Correct Use of Repeated Measures Analysis of Variance

Eunsik Park; Meehye Cho; Chang-Seok Ki

doi:10.3343/kjlm.2009.29.1.1

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Park, Cho, and Ki: Correct Use of Repeated Measures Analysis of Variance

Original Article

Korean J Leg Med 2009;29(1):1-9.

Published online: 14 February 2009

DOI: https://doi.org/10.3343/kjlm.2009.29.1.1

Correct Use of Repeated Measures Analysis of Variance

Eunsik Park, Ph.D.^1,, Meehye Cho, B.Sc.¹, Chang-Seok Ki, M.D.²

¹Department of Statistics, College of Natural Sciences, Chonnam National University, Gwangju, Korea

²Department of Laboratory Medicine and Genetics, Samsung Medical Center, Sungkyunkwan University School of Medicine, Seoul, Korea

Corresponding author: Eunsik Park, Ph.D. Department of Statistics, College of Natural Sciences, Chonnam National University, 300 Yongbong-ro, Buk-gu, Gwangju 500-757, Korea Tel: +82-62-530-3448, Fax: +82-62-530-3449 E-mail: espark02@chonnam.ac.kr

^∗This work was supported by a Korea Science and Engineering Foundation (KOSEF) grant funded by the Korean government (MOST) (R01-2006-000-11087-0).

Received 2 December 20086 February 2009 Accepted 21 February 2009

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In biomedical research, researchers frequently use statistical procedures such as the t-test, standard analysis of variance (ANOVA), or the repeated measures ANOVA to compare means between the groups of interest. There are frequently some misuses in applying these procedures since the conditions of the experiments or statistical assumptions necessary to apply these procedures are not fully taken into consideration. In this paper, we demonstrate the correct use of repeated measures ANOVA to prevent or minimize ethical or scientific problems due to its misuse. We also describe the appropriate use of multiple comparison tests for follow-up analysis in repeated measures ANOVA. Finally, we demonstrate the use of repeated measures ANOVA by using real data and the statistical software package SPSS (SPSS Inc., USA).

Keywords: Ethics, ANOVA, Repeated measures, Multiple comparison

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Table 1.

ESR means and SDs

Vacuum tube	Day
	0		1		2
	Mean	SD	Mean	SD	Mean	SD
BD Vacutainer	8.60	7.96	9.85	9.16	7.10	6.91
Sekisui INSEPACK	7.80	7.49	8.80	8.51	6.75	6.54
Green Cross Green-Vac-Tube	10.70	9.19	10.40	9.16	7.40	7.16

Abbreviation: ESR, erythrocyte sedimentation rate; SD, standard deviation; BD, becton dickison.

Table 2.

Repeated measures univariate ANOVA results

Source	Unadjusted DF	Unadjusted Mean square	F value	Unadjusted P value	Adjusted P value by G-G	Adjusted P value by H-F
Day	2	109.850	20.477	0.000	0.000	0.000
Error (day)	38	5.365
Tube	2	44.517	10.671	0.000	0.000	0.000
Error (tube)	38	4.172
Day^∗Tube	4	7.842	7.732	0.000	0.001	0.000
Error (day^∗tube)	76	1.014

Abbreviations: ANOVA, analysis of variance; DF, degrees of freedom; G-G, Greenhouse-Geisser Epsilon; H-F, Huynh-Feldt epsilon.

Table 3.

Multivariate ANOVA tests for two within-subject effects and their interaction effect

Statistic	Day		Tube		Day^∗Tube
Statistic	F value	P value	F value	P value	F value	P value
Pillai's trace	11.35	0.001	11.66	0.001	7.61	0.001
Wilks’ lambda	11.35	0.001	11.66	0.001	7.61	0.001
Hotelling's trace	11.35	0.001	11.66	0.001	7.61	0.001
Roy's largest root	11.35	0.001	11.66	0.001	7.61	0.001

Abbreviation: ANOVA, analysis of variance.

Table 4.

Multiple comparisons of vacuum tube types at each day

Day	Vacuum tube comparison^∗	Mean difference	Unadjusted P value	P value using Holm-Bonferroni procedure	Unadjusted 95% confidence limits	95% confidence limits using Holm-Bonferroni procedure
0	B-S	0.80	0.0608	0.0608	(−0.040, 1.640)	(−0.040, 1.640)
	B-G	-2.10	0.0036	0.0072	(−3.423, −0.777)	(−3.638, −0.562)
	S-G	-2.90	0.0001	0.0003	(−4.142, −1.658)	(−4.458, −1.342)
1	B-S	1.05	0.0252	0.0504	(0.146, 1.954)	(−0.001, 2.101)
	B-G	-0.55	0.2749	0.2749	(−1.574, 0.474)	(−1.574, 0.474)
	S-G	-1.60	0.0002	0.0006	(−2.319, −0.881)	(−2.501, −0.699)
3	B-S	0.35	0.3672	0.7344	(−0.443, 1.143)	(−0.572, 1.272)
	B-G	-0.30	0.5163	0.5163	(−1.249, 0.649)	(−1.249, 0.649)
	S-G	-0.65	0.0115	0.0345	(−1.137, −0.163)	(−1.260, −0.040)

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