# One-Way ANOVA

This feature requires the Statistics Base option.

The One-Way ANOVA procedure produces a one-way analysis of variance for a quantitative dependent
variable by a single factor (independent) variable and estimates the effect size in one-way ANOVA.
Analysis of variance is used to test the hypothesis that several means are equal. This technique is
an extension of the two-sample *t* test.

In addition to determining that differences exist among the means, you may want to know which
means differ. There are two types of tests for comparing means: a priori contrasts and post hoc
tests. Contrasts are tests set up *before* running the experiment, and post hoc tests are run
*after* the experiment has been conducted. You can also test for trends across categories.

- Example
- Doughnuts absorb fat in various amounts when they are cooked. An experiment is set up involving three types of fat: peanut oil, corn oil, and lard. Peanut oil and corn oil are unsaturated fats, and lard is a saturated fat. Along with determining whether the amount of fat absorbed depends on the type of fat used, you could set up an a priori contrast to determine whether the amount of fat absorption differs for saturated and unsaturated fats.
- Statistics
- For each group: number of cases, mean, standard deviation, standard error of
the mean, minimum, maximum, 95% confidence interval for the mean, and the estimation of the effect
size for in a one-way ANOVA. Levene tests for homogeneity of variance, analysis-of-variance table
and robust tests of the equality of means for each dependent variable, user-specified a priori
contrasts, and post hoc range tests and multiple comparisons: Bonferroni, Sidak, Tukey's honestly
significant difference, Hochberg's GT2, Gabriel, Dunnett, Ryan-Einot-Gabriel-Welsch
*F*test (R-E-G-W*F*), Ryan-Einot-Gabriel-Welsch range test (R-E-G-W*Q*), Tamhane's T2, Dunnett's T3, Games-Howell, Dunnett's*C*, Duncan's multiple range test, Student-Newman-Keuls (S-N-K), Tukey's*b*, Waller-Duncan, Scheffé, and least-significant difference.

## Data considerations

- Data
- The dependent variable should be quantitative (interval level of measurement).
- Assumptions
- Each group is an independent random sample from a normal population. Analysis of variance is robust to departures from normality, although the data should be symmetric. The groups should come from populations with equal variances. To test this assumption, use Levene's homogeneity-of-variance test.

## Obtaining a One-Way analysis of variance

This feature requires the Statistics Base option.

- From the menus choose:
- Select one or more dependent variables.
- Select a single independent factor variable.

Optionally, you can:

- Select Estimate effect size for overall tests to control the calculation of the effect size for the overall test. When selected, the “ANOVA Effect Sizes” table displays in the output.

- Click Contrasts to partition the between-groups sums of squares into trend components or specify a priori contrasts.
- Click Post Hoc to use post hoc range tests and pairwise multiple comparisons to determine which means differ.
- Click Options to control the treatment of missing data and the level of the confidence interval.
- Click Bootstrap for deriving robust estimates of standard errors and confidence intervals for estimates such as the mean, median, proportion, odds ratio, correlation coefficient or regression coefficient.

This procedure pastes ONEWAY command syntax.