Fundamental concepts in statistics: elucidation and illustration

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Abstract
Fundamental concepts in statistics form the cornerstone of scientific inquiry. If we fail to understand fully these fundamental concepts, then the scientific conclusions we reach are more likely to be wrong. This is more than supposition: for 60 years, statisticians have warned that the scientific literature harbors misunderstandings about basic statistical concepts. Original articles published in 1996 by the American Physiological Society’s journals fared no better in their handling of basic statistical concepts. In this review, we summarize the two main scientific uses of statistics: hypothesis testing and estimation. Most scientists use statistics solely for hypothesis testing; often, however, estimation is more useful. We also illustrate the concepts of variability and uncertainty, and we demonstrate the essential distinction between statistical significance and scientific importance. An understanding of concepts such as variability, uncertainty, and significance is necessary, but it is not sufficient; we show also that the numerical results of statistical analyses have limitations.