Category:BMI560-W-08

Quantitative technique: One-Way Analysis of Variance (ANOVA)

Description: The analysis of variance is a partitioning of the total variance in a set of data into a number of component parts, so that the relative contributions of identifiable sources of variation to the total variation in measured responses can be determined. From this partition, suitable F-tests can be derived that allow differences between sets of means to be assessed.1

Thus ANOVA is a biostatistical method for determining whether a difference exists between the means of three or more independent populations. Expressed mathematically, it tests the null hypothesis- H0: 41 = 42 = 43 The one-way ANOVA parametric test will result in either accepting or rejecting this null hypothesis. If we reject the null hypothesis, then we can conclude that the population means are not equal. We do not know however whether all the means are different from one another or only some of them are different. This additional specificity is determined by conducting multiple comparison procedures, i.e. additional statistical tests.2

History: The phrase “analysis of variance” was coined by Sir Ronald Aylmer Fisher, a statistician of the twentieth century, who defined it as “the separation of variance ascribable to one group of causes from the variance ascribable to the other groups.”1

Principal use: One-way ANOVA is used when the researcher is comparing multiple groups (more than two) because it can control the overall Type I error rate.

Advantages: • It provides the overall test of equality of group means • It can control the overall type I error rate (i.e. false positive finding) • It is a parametric test so it is more powerful, if normality assumptions hold true

Shortcomings: • Requires that the population distributions are normal • It assumes equality of variances for each group

Examples in bioinformatics:

Maker VK, Donnelly MB. Surgical resident peer evaluations – what have we learned. J Surg Educ. 2008 jan-Feb;65(1):8-16.

McCloskey DJ. Nurses’ perceptions of research utilization in a corporate health care system. J Nurs Scholarsh. 2008;40(1):39-45.

Cohen A, Fleischer JB, Johnson MK, Brown IN, Joe AK, Hershman DL, McMahon DJ, Silverberg SJ. Prevention of bone loss after withdrawal of tamoxifen. Endocr Pract. 2008 Mar;14(2):162-7.

Sources: 1. Landau S, Everitt BS. A Handbook of Statistical Analyses Using SPSS, Chapman & Hall/CRC, 2004.

2. Pagano M, Gauvreau K. Principles of Biostatistics, 2nd Edition, Duxbury Press, Pacific Grove, CA, 2000.