Analysis of Variance (ANOVA) is a hypothesis testing procedure that tests whether two means are significantly different from each other. One-way ANOVA tests the relationship between a numeric variable and a categorical variable.

This article describes how to create a one-way ANOVA table as shown below. The table below shows the pairwise comparison of *Total Spend* grouped by *Household description.*

## Requirements

- Familiarity with the
*Structure*and*Value Attributes*of Variable Sets. - A numeric variable to be used as an outcome (also known as dependent) variable.
- A categorical variable to be used as a predictor.

## Method

- In the
**Anything**menu select**Advanced Analysis > Analysis of Variance > One-Way ANOVA**. - In the
**object inspector**go to the**Inputs**tab. - In the
**Outcome**dropdown select a*numeric*variable*.* - Select the
*categorical*predictor variable from the**Predictor**dropdown. - In the
**Compare**menu select the*contrasts*to be performed.**To mean**- The*post hoc*testing compares the mean of each category to the overall average (i.e., the*grand mean*).**To first**- The*post hoc*testing compares the mean of each category to the mean of the first category.**Pairwise**- The*post hoc*testing compares the mean of each pair of categories.

- OPTIONAL: Select a multiple comparisons
**Correction**to apply when calculating*p-values*. This correction is applied within each variable (i.e., there is no adjustment for multiple comparisons across variables within this function). Such adjustments are possible in Statistical Assumptions for ordinary tables. The**Correction**calculations take into account the settings in**Compare**. For example, when**Tukey Range**is selected in conjunction with**Pairwise**,**Tukey's HSD**is performed, whereas when set with**To First**,**Dunnett's test**is performed (both tests are based on the same statistical notion of ranges in t-statistics, with the difference between the two being which comparisons are performed).**Tukey Range**correction is used by default. - OPTIONAL: To compute standard errors that are robust to violations of the assumption of constant variance (i.e., heteroscedasticity) select
**Robust standard errors.**See Robust Standard Errors for more information. - OPTIONAL: Set the
**Alternative hypothesis**to be used in computing the*p*-values in the post hoc tests. You can choose between**Two sided**(default),**Greater**or**Less.** - OPTIONAL: If the output returns an error due to missing data, go to the
**Missing Data**menu and select**Exclude Cases with Missing Data**. See Missing Data Options for more information. - OPTIONAL: Select
**Variable names**to display variable names in the output instead of labels.

### Technical details

When **Tukey Range** is selected, p-values are computed using t-tests, with a correction for the family-wise error rate such that the p-values are correct for the largest range of values being compared (i.e., the biggest difference between the smallest and largest means). This is a single-step test.

The method of calculation for all the post hoc corrections is valid for balanced, unbalanced samples (Bretz et al. 2011), weighted samples and consequently the results may differ from those in other programs (which typically are only valid for balanced samples).

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