Chapter 13 Two Groups Too Many? Try Analysis of Variance (ANOVA) Part IV Significantly Different: Using Inferential Statistics.

Chapter 13 Two Groups Too Many?

Try Analysis of Variance (ANOVA)

Part IVSignificantly Different:

Using Inferential Statistics

What you will learn in Chapter 13

What Analysis of Variance (ANOVA) is and when it is appropriate to use

How to compute the F statistic

How to interpret the F statistic

How to use SPSS to conduct an ANOVAsingle factor design

Analysis of Variance (ANOVA)

Used when more than two group means are being tested simultaneouslyGroup means differ from one another on a

particular score / variableExample: DV = GRE Scores & IV = Ethnicity

Test statistic = F testR.A. Fisher, creator

Path to Wisdom & KnowledgeHow do I know if ANOVA is the right test?

Different Flavors of ANOVA

ANOVA examines the variance between groups and the variances within groupsThese variances are then compared against

each otherSimilar to the t Test…only in this case you

have more than two groupsOne-way ANOVA

Simple ANOVASingle factor (grouping variable)

More Complicated ANOVAFactorial Design

More than one treatment/factor examinedMultiple Independent Variables

One Dependent VariableExample – 3x2 factorial design

Number of Hours in Preschool

Gender

Male5 hours per week

10 hours per week

20 hours per week

Female 5 hours per week

10 hours per week

20 hours per week

Computing the F Statistic

Rationale…want the within group variance to be small and the between group variance to be large in order to find significance.

Hypotheses

Null hypothesis

Research hypothesis

Source Table

Source SS df MS F

Between 1,133.07 27 566.54 8.799

Within 1,738.40 29 64.39

Note: F value for two group is the same as t2

Degrees of Freedom (df)

NumeratorNumber of groups minus onek-13 groups --- 3 – 1 = 2

DenominatorTotal number of observations minus the number

of groupsN-1100 participants --- 30 – 3 = 97

Represented: F (2, 27)

How to Interpret

F (2,27) = 8.80, p < .05F = test statistic 2,27 = df between groups & df within groups

{Ah ha…3 groups and 30 total scores examined}8.80 = obtained value

Which we compared to the critical valuep < .05 = probability less than 5% that the

null hypothesis is trueMeaning the obtained value is GREATER than the

critical value

Omnibus Test

The F test is an “omnibus test” and only tells you that a difference exists

Must conduct follow-up t tests to find out where the difference is…BUT…Type I error increases with every follow-

up test / possible comparison made1 – (1 – alpha)k

Where k = number of possible comparisons

Using the ComputerSPSS and the One-Way ANOVA

What does it all mean?

SPSS Output

Post Hoc Comparison

Glossary Terms to Know

Analysis of varianceSimple ANOVAOne-way ANOVAFactorial design

Omnibus testPost Hoc comparisonsSource table

Chapter 17 What to Do When You’re Not Normal:

Chi-Square and Some Other Nonparametric Tests

Part IVSignificantly Different:

Using Inferential Statistics

What you will learn in Chapter 17

A brief survey of nonparametric statisticsWhen they should be usedHow they should be used

Introduction

Parametric statistics have certain assumptionsVariances of each group are similarSample is large enough to represent the

populationNonparametric statistics don’t require the

same assumptionsAllow data that comes in frequencies to be

analyzed…they are “distribution free”

One-Sample Chi-Square

Chi-square allows you to determine if what you observe in a distribution of frequencies is what you would expect to occur by chance.One-sample chi-square (goodness of fit test)

only has one dimensionTwo-sample chi-square has two dimensions

Computing Chi-Square

What do those symbols mean?

22 (O E)

Ex

More Hypotheses

Null hypothesis

H0: P1 = P2 = P3

Research hypothesis

H1: P1 P2 P3

Computing Chi Square

Category O E D (O-E)2 (O-E)2/2

For 23 30 7 49 1.63

Maybe 17 30 13 169 5.63

Against 50 30 20 400 13.33

Total 90 90 C2 = 20.6

So How Do I Interpret…

x2(2) = 20.6, p < .05

x2 represents the test statistic2 is the number of degrees of freedom20.6 is the obtained valuep < .05 is the probability

Using the ComputerOne-Sample Chi Square using SPSS

SPSS Output

What does it all mean?

Other Nonparametric Tests

Glossary Terms to Know

ParametricNonparametricOne-sample Chi Square