# Comparing Means of Two Populations

Gnumeric provides four similar tools to test whether the difference of two population means is equal to a hypothesized value. These four tools use the same dialog (see Figure 8-86).

Figure 8-86t- and z-Test Tool Dialog

Depending on the options settings, the appropriate test will be performed. The entries in the Input, Test, and Output frames are independent from the specific test.

Enter the first variable in the Variable 1 Range entry and the second variable in the Variable 2 Range entry.

Enter the hypothesized difference between the population means in the Hypothesized Mean Difference entry, which has a default of 0. Enter the significance level in the Alpha entry, which has a default of 5 %.

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

There are up to three possible options that can be selected:

Paired versus Unpaired

If the variables are dependent (or paired) select the Paired option.

Known versus Unknown

For unpaired or independent variables, the population variances may be known or unknown. In the latter case they will be estimated using the sample variances. Select the Known option if you in fact know the population variances prior to collecting the sample.

Equal versus Unequal

For paired variables with unknown population variances, we may either assume that the population variances are equal or not. If the population variances are assumed to be equal, Gnumeric will estimate the common variance by pooling the sample variances. Select the Equal option to assume that the population variances are equal.

## 8.6.1.1. t-Test: Paired Two Sample for Means Tool

Figure 8-87t-Test (Paired) Tool Dialog Options

For paired variables, when you click on , Gnumeric will test whether the mean of the difference between the paired variables is equal to the given hypothesized mean difference.

Example 8-19Using the t-Test (Paired) Tool

See Figure 8-88 for an example of a completed dialog and Figure 8-89 for the corresponding output.

Figure 8-88t-Test (Paired) Example Data
Figure 8-89Output from the t-Test (Paired) Tool

## 8.6.1.2. t-Test: Two-Sample Assuming Equal Variances Tool

Figure 8-90t-Test (Equal Variances) Tool Dialog Options

For unpaired variables with unknown but assumed equal population variances, when you click on , Gnumeric will test whether the mean of the difference between the paired variables is equal to the given hypothesized mean difference.

Example 8-20Using the t-Test (Unknown but Equal Variances) Tool

See Figure 8-91 for an example of a completed dialog and Figure 8-92 for the corresponding output.

Figure 8-91t-Test (Unknown but Equal Variances) Example Data
Figure 8-92Output from the t-Test (Unknown but Equal Variances) Tool

## 8.6.1.3. t-Test: Two-Sample Assuming Unequal Variances Tool

Figure 8-93t-Test (Unknown and Unequal Variances) Tool Dialog Options

For unpaired variables with unknown and assumed unequal population variances, when you click on , Gnumeric will test whether the mean of the difference between the paired variables is equal to the given hypothesized mean difference.

Example 8-21Using the t-Test (Unknown and Unequal Variances) Tool

See Figure 8-94 for an example of a completed dialog and Figure 8-95 for the corresponding output.

Figure 8-94t-Test (Unknown and Unequal Variances) Example Data
Figure 8-95Output from the t-Test (Unknown and Unequal Variances) Tool

## 8.6.1.4. z-Test: Two Samples for Means Tool

Figure 8-96z-Test Tool Dialog Options

For unpaired variables with known population variances, enter those variances in the Variable 1 Pop. Variance and Variable 2 Pop. Variance entries. When you click on , Gnumeric will test whether the mean of the difference between the paired variables is equal to the given hypothesized mean difference.

Example 8-22Using the z-Test Tool

See Figure 8-97 for an example of a completed dialog and Figure 8-98 for the corresponding output.

Figure 8-97z-Test Example Data
Figure 8-98Output from the z-Test Tool