Analysis of Variance(ANOVA)
Hirotaka Onishi, MD, MHPE, PhD
Dept. of International Cooperation for Medical Education,
International Research Center for Medical Education,
Graduate School of Medicine, The University of Tokyo

What Is H0 Meaning?
_ _ _ H0: x1= x2= x3

Even if H0 is rejected, it does not automaticallymean x1< x2 or x2 < x3
 To prove the difference between specific twovariables, post-hoc tests will be used.
 Scheffé test: most stringent
 Bonferroni: α is divided by the number of tests.
 Tukey’s Honestly Significant Difference(HSD): numbers of cases must be the sameDifferentiate Within-subject
from Between-subject Data

Within-subject dataLongitudinally (repeatedly) collected dataMultiple items in a questionnaire

Between-subject
Different groups of subjects
Demographic data: Gender, age group…
 Study vs control groupsData Formatcontrol

APN
phone
17342223395474482615__x = 3.0x = 5.2
sd = 1.89 sd = 2.25

APN ph +visits586979108710_x = 7.9sd = 1.66

Data Format
In SPSS or ExcelWithin-subject data are putin parallel You
have to define the group toconduct the analysis
Between-subject data are
put in tandem

Nation HiB
1101121
91
102
82
102
82
938373
11
3
7

HiY
6118
97
7
9915
19
14
18

HiR
1916
19
19
20
20
16
19
9668

Select Post-hoc Test
When three or more options are

Within-subject
Sidak is often selected

Between-subject
Tukey is one of the most frequently used
post-hoc testSphericity


If within-subject data has three or more
options, sphericity might be a problem.
When “test of homogeneity of variances” issignificant, 3 Steps will be taken:
 (1) sphericity supposed (2) lowest, and (3) Greenhouse-Geisser’s modification
Interaction
MaleFemale

Young

51015Old

105151515

Main effect for Sex

Maineffectfor Age

H0: µyoung = µold
H1: H0 is false

H0: µmale = µfemale
H1: H0 is false
H0: There is no interaction
H1: H0 is false

MaleFemale
YoungOld2way, 3way ANOVA
More than one factors are compared simultaneously.
 Both within-subject and between subject data are
combined for one analysis.
 Interaction is another issue for 2way ANOVA or more.
group１

group１group２group２Pre-test

Post-test

With interaction

Pre-test

Post-test

Without interaction

水本，竹内．研究論文における効果量の報告のために．英語教育研究 31, 57-66, 2008

Exercise 1
Open 2wayANOVA.xlsx
 Seek for the relationship (1) age (2) # ofdelivery and (3) sex of the baby (1 male,0 female)対馬栄輝．SPSSで学ぶ医療系データ解析：分析内容の理解と手順解説、バランスのとれた医療統計入門．pp166-174

Exercise 2Open repANOVA.xlsx
 23 young subjects measured height in3 consecutive years.
 Are they growing?
 Change in the data format might beneeded.
対馬栄輝．SPSSで学ぶ医療系データ解析：分析内容の理解と手順解説、バランスのとれた医療統計入門．pp182-188

Exercise 3
Open water learning.xlsx
9 divers participated in the experiments oflearning words in 8 conditions


1st digit: reproduction–1, reaffirmation–2
Reproduction: recall what was experienced as it was Reaffirmation: confirm that what is being questioned iswhat was experienced.
2nd digit: learning on the ground–1, in the water–2rd digit: testing on the ground–1, in the water–2
 3山内光哉．心理・教育のための分散分析と多重比較ーエクセル・SPSS
解説付き．pp199-212

Exercise 4Open MixedANOVA.xlsx
 12 workers from 3 countries (Japan – 1,Korea – 2, US – 3) participated in thephysical exercise.
 Conditions
Color lighting: blue, red and yellowTemperature: high, normal and low
竹原卓真．SPSSのススメ(2)３要因の分散分析をすべてカバー．pp198-302