insight on your data: These methods are widely used when it comes to inferential statistics and enable to test a general hypothesis called the null hypothesis. Two-sample t-test and z-test are popular parametric tests in statistics.
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