Cesar Chew at 17:57, 25 November 2014

2014-11-25T17:57:24Z

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{{Cat|ANOVA| 1}}

== Questions ==
* What null hypothesis is tested by ANOVA?
* What are the uses of ANOVA?

== What is ANOVA? ==
* Analysis of Variance (ANOVA) is a statistical method used to '''compare two or more means'''
* Inferences about means are made by analyzing variance (therefore it is not called analysis of mean)
* ANOVA is used to test general rather than specific differences among means

== Smiles and Leniency Example ==
* Let us investigate types of smiles on the leniency
* Types of smiles: neutral, false, felt, miserable

The results from the Tukey hsd test (Six Pairwise Comparisons):
{| class="wikitable"
|-
! Comparison !! Mi-Mj !! Q !! p
|-
| False - Felt || 0.46 || 1.65 || 0.649
|-
| False - Miserable || 0.46 || 1.65 || 0.649
|-
| False - Neutral || 1.25|| 4.48|| 0.010
|-
| Felt - Miserable || 0.00 || 0.00 || 1.000
|-
| Felt - Neutral || 0.79 || 2.83 || 0.193
|-
| Miserable - Neutral || 0.79 || 2.83|| 0.193
|}

* Notice that the only significant difference is between the False and Neutral conditions.
* ANOVA tests the non-specific null hypothesis that all four populations means are equal
μfalse = μfelt = μmiserable = μneutral

* This non-specific null hypothesis is sometimes called the '''omnibus null hypothesis'''
* When the omnibus null hypothesis is rejected, the conclusion is that '''at least one population mean is different from at least one other mean'''
* ANOVA does not reveal which means are different from which
* It offers less specific information than the Tukey hsd test
* The Tukey hsd is therefore preferable to ANOVA in this situation
== Why to use ANOVA instead of HSD Tukey ==
* There are complex types of analyses that can be done with ANOVA and not with the Tukey test
* ANOVA is by far the most commonly-used technique for comparing means
* Is important to understand ANOVA in order to understand research reports.

== Questions ==

<quiz display=simple >
{The omnibus null hypothesis when performing an analysis of variance is there are differences between group means, however, no prediction is made concerning where the differences lie.
|type="()"}
- True
+ False

{
{{Show Answer|
False, the omnibus null is that all group means are the same.
}}
}

{Unlike t-tests an ANOVA may be used to test for differences among more than 2 groups.
|type="()"}
+ True
- False

{
{{Show Answer|
True, An analysis of variance (ANOVA) is most often used to determine if there are differences among 3 or more group means. However, if there are more than 2 groups an ANOVA does not provide information regarding where the differences lie.
}}
}

{Unlike t-tests, an ANOVA uses both differences between group means and differences within groups to determine whether the difference are significant.
|type="()"}
- True
+ False

{
{{Show Answer|
False, both t-tests and ANOVAs use both. In a t test the difference between means is in the numerator. In an ANOVA, the variance of the grouop means (multiplied by n) is in the numerator.
}}
}

{It is valid to do the Tukey HSD test without first finding a signficant effect with an ANOVA.
|type="()"}
+ True
- False

{
{{Show Answer|
True, the Tukey HSD controls the Type I error rate and is valid without first running an ANOVA.
}}
}
</quiz>

Introduction to ANOVA - Revision history

Cesar Chew at 17:57, 25 November 2014