Within-GroupsANOVA

Chapter 13

One-Way Within-Groups ANOVA

> Similar to paired-samples t-tests• Same participants do something multiple

(more than 2) times> Are used when we have one IV with at

least 3 levels, a scale DV, and the same participants in each group

Benefits of Within-Groups ANOVA

> We reduce error due to differences between the groups.

> We know that the groups are identical for all of the relevant variables because each group includes exactly the same participants.

> We are able to reduce within-groups variability due to differences for the people in our study across groups.

Steps of Hypothesis Testing

> Step 1. Identify populations, distribution, and assumptions.

> Step 2. State the null and the research hypotheses.

> Step 3. Determine characteristics of the comparison distribution.

> Step 4. Determine critical values.> Step 5. Calculate the test statistic.> Step 6. Make a decision.

Formulae

1 groupsbetween Ndf

1ndf subjects

))(( subjectsbetweenwithin dfdfdf

1 totaltotal Ndf

2)( GMXSStotal

2)( GMMSSbetween

2)( GMMSS tparticipansubjects

subjectsbetweentotalwithin SSSSSSSS between

betweenbetween df

SSMS

subjects

subjectssubjects df

SSMS

within

withinwithin df

SSMS

within

subjectssubjects MS

MSF

within

betweenbetween MS

MSF

Effect Size

> R2 can be calculated for this type of ANOVA, too!

)(2

subjectstotal

between

SSSS

SSR

> Post hoc test to identify where you have differences if your F is significant

> You need to calculate the standard error before using the Tukey HSD test

Tukey HSD

N

MSs withinM

MS

MMHSD

)( 21

> Matched groups use different people who are similar on all of the variables that we want to control.

> We can analyze our data as if the same people are in each group, giving us additional statistical power.

Matched Groups