Skip to content Skip to navigation Skip to collection information

Connexions

You are here: Home » Content » Collaborative Statistics » ANOVA

Navigation

Table of Contents

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.
 

ANOVA

Module by: Susan Dean, Barbara Illowsky, Ph.D.. E-mail the authors

Summary: This module describes the assumptions needed for implementing an One-Way ANOVA and how to set up the hypothesis test for the ANOVA.

F Distribution and One-Way ANOVA: Purpose and Basic Assumptions of One-Way ANOVA

The purpose of a One-Way ANOVA test is to determine the existence of a statistically significant difference among several group means. The test actually uses variances to help determine if the means are equal or not.

In order to perform a One-Way ANOVA test, there are five basic assumptions to be fulfilled:

  • Each population from which a sample is taken is assumed to be normal.
  • Each sample is randomly selected and independent.
  • The populations are assumed to have equal standard deviations (or variances).
  • The factor is the categorical variable.
  • The response is the numerical variable.

The Null and Alternate Hypotheses

The null hypothesis is simply that all the group population means are the same. The alternate hypothesis is that at least one pair of means is different. For example, if there are kk groups:

H o : μ 1 = μ 2 = μ 3 = ... = μ k H o : μ 1 = μ 2 = μ 3 =...= μ k

H a : H a : At least two of the group means μ 1 , μ 2 , μ 3 , ... , μ k μ 1 , μ 2 , μ 3 ,..., μ k are not equal.

The graphs help in the understanding of the hypothesis test. In the first graph (red box plots), H o : μ 1 = μ 2 = μ 3 H o : μ 1 = μ 2 = μ 3 and the three populations have the same distribution if the null hypothesis is true. The variance of the combined data is approximately the same as the variance of each of the populations.

If the null hypothesis is false, then the variance of the combined data is larger which is caused by the different means as shown in the second graph (green box plots).

Three boxplots with equal means

Three boxplots with unequal means

Glossary

Analysis of Variance:
Also referred to as ANOVA. A method of testing whether or not the means of three or more populations are equal. The method is applicable if:
  • All populations of interest are normally distributed.
  • The populations have equal standard deviations.
  • Samples (not necessarily of the same size) are randomly and independently selected from each population.
The test statistic for analysis of variance is the F-ratio.
Variance:
Mean of the squared deviations from the mean. Square of the standard deviation. For a set of data, a deviation can be represented as x-x¯x- x where xx is a value of the data and x¯ x is the sample mean. The sample variance is equal to the sum of the squares of the deviations divided by the difference of the sample size and 1.

Collection Navigation

Content actions

Download module as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Add:

Collection to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks

Module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks