The Gnumeric Manual
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# 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 49).

Figure 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.

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

Figure 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. Using the `t`-Test (Paired) Tool

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Figure 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 17. Using the `z`-Test Tool

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

Figure 60. `z`-Test Example Data

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

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