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Lecture14_OneWayANOVA (3)

# Lecture14_OneWayANOVA (3)

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05/07/2011

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What type of therapy is most

effective in curing phobias?

±General counseling

±Systematic desensitization

±Counter conditioning

Comparing 3 (or more) groups

The IV is nominal (3 categories)

±Regression requires an ordered (ordinal)

IV so we can¶t use that

Comparing 3 (or more) groups

The IV is nominal (3 categories)

±Regression requires an ordered (ordinal)

IV so we can¶t use that

±If we used a t-test, we would have to do

three comparisons:

General counseling vs. Systematic

desensitization

General counseling vs. Counter conditioning

Systematic desensitization vs. counter

conditioning

±What¶s the problem with this?

Comparing 3 (or more) groups:

Problem with t-test approach

Whenever you do more than one

comparison in an experiment, you increase
the chance of a Type I error

±If we used the t-test approach, we would

compare



1&

2 with = .05



2&

3 with = .05



1&

3 with = .05

±So you would end up with an experiment-wise

error rate of .05*3 = .15

±Increasing the number of groups makes this

much worse

One-way ANOVA

A ³one-way ANOVA´ is an

experimental design with one

independent variable that represents

more than 2 levels of groups

One-way ANOVA

A ³one-wayANOVA´ is an experimental

design with one independent variable

that represents more than 2 levels or

groups

One-way ANOVA

A ³one-wayANOVA´ is an experimental

design with one independent variable

that represents more than 2 levels or

groups

±The IV in an ANOVA is called a factor

E.g., Type of therapy, grade level in school (2nd

,

3rd

, or 4th

), dosage of a drug (0mg, 100mg, 500

mg)

One-way ANOVA

A ³one-wayANOVA´ is an experimental

design with one independent variable

that represents more than 2 levels or

groups

±The IV in an ANOVA is called a factor

E.g., Type of therapy, grade level in school (2nd

,

3rd

, or 4th

), dosage of a drug (0mg, 100mg, 500

mg)

³ANOVA´ stands for ³analysis of variance´

Analysis of Variance

When you break up people into groups

(e.g., types of therapy), there are two

sources of variance that are important

Analysis of Variance

When you break up people into groups

(e.g., types of therapy), there are two

sources of variance that are important

±Variance within each group

Even in the same type of therapy, people will

differ on how much improvement they make (for

This is the noise

Analysis of Variance

When you break up people into groups (e.g.,

types of therapy), there are two sources of
variance that are important

±

Variance within each group



Even in the same type of therapy, people will differ on
how much improvement they make (for reasons we

This is the noise

±Variance between each group

We are really interested in the differences between the

groups±does one group improve more than the other
two?

The variance between the groups is our ³signal´

Analysis of Variance

In some ways, ANOVA should be called

³analysis of sums of squares´

±SS

total= Ss

between-groups+ SS

within-groups

The point is to parse out how much of the

variance is happening between the

groups (signal that the group is making a

difference), and how much is happening

within the group (random error, or noise)

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