Practical Biostatistics in Translational Healthcare by Allen M. Khakshooy & Francesco Chiappelli

Author:Allen M. Khakshooy & Francesco Chiappelli
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

6.5.1 ANOVA

While Gosset argued that a comp arison of distributions should be done through means, Sir Ronald Aylmer Fisher contended that it is the variances of distributions that need be compared for the existence of an effect. Without even introducing the reasoning, we can surmise the plausibility of using variances rather than means to facilitate a comparison. Our extensive discussion on descriptive statistics (Chap. 4) proved to us that measures of central tendency and variability were simply two different, yet related and equally important, perspectives of describing a distribution. Subsequently, testing a hypothesis with a statistical test rooted in variability should not be alarming; neither should the fact that this technique is utilized within the context of testing for population means .

Fisher went on to develop the F-statistic and the corresponding statistical analysis technique referred to as ANOVA (analysis of variance) or, as used in hypothesis testing, the F test . Indeed, it is the variance of the different groups that must be analyzed in order to test a null hypothesis for multiple parameters. This technique allots the study of multiple independent groups by analyzing the variability between the groups and comparing it to the variability within the groups. In essence, the basic conceptual format of the F-statistic is:

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