# 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.

Analyze > Compare Means > One-Way ANOVA...

2. Select one or more dependent variables.
3. 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.