analysis of variance. anova tests of differences reflect differences in central tendency of...

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

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

ANOVA

ANOVA

ANOVA

ANOVA vs multiple T-Test

ANOVA

ANOVA

H0: µ1 = µ2 = µ3 = … = µk

HA: ?

ANOVA

H0: µ1 = µ2 = µ3 = … = µk

HA: at least two means are significantly different

ANOVA

VARIABILITY BETWEEN

VARIABILITY WITHIN

Between-group and within-group variance

ANOVA

VARIABILITY BETWEENVARIABILITY WITHIN

ANOVA

VARIABILITY BETWEENVARIABILITY WITHIN

ANOVA

VARIABILITY BETWEEN

VARIABILITY WITHIN

ANOVA

VARIABILITY BETWEEN

VARIABILITY WITHIN

ANOVA

VARIABILITY BETWEEN

VARIABILITY WITHINF=

1-way ANOVA

Poultry BeefMixed (Pork&Beef)

129 186 173132 181 191102 176 182106 149 19094 184 172

102 190 14787 158 14699 139 139

107 175 175113 148 136135 152 179142 111 15386 141 107

143 153 195152 190 135146 157 140144 131 138

149135132

118,76 156,85 158,70

Overall mean = 145,44

𝑠2=∑ (𝑥 𝑖− 𝑥¿)2

𝑛−1¿

SSC

SSE

SST

N = 54

1-way ANOVA

1-way ANOVA

Poultry BeefMixed (Pork&Beef)

129 186 173132 181 191102 176 182106 149 19094 184 172

102 190 14787 158 14699 139 139

107 175 175113 148 136135 152 179142 111 15386 141 107

143 153 195152 190 135146 157 140144 131 138

149135132

118,76 156,85 158,70

Overall mean = 145,44

N = 54

Univariate Tests of Significance for Calories (Spreadsheet2) Sigma-restricted parameterization Effective hypothesis decomposition

SS df MS F p

Type 17692 2 8846 16,074 0,000004

Error 28067 51 550

Types of ANOVA

1. 1-way ANOVAAnalyze design with single categorical variable.

2. Factorial ANOVAMultiple categorical variables

3. Repeated measures ANOVACompares how a within-subjects experimental group performs in three or more experimental conditions

4. MANOVAMultivariate ANOVA (More than 1 DV)

Types of ANOVA

Types of ANOVA

Types of ANOVA

Repeated measures ANOVA

ANOVA

VARIABILITY BETWEENVARIABILITY WITHIN

Noise filter story

NOISE Noise level reading (decibels)SIZE Vehicle size: 1 small 2 medium 3 largeTYPE 1 standard silencer 2 Octel filterSIDE 1 right side 2 left side of car

Noise filter story

NOISE Noise level reading (decibels)SIZE Vehicle size: 1 small 2 medium 3 largeTYPE 1 standard silencer 2 Octel filterSIDE 1 right side 2 left side of car

Univariate Tests of Significance for NOISE

SSDegr. of - Freedom

MS F p

Intercept 23627701 1 23627701 264810,6 0,000000

SIZE 26051 2 13026 146,0 0,000000

TYPE 1056 1 1056 11,8 0,001679

SIDE 1 1 1 0,0 0,930268

Error 2766 31 89

Noise filter story

SIZE; LS Means

Current effect: F(2, 31)=145,99, p=,00000

Effective hypothesis decomposition

Vertical bars denote 0,95 confidence intervals

1 2 3

SIZE

750

760

770

780

790

800

810

820

830

840

850

NO

ISE

Noise filter story

TYPE; LS Means

Current effect: F(1, 31)=11,838, p=,00168

Effective hypothesis decomposition

Vertical bars denote 0,95 confidence intervals

1 2

TYPE

798

800

802

804

806

808

810

812

814

816

818

820

822

824

NO

ISE

Noise filter story

SIDE; LS Means

Current effect: F(1, 31)=,00778, p=,93027

Effective hypothesis decomposition

Vertical bars denote 0,95 confidence intervals

1 2

SIDE

804

805

806

807

808

809

810

811

812

813

814

815

816

NO

ISE

Interaction between IV

Interaction between IV

Noise filter story

Univariate Tests of Significance for NOISE

SS Degr. of - Freedom MS F p

Intercept 23627701 1 23627701 1620185 0,000000

SIZE 26051 2 13026 893 0,000000

TYPE 1056 1 1056 72 0,000000

SIDE 1 1 1 0 0,829104

SIZE*TYPE 804 2 402 28 0,000001

SIZE*SIDE 1293 2 647 44 0,000000

TYPE*SIDE 17 1 17 1 0,286067

SIZE*TYPE*SIDE 301 2 151 10 0,000579

Error 350 24 15

Noise filter story

SIZE*TYPE; LS Means

Current effect: F(2, 24)=27,571, p=,00000

Effective hypothesis decomposition

Vertical bars denote 0,95 confidence intervals

TYPE 1 TYPE 2

1 2 3

SIZE

750

760

770

780

790

800

810

820

830

840

850

860

NO

ISE

1-way ANOVA

1-way repeated measures ANOVA

Factorial ANOVA

Mixed ANOVA

MANOVA