# One Way ANOVA

## Contents

### Overview

The One Way ANOVA is a statistical procedure used to determine whether the mean of three or more samples are statistically different (in case of two samples a t-test can be performed). The samples must be independent and identically distributed normal random variables (the normality of data can be tested via a Normality test).

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 for a One-Way ANOVA:

Null hypothesis Alternate hypothesis
All sample means are equal At least one sample mean is different

Before running a statistical test, the analyst must choose a significance level, or the probability of rejecting the null hypothesis given that it were true (i.e. the probability of making a wrong decision). An alpha value of 0.05 (5%) is usually adopted but a different value may be used depending on the field of the study. If the p-value obtained at the end of the test is less than the selected significance level, the Null Hypothesis should be rejected in favour of the Alternate Hypothesis.

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

### Practical Example

Suppose a university Professor wants to compare the test scores of the end-semester exams, for the following groups of students attending his lectures:

• Students attending the Monday morning lecture
• Students attending the Tuesday afternoon lecture
• Students attending the online lecture

A One Way ANOVA test performed on the three samples produces the following results:

 Null hypothesis All sample means are equal At least one sample mean is different 0.014

Being the p-value less than the adopted significance level of 0.05, the Professor should reject the null hypothesis and conclude that at least one student group performs different from the others.

### Within Grapheme

To perform a One-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 “One-Way ANOVA” from the list. Click on Next.

In the "Sources" tab add a column for each sample you want to include in the analysis and select, for each of them, the source table, the view and the view column.

Move to the "Configuration" tab and select:

• Select "Assuming equal variance" if you can assume samples have equal variance, select "Not Assuming equal variance" otherwise.
• 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. Select then the type of confidence interval you want to evaluate (to choose between Two-sides, Upper, Lower)
• 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. 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