The Gnumeric Manual
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# 14.14. Comparing Means of 2 Populations

Gnumeric provides 4 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 14-49).

Figure 14-49. `t`- 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.

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

Figure 14-50. `t`-Test (Paired) Tool Dialog Options

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

Example 14-14. Using the `t`-Test (Paired) Tool

See Figure 14-51 for an example of a completed dialog and Figure 14-52 for the corresponding output.

Figure 14-51. `t`-Test (Paired) Example Data

Figure 14-52. Output from the `t`-Test (Paired) Tool

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

Figure 14-53. `t`-Test (Equal Variances) Tool Dialog Options

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

Example 14-15. Using the `t`-Test (Unknown but Equal Variances) Tool

See Figure 14-54 for an example of a completed dialog and Figure 14-55 for the corresponding output.

Figure 14-54. `t`-Test (Unknown but Equal Variances) Example Data

Figure 14-55. Output from the `t`-Test (Unknown but Equal Variances) Tool

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

Figure 14-56. `t`-Test (Unknown and Unequal Variances) Tool Dialog Options

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

Example 14-16. Using the `t`-Test (Unknown and Unequal Variances) Tool

See Figure 14-57 for an example of a completed dialog and Figure 14-58 for the corresponding output.

Figure 14-57. `t`-Test (Unknown and Unequal Variances) Example Data

Figure 14-58. Output from the `t`-Test (Unknown and Unequal Variances) Tool

## 14.14.4. `z`-Test: Two Samples for Means Tool

Figure 14-59. `z`-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 "OK", Gnumeric will test whether the mean of the difference between the paired variables is equal to the given hypothesized mean difference.

Example 14-17. Using the `z`-Test Tool

See Figure 14-60 for an example of a completed dialog and Figure 14-61 for the corresponding output.

Figure 14-60. `z`-Test Example Data

Figure 14-61. Output from the `z`-Test Tool

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