StatTools : Sample Size Introduction and Explanation

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Probability Introduction and Explanation Page

Introduction Nomenclature Approximate Sample Size Associated Calculations References
As explained in the Probability Introduction and Explanation Page , statistical decisions became possible with the development of Type I Error by Fisher. A later improvement came through the use of Type II Error and the statistical significance model by Pearson. Pearson's model was developed with the intension of providing a statistical decision. However, it provides a theoretical framework to mathematically relate between Type I Error (α), Type II Error (β), a non trivial value that represents a difference that matters, Standard Deviation (SD), and sample size. If four (4) of these parameters are known, then the fifth can be calculated.

From this, the sample size required to compare two groups can be estimated if the other four (4) parameters are available. In other words, researchers are able to know the sample size they need for their results to be interpreted with confidence.

Understanding this model and the availability of an objective method to calculate optimal sample size allow further development and emphasis on sample size theories and practices.

At the technical level, statistical modelling allows sample size calculations to extend to data with different types of distributions (e.g., proportions, counts, time to events, ranks) and specialised research situations (e.g., phase II drug trials, post marketing trials, quality testing).

From the researcher's point of view, the availability of sample size estimation greatly assists planning and evaluation of research situations. Knowledge of the appropriate sample size allows the researcher to estimate the time and resources required to complete the study and therefore, the feasibility and viability of the project.

An undersized study produces either uninterpretable results or results that will not stand the test of time. On the other hand, a study larger than necessary wastes resources, inconveniences colleagues and imposes unnecessary risks and discomfort to research subjects.

The absence of adequate sample size considerations therefore symbolises poor research design and indicates bad and possibly unethical research. Increasingly, if sample size considerations are inadequate, granting bodies will not support, regulating bodies will not approve, and editors of scientific publications will not accept results of the research project.

The importance of sample size is discussed clearly and comprehensively by Cohen (see references) and this is very much a recommended reading.