Introduction to ANOVA

2009 Methodology A - Lecture 3

1. Review of Last Week

2. Today’s Learning Objectives

3. What is ANOVA?

4. Types of ANOVA

5. Assumptions

6. Considerations

7. Test of Learning Objectives

8. Vocabulary

Outline Review of Last WeekDescriptive Statistics

1. What are the three most common measures of central tendency?

2. How do you calculate the mean?3. How do you calculate the median?4. How do you calculate the mode?5. What are the two measures of

variability?6. How are these two measures

related?

Hypothesis Testing7. What is the null hypothesis?8. What is the difference between

one-tailed and two-tailed alternative hypotheses?

9. How do p-values relate to the null and alternative hypotheses?

10. How do Type I and Type II errors differ?

The t-test11. What are the three types of t-test?12. What do you need to know about

your data to compute the t statistic?

13. What are the assumptions of the t-test?

14. How do you test for equal variance?

15. What do you do if variance is not equal?

16. What are degrees of freedom?17. How do you calculate effect size?18. How do you report the outcome of

a t-test?19. Given sample data, which type of

t-test is most appropriate?

What is ANOVA

1. What does ANOVA stand for?

2. How is ANOVA similar to a t-test?

3. How is it different?

4. What is a factor?

Types of ANOVA

5. What is the difference between

univariate and multivariate ANOVAs?

6. What is the difference between

between-subjects and within-subject

factors?

7. What is the difference between one-

way and factorial ANOVAs?

8. For a univariate design, what 2 things

do you need to know to determine

what type of ANOVA to use?

9. What type of ANOVA is required if

you have both between-subjects and

within-subject factors?

Assumptions

10. What are the three main assumptions

of ANOVA?

11. What descriptive statistics do you

report to assess normality?

12. What are the two tests for

homogeneity of variance?

13. When should you use each of the

tests for homogeneity of variance?

14. How do you compute Fmax?

15. When do you need to check for

sphericity?

16. What values of Levene’s Test, Fmax

and Mauchly’s Test allow you to do

ANOVA?

Other Considerations

17. Why should you consider sample size

when planning an experiment?

18. What is meant by ‘cases must be

independent’?

Today’s Learning Objectives! ANalysis Of VAriance

! Like a t-test for 2 or more conditionsfor 2 conditions, F = t2

! Also used for multiple factors (>1 independent variable)

! A parametric statistic (has assumptions)

What is ANOVA?

Number of Independent Variables (IV)

! One-way - 1 factor

! Factorial - 2 or more orthogonal factors

Types of ANOVA

Groups of Subjects

! Between-subjects - 2 or more groups of subjects, each subject participates in 1 condition

! Within-subjects - 1 group of subjects, each subject participates in all conditions

Number of Dependent Variables (DV)

! Univariate - 1 DV! Repeated-measures - 1 DV measured 2 or more times

! Multivariate - 2 or more different DVs

Types of ANOVA

One IV More than one IV

OneOne-way between-subjects

Factorialbetween-subjects

Mixed-design(split-plot)

AllOne-way

within-subjectFactorial

within-subject

Number of Independent Variables

Conditio

ns p

er

Subje

ct

plus 1 or more continuous IVs = ANCOVA

1. The sample is drawn from a normally-distributed population

2. Homogeneity of variance

3. Sphericity (only for within-subjects designs)

Assumptions

155-6

Always look at your data first. Remove outliers and “eyeball” for normality.

SPSS ! Graphs ! Chart Builder...

1. Normal Distribution

1. Normal DistributionThere are many ways to determine if data are normally distributed and ANOVA is robust to most violations of normality. For this course, assume data meet the assumptions and just report skewness and kurtosis

platykurtic mesokurtic leptokurtic

negative skew zero skew positive skew

1. Normal DistributionReporting skewness and kurtosis

1. Normal DistributionReporting skewness and kurtosis

Test that the variance of each condition is roughly equal using Levene’s Test for between-subjects factors and Fmax for within-subject factors.

2. Homogeneity of Variance

equal variance unequal variance

Test that the variance of each condition is roughly equal using Levene’s Test for between-subjects factors and Fmax for within-subject factors.

If p > .05, variance is equal enough for ANOVA

2. Homogeneity of VarianceTest that the variance of each condition is roughly equal using Levene’s Test for between-subjects factors and Fmax for within-subject factors.

Fmax =largest variance

smallest variance Fmax = = 1.6389.783

55.201

If Fmax < 4, variance is equal enough for ANOVA

2. Homogeneity of Variance

3. Sphericity! For within-subject factors with more than 2 levels, you must

check for and report sphericity.

! Sphericity is like homogeneity of variance for difference scores (the difference between pairs of within-subject factors).

! SPSS does this automatically via Mauchly’s Test of Sphericity.

! If p > 0.05, report the ‘Sphericity Assumed’ statistics, else, report the Greenhouse-Geisser statistics.

1. Cases must be independent

2. Sample size should be approximately equal for each group

3. Samples should not be too small

Considerations when designing experiments to be analysed by ANOVA

ANCOVAANOVAbetween-subejctsdependent variable (DV)Fmax

factorfactorialGreenhouse-Geiserhomogeneity of variancehomoscedasticitykurtosisLevene statisticMANOVA

Mauchly’s testmixed-designmultivariateindependent variable (IV)one-wayorthogonalrepeated-measuresrobustskewnesssphericitysplit-plot ANOVAunivariatewithin-subject

Vocabulary