# Analysis of Variance - One-Way MANOVA

A statistical test which tests the relationship between a set of numeric variables and a single categorical variable

One-Way MANOVA is a statistical test which tests the relationship between a set of numeric variables and a single categorical variable

## How to Run a One-Way MANOVA

1. Add the object by selecting from the menu Anything > Advanced Analysis > Analysis of Variance > One-Way MANOVAAutomate > Browse Online Library > Analysis of Variance > One-Way MANOVA
2. In Inputs > Outcome specify the outcome variable.
3. Specify the predictor variable in Inputs > Predictor

## Example

In the example below, shading is proportional to the t-statistics comparing against the row means (See How to Read a Standard R Table), and the font of the cells is bold where the p-value, adjusted for multiple comparisons using the False Discovery Rate correction, is less than or equal to 0.05. The p value column shows the lowest p-value for each row. The overall significance of the table, as shown in the sub-title, is determined by the lowest adjusted p-value in the table. The R-Squared shows the strength of relationship between each outcome variable, one-by-one, and the predictor.

## Options

The options in the Object Inspector are organized into two tabs: Inputs and Properties.

### Inputs

Outcomes The variables to be predicted.

Predictor A variable containing 2 or more groups. If not categorical, it is converted into categories in the analysis.

Robust standard errors Computes standard errors that are robust to violations of the assumption of constant variance. See Robust Standard Errors.

Missing data (see Missing Data Options):

Error if missing data
Exclude cases with missing data

Variable names Displays Variable Names in the output.

Categorical as binary Represent unordered categorical variables as binary variables. Otherwise, they are represented as sequential integers (i.e., 1 for the first category, 2 for the second, etc.). Numeric - Multi variables are treated according to their numeric values and not converted to binary.

Filter The data is automatically filtered using any filters prior to estimating the model.

Weight Where a weight has been set for the R Output, the calibrated weight is used. See Weights in R.

### Properties

This tab contains options for formatting the size of the object, as well as the underlying R code used to create the visualization, and the JavaScript code use to customize the Object Inspector itself (see Object Inspector for more details about these options). Additional options are available by editing the code.

## Technical details

• Tests of individual means are two-sided and comparing to the Grand Mean (i.e., "To mean"). See Analysis of Variance - One-Way ANOVA for more information as well as more options for post hoc testing.
• By modifying the code so that Pillai = TRUE, Pillai's Trace and F-tests can be computed for the overall and row null hypotheses, and Tukey's Range test is used to test within rows; Pilla's trace is not valid where the data is weighted.

The Magic Trick that Highlights Interesting Results on Any Table

## Acknowledgements

The linear model is fitted using the lm and manova functions in R. See Analysis of Variance - One-Way ANOVA for acknowledgements relating to the ANOVAs in the outputs.

## Code

```var heading_text = 'One-Way MANOVA';
if (!!form.setObjectInspectorTitle)
else
form.dropBox({label: "Outcomes",
types:["Variable: Numeric, Date, Money, Categorical, OrderedCategorical"],
name: "formOutcomeVariables",
prompt: "Numeric dependent variables to be predicted",
multi:true})
form.dropBox({label: "Predictor",
types:["Variable: Numeric, Date, Money, Categorical, OrderedCategorical"],
prompt: "Categorical grouping variable used to predict the outcome variables",
name: "formPredictor"})
form.checkBox({label: "Robust standard errors", name: "formRobust", default_value: false,
prompt: "Compute standard errors that are robust to violations of the assumption of constant variance"})
form.comboBox({label: "Missing data",
alternatives: ["Error if missing data", "Exclude cases with missing data", "Use partial data"],
name: "formMissing", default_value: "Exclude cases with missing data", prompt: "Treatment of missing data values"})
form.checkBox({label: "Variable names", name: "formNames", default_value: false, prompt: "Whether to use variable names instead of labels"})
form.checkBox({label: "Categorical as binary", name: "formBinary", default_value: false, prompt: "Whether to convert categorical outcome variables to binary variables"})
```
```library(flipAnalysisOfVariance)
manova <- OneWayMANOVA(data.frame(QInputs(formOutcomeVariables)),
QInputs(formPredictor),
subset = QFilter,
weights = QPopulationWeight,
robust.se = formRobust,
missing = formMissing,
show.labels = !formNames,
binary = formBinary,
pillai = FALSE,
fdr = TRUE)
```