# Two Way ANOVA

### From Grapheme wiki

### Overview

The Two-Way ANOVA is a statistical procedure used to evaluate the influence of two different categorical independent variables (called factors) on one continuous dependent variable (called response).

Any Hypothesis test in statistics requires the definition of a *null hypothesis* and an *alternate hypothesis*. The goal of the test is to aid the analyst in deciding which one of the two hypothesis is true. The table below shows the null and the alternate hypothesis defining for each test performed during a Two-Way ANOVA Comparison procedure:

Null hypothesis | Alternate hypothesis |
---|---|

The response mean for the first factor are equal | The response mean for the first factor not are equal |

The response mean for the second factor are equal | The response mean for the second factor not are equal |

There is no interaction between the two factors | There is interaction between the two factors |

If the p-value obtained at the end of the test is less than the adopted significance level, the Null Hypothesis should be rejected in favour of the Alternate Hypothesis.

More details on the Two Way ANOVA can be found here:

### Practical Example

Suppose a production quality engineer, working for a food company specialized in confectionery, wants to evaluate how the units produced weekly perform against the location of the factory and the level of automation used on the production line.

The company has to factories, one in Manchester and one in Liverpool, and each factory is currently testing three different type of production lines with different levels of automation (minimum, medium and high level).

He performs a Two-Way ANOVA analysis which produces following results:

Observation | p-Value |
---|---|

First Factor (Location) | 0.980 |

Second Factor (Level of automation) | 0.001 |

Interaction | 0.182 |

Based on the adopted significance level of 0.05, the engineer can draw following conclusions:

- The association between the location of the factory and the number of units produced is not statistically significant
- The association between the level of automation and the number of units produced is statistically significant
- The relationship between the level of automation and the number of units produced does not depend from the location of the factory

### Within Grapheme

To perform a Two-Way ANOVA in Grapheme, click on **Create New Analysis** from the toolbar of the *Statistical Analysis View*. Assign a name to the panel and select “Two-Way ANOVA” from the list. Click on **Next**.

In the *Sources* tab select the source tables, the views and the view columns to be used as Response, Factor 1, and Factor 2.

Move to the *Configuration* tab and define the following analysis settings:

- select
*Save data to display Individual and Residual Plots*if you want to have available, within the chart area, the individual plot for each sample and the related residual plots - If you want Grapheme to evaluate the confidence interval range, check the setting
*Compute Confidence Interval*and insert the probability value to be used for its evaluation. Click on**Finish**.

##### Remarks

- All the data available in the panel are updated on the fly, so that any change in the table values, is immediately reflected by the panel tables and charts. Automatic update can be temporary suspended, by clicking on the lock button in the main panel toolbar.
- All the data contained in each table, can be copied to the clipboard for further reporting by clicking on the button available in the toolbar.
- Each chart can be exported as Image by clicking on the “Save as Image” button available in the toolbar