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ANalysis Of VAriance

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Page 1: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

ANalysis Of VAriance

Page 2: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

ANOVA

Page 3: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

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

Page 4: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

Correlational vs difference statistics

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

Page 5: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

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?

Page 6: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

T-test

Page 7: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

ANOVA

Page 8: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

ANOVA

Page 9: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

ANOVA

Page 10: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

ANOVA

Page 11: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

ANOVA

Page 12: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

ANOVA vs multiple T-Test

Page 13: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

ANOVA

Page 14: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

ANOVA

H0: µ1 = µ2 = µ3 = … = µk

HA: ?

Page 15: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

ANOVA

H0: µ1 = µ2 = µ3 = … = µk

HA: at least two means are significantly different

Page 16: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

ANOVA

VARIABILITY BETWEEN

VARIABILITY WITHIN

Page 17: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

Between-group and within-group variance

Page 18: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

ANOVA

VARIABILITY BETWEENVARIABILITY WITHIN

Page 19: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

ANOVA

VARIABILITY BETWEENVARIABILITY WITHIN

Page 20: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

ANOVA

VARIABILITY BETWEEN

VARIABILITY WITHIN

Page 21: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

ANOVA

VARIABILITY BETWEEN

VARIABILITY WITHIN

Page 22: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

ANOVA

VARIABILITY BETWEEN

VARIABILITY WITHINF=

Page 23: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

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

Page 24: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

1-way ANOVA

Page 25: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

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

Page 26: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

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)

Page 27: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

Types of ANOVA

Page 28: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

Types of ANOVA

Page 29: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

Types of ANOVA

Page 30: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

Repeated measures ANOVA

Page 31: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

ANOVA

VARIABILITY BETWEENVARIABILITY WITHIN

Page 32: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

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

Page 33: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

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

Page 34: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

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

Page 35: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

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

Page 36: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

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

Page 37: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

Interaction between IV

Page 38: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

Interaction between IV

Page 39: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

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

Page 40: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

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

Page 41: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression
Page 42: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

1-way ANOVA

Page 43: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

1-way repeated measures ANOVA

Page 44: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

Factorial ANOVA

Page 45: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

Mixed ANOVA

Page 46: ANalysis Of VAriance. ANOVA Tests of differences reflect differences in central tendency of variables between groups and measures. Correlation and regression

MANOVA


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