The mean and standard deviation: what does it all mean?

Abstract

With today’s computer technology, any investigator has access to the most powerful statistical analytic tools. However, without understanding the basic assumptions that statistical analyses use in deriving their results, erroneous conclusions regarding significance may be made. Several good textbooks present these concepts in relatively simple terms [1–4], yet many investigators have a limited understanding of the tests they use. Exclusive of the few texts oriented for biologists, most statistical treatments present the underpinnings of statistical concepts in mathematical terms that are difficult for biologists to understand. Worse yet, the terminology used is replete with double negatives, such as disproving the null hypothesis. Our intent is to present an overview of statistical concepts in terms that are easier to understand and will hopefully improve the ability for biologists to perform meaningful statistical analysis. We also present an expanded discussion on issues receiving little coverage in statistical texts, such as why n 1 rather than n is used when calculating standard deviations, to provide the reader with a better understanding of statistics. Statistics analyze groupings of numbers that represent outcomes from experimental observations. A series of steps are necessary to perform a statistical analysis of experimental data. First, the data need to be classified into one of three major categories: descriptive or nominal data, as the words imply, describe features that can be described, such as race, eye color, and so on. They cannot be ordered into any particular sequence or hierarchy. Statistical differences between groups classified into nominal data categories are most