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Introduction toANOVA

2009 Methodology A - Lecture 3

1. Review of Last Week

2. Todays 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 commonmeasures 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 betweenone-tailed and two-tailedalternative hypotheses?

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

10. How do Type I and Type II errorsdiffer?

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

your data to compute the tstatistic?

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

14. How do you test for equalvariance?

15. What do you do if variance is notequal?

16. What are degrees of freedom?17. How do you calculate effect size?

18. How do you report the outcome ofa t-test?

19. Given sample data, which type oft-test is most appropriate?

What is ANOVA1. 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 ANOVA5. 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 thingsdo you need to know to determinewhat type of ANOVA to use?

9. What type of ANOVA is required ifyou have both between-subjects and

within-subject factors?

Assumptions10. What are the three main assumptions

of ANOVA?11. What descriptive statistics do you

report to assess normality?

12. What are the two tests forhomogeneity 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 forsphericity?

16. What values of Levenes Test, Fmax

and Mauchlys Test allow you to doANOVA?

Other Considerations

17. Why should you consider sample sizewhen planning an experiment?

18. What is meant by cases must beindependent?

Todays Learning Objectives!ANalysis Of VAriance

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

!Also used for multiple factors (>1independent 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 participatesin 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-waybetween-subjects

Factorialbetween-subjects

Mixed-design(split-plot)

AllOne-way

within-subjectFactorial

within-subject

Number of Independent Variables

ConditionsperSubject

plus 1 or more continuous IVs = ANCOVA

1. The sample is drawn froma normally-distributedpopulation

2. Homogeneityof 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

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1. Normal DistributionThere are many ways to determine if data are normallydistributed and ANOVA is robust to most violations ofnormality. For this course, assume data meet theassumptions 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 equalusing Levenes Test for between-subjects factors andFmax for within-subject factors.

2. Homogeneity of Variance

equal variance unequal variance

Test that the variance of each condition is roughly equalusing Levenes Test for between-subjects factors andFmax for within-subject factors.

If p > .05,variance isequal enoughfor ANOVA

2. Homogeneity of VarianceTest that the variance of each condition is roughly equalusing Levenes Test for between-subjects factors andFmax for within-subject factors.

Fmax =largest variance

smallest variance Fmax = = 1.6389.783

55.201

If Fmax < 4,variance is equalenough forANOVA

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 Mauchlys Test of Sphericity.

! If p > 0.05, reportthe Sphericity

Assumed statistics,else, report theGreenhouse-Geisser statistics.

1. Cases must beindependent

2. Sample size shouldbe approximatelyequal for eachgroup

3. Samples should notbe too small

Considerations when designingexperiments to be analysed by ANOVA

ANCOVAANOVAbetween-subejctsdependent variable (DV)FmaxfactorfactorialGreenhouse-Geiserhomogeneity of variancehomoscedasticitykurtosisLevene statisticMANOVA

Mauchlys testmixed-designmultivariateindependent variable (IV)one-wayorthogonalrepeated-measuresrobustskewnesssphericitysplit-plot ANOVAunivariatewithin-subject

Vocabulary