ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression.

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Presentation transcript:

ANalysis Of VAriance

ANOVA

Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression techniques reflect the strength of association Correlational vs difference statistics

In ANOVA we see the world as made of differences. Everywhere we look we see differences.

What is the difference between the heights of human males and females? Correlational vs difference statistics What is the relationship between gender and height in humans?

T-test

ANOVA

ANOVA vs multiple T-Test

ANOVA

H 0 : µ 1 = µ 2 = µ 3 = … = µ k H A : ?

ANOVA H 0 : µ 1 = µ 2 = µ 3 = … = µ k H A : at least two means are significantly different

ANOVA VARIABILITY BETWEEN VARIABILITY WITHIN

Between-group and within-group variance

ANOVA VARIABILITY BETWEEN VARIABILITY WITHIN

ANOVA VARIABILITY BETWEEN VARIABILITY WITHIN

ANOVA VARIABILITY BETWEEN VARIABILITY WITHIN

ANOVA VARIABILITY BETWEEN VARIABILITY WITHIN

ANOVA VARIABILITY BETWEEN VARIABILITY WITHIN F=

1-way ANOVA PoultryBeef Mixed (Pork&Beef) ,76156,85158,70 Overall mean = 145,44 SSC SSE SST N = 54

1-way ANOVA

PoultryBeef Mixed (Pork&Beef) ,76156,85158,70 Overall mean = 145,44 N = 54 Univariate Tests of Significance for Calories (Spreadsheet2) Sigma-restricted parameterization Effective hypothesis decomposition SSdfMSFp Type ,0740, Error

Types of ANOVA 1.1-way ANOVA Analyze design with single categorical variable. 2. Factorial ANOVA Multiple categorical variables 3. Repeated measures ANOVA Compares how a within-subjects experimental group performs in three or more experimental conditions 4. MANOVA Multivariate ANOVA (More than 1 DV)

Types of ANOVA

Repeated measures ANOVA

ANOVA VARIABILITY BETWEEN VARIABILITY WITHIN

Noise filter story NOISE Noise level reading (decibels) SIZE Vehicle size: 1 small 2 medium 3 large TYPE 1 standard silencer 2 Octel filter SIDE 1 right side 2 left side of car

Noise filter story NOISE Noise level reading (decibels) SIZE Vehicle size: 1 small 2 medium 3 large TYPE 1 standard silencer 2 Octel filter SIDE 1 right side 2 left side of car Univariate Tests of Significance for NOISE SS Degr. of - Freedom MSFp Intercept ,60, SIZE ,00, TYPE ,80, SIDE1110,00, Error

Noise filter story

Interaction between IV

Noise filter story Univariate Tests of Significance for NOISE SS Degr. of - Freedom MSFp Intercept , SIZE , TYPE , SIDE11100, SIZE*TYPE , SIZE*SIDE , TYPE*SIDE171 10, SIZE*TYPE*SIDE , Error

Noise filter story

1-way ANOVA

1-way repeated measures ANOVA

Factorial ANOVA

Mixed ANOVA

MANOVA