Presented toMs Maryium Gul

Presented by Aamna Haneef

Roll no: 05MS (2012-2014)

Lahore College for Women University

Repeated Measures ANOVA

Repeated measures ANOVA is also referred to as a • “within-subjects ANOVA”,• “Dependent groups” or • “ANOVA for correlated

samples”

Other Names

Why the repeated factor is called a “within” subjects factor?

Because comparisons are made multiple times ("repeated") “within” the same subject rather than across ("between") different subjects

In within subject design

• Each participant is measured more than once

• Same subjects across the levels of the IV

• Levels can be ordered like time or treatment

• Or levels can be un-ordered (e.g. cases take three different types of depression inventories)

What RM ANOVA does?Like T-Tests, repeated measures ANOVA gives the statistic tools to determine whether or not change has occurred over timeT-Tests compare average scores at two different time periods

RM ANOVA compared the average score at multiple time periods

The logic of RM ANOVA

Any differences that are found between treatments can be explained by only two factors:1. Treatment effect2. Error or Chance

Cont…

A particular subject’s scores will be more alike than scores collected from multiple subjects

Less variability decrease in sampling error

Cont…

Subject A B C

Each row

represents

one

subject

measured

under

each of k

conditions.

1subj1 under

condition A

subj1 under

condition B

subj1 under

condition C

2subj2 under

condition A

subj2 under

condition B

subj2 under

condition C

3subj3 under

condition A

subj3 under

condition B

subj3 under

condition C

And so on…

Assumptions

Dependent variableIt should be measured at the interval or ratio level (continuous), such as • revision time • Intelligence• exam performance • weight

Assumptions Cont…

Independent variable It should consist of at least two categorical, "related groups" or "matched pairs“• 10 individuals' performance in a

spelling test before and after new form of computerized teaching method

• measuring changes in blood pressure due to an exercise-training program

Assumptions Cont…

No significant outliers differencesData values that are "far away" from the main group of data• Distorting the differences between the related groups• Reduces the accuracy of results

Assumptions Cont…Normally distributed Dependent

variable• The dependent variable between the

two or more related groups should be approximately normally distributed

• It is quite "robust" to violations of normality

• The Shapiro-Wilk test of normality can test for normality

Assumptions Cont…

Sphericity• Refers to differences between

variances in levels of the repeated-measures factor (Time)

• Violation of the assumption of sphericity, causes the test to become too liberal (leads to an increase in the Type I error)

• Mauchly's Test of Sphericity can help to test for its violation

Hypothesis for RM ANOVA

The repeated measures ANOVA tests for whether there are any differences between related population means

H0: µ1 = µ2 = µ3 = … = µk

H0: There are no differences between population means.HA: At least one treatment or observation mean is significantly different

Sources of Variability• In repeated measure ANOVA, there are

three potential sources of variability: 1. Treatment variability: between columns, 2. Within subjects variability: between

rows, and 3. Random variability: residual(chance

factor or experimental error beyond the control of a researcher) .

• A repeated measure design is powerful, as it controls for all potential sources of variability.

FORMULA

variance between treatmentsF = ------------------------------------------

Error variance • A large F value indicates that the

differences between treatments/observations are greater than would be expected by chance or error alone.

Approaches to RM ANOVA

SPSS conducts 3 types of tests if the within-subject factor has more than 2 levels• The standard univariate ANOVA test• The alternative univariate tests• The multivariate test

Advantages • Using the same participants in

different experimental manipulations • Exclude the effects of individual

differences • This design is also very economical • Removing variance due to differences

between subjects from the error variance greatly increases the power (probability of correctly rejecting a false null hypothesis)

Disadvantages

• Practice effects causing participants’ results to improve • Carry-over effects (bias)• Demand characteristics (more

exposure, more time to think about meaning of the experiment).• Boredom and lack of concentration

Tidbits

Why it is always called F statistic?

The F statistic was named after Ronald A. Fisher, who mainly developed ANOVA