9.14. Comparing Means of 2 Populations

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

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

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

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9.14.4. 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 wheater 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.