10.15. Comparing Means of 2 Populations

10.15.1. t-Test: Paired Two Sample for Means Tool

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10.15.2. t-Test: Two-Sample Assuming Equal Variances Tool

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10.15.3. t-Test: Two-Sample Assuming Unequal Variances Tool

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10.15.4. z-Test: Two Samples for Means Tool

Use the z-Test tool to analyze whether the means of two variables are significantly different or not. The values of the first variable are specified in the "Variable 1 Range:" entry. Correspondingly, the values of the second variable are given in the "Variable 2 Range:" entry. You should also specify the variances of both variables in the "Variable 1 Variance (known):" and "Variable 2 Variance (known):" entries.

If you want to test whether the difference of the means is larger than a given value, specify also the "Hypothesized Mean Difference:" entry. "Alpha:" entry specifies the level of significance which is by default 95%.

If the output is printed into a range, it should have at least three columns and ten rows.

The results are given in a table. The tool calculates and prints the mean, known variance, and count of observations of both variables. It also calculates the z-value, the one-tailed and two-tailed probability for the z-value, and the z Critical value for one-tailed and two-tailed tests. The one-tailed probability for the z-value ("P(Z<=z) one-tail" row) describes the risk of making a Type I error of one-tailed test.