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# Analysis of Variance

## ANOVA: Single Factor Tool

Use this tool to perform a single factor analysis of the variances of given variables. The variables are specified by the "`Input Range:`" entry. The given range can be grouped into the variables either by columns, by rows or by areas. The "`Alpha:`" entry specifies the significance level which is by default 5%.

If the first row or first column of the given range, or the first field of each area contains labels, select the "Labels " option. The names of the variables will be included in the output table.

The results of this analysis of variance are presented in a standard ANOVA table. The "`F critical`" value is the largest value of F that is statistically significant using the given significance level ("`Alpha`").

This tool also calculates the count, sum, average, and the variance of each variable.

Figure 4. 1-factor ANOVA Dialog and Example Data

Example 1. Using the single factor ANOVA

See Figure 4 for an example of a completed dialog and Figure 5 for the corresponding output.

Figure 5. Output From a 1-factor ANOVA

## ANOVA: Two-Factor Tool

`Gnumeric` can perform two factor fixed effects ANOVAs with and without replication. The same dialog is used and the appropriate tool is selected depending on whether the number of rows per sample is 1 or larger than 1.

### ANOVA: Two-Factor Without Replication Tool

If the number of rows per sample is given as 1, `Gnumeric` performs a two factor fixed effects ANOVA without replication. Each column of the input range is interpreted as a level of the first factor while each row is interpreted as a level of the second factor.

The first row and column of the range may contain labels for these levels. In this case the "Labels" option should be selected.

The "`Alpha:`" entry specifies the significance level which is by default 5%.

Example 2. Using the 2-factor ANOVA Without Replication Tool

See Figure 6 for an example of a completed dialog and Figure 7 for the corresponding output.

Figure 6. 2-factor ANOVA Without Replication Dialog

Figure 7. Output From a 2-factor ANOVA Without Replication

### ANOVA: Two-Factor With Replication Tool

If the number of rows per sample is larger than 1, `Gnumeric` performs a two factor fixed effects ANOVA with replication. Each column of the input range is interpreted as a level of the first factor while groups of rows (the number of rows in each group given by the "`number of rows per sample`" value) are interpreted as levels of the second factor.

The first row and column of the range may contain labels for these levels. In this case the "Labels" option should be selected.

The "`Alpha:`" entry specifies the significance level which is by default 5%.

See Figure 8 for an example of a completed dialog and Figure 9 for the corresponding output.

Figure 8. 2-factor ANOVA With Replication Dialog

Figure 9. Output From a 2-factor ANOVA With Replication

`Gnumeric` will estimate missing values for each level combination as the mean of the existing values in that combination. The degrees of freedom are adjusted appropriately.

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