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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