# Means

This feature requires the Statistics Base option.

The Means procedure calculates subgroup means and related univariate statistics for dependent variables within categories of one or more independent variables. Optionally, you can obtain a one-way analysis of variance, eta, and tests for linearity.

**Example.** Measure the average amount of fat absorbed by
three different types of cooking oil, and perform a one-way analysis
of variance to see whether the means differ.

**Statistics.** Sum, number of cases, mean, median, grouped
median, standard error of the mean, minimum, maximum, range, variable
value of the first category of the grouping variable, variable value
of the last category of the grouping variable, standard deviation,
variance, kurtosis, standard error of kurtosis, skewness, standard
error of skewness, percentage of total sum, percentage of total *N*,
percentage of sum in, percentage of *N* in, geometric mean, and
harmonic mean. Options include analysis of variance, eta, eta squared,
and tests for linearity *R* and *R* ^{2}.

Means Data Considerations

**Data.** The dependent variables are quantitative, and the
independent variables are categorical. The values of categorical variables
can be numeric or string.

**Assumptions.** Some of the optional subgroup statistics,
such as the mean and standard deviation, are based on normal theory
and are appropriate for quantitative variables with symmetric distributions.
Robust statistics, such as the median, are appropriate for quantitative
variables that may or may not meet the assumption of normality. Analysis
of variance is robust to departures from normality, but the data in
each cell should be symmetric. Analysis of variance also assumes that
the groups come from populations with equal variances. To test this
assumption, use Levene's homogeneity-of-variance test, available in
the One-Way ANOVA procedure.

To Obtain Subgroup Means

This feature requires the Statistics Base option.

- From the menus choose:
- Select one or more dependent variables.
- Use one of the following methods to select categorical independent
variables:
- Select one or more independent variables. Separate results are displayed for each independent variable.
- Select one or more layers of independent variables. Each layer further subdivides the sample. If you have one independent variable in Layer 1 and one independent variable in Layer 2, the results are displayed in one crossed table, as opposed to separate tables for each independent variable.

- Optionally, click Options for optional
statistics, an analysis of variance table, eta, eta squared,
*R*, and*R*^{2}.

This procedure pastes MEANS command syntax.