Introduction

When designing a new study, a very useful exercise to carry out is that of determining an appropriate sample size. This is an important step in helping to ensure that the study achieves the outcomes it set out to achieve. As you may be able to imagine, if the sample size is not big enough, then the results of the study may not be strong enough to draw any significant or meaningful conclusions. On the other hand, increasing the sample size can come at a cost in many situations. This is why choosing an appropriate sample size is so important - so that a balance between these competing factors can be found. Sample size calculations are very much related to the concept of statistical power, which we will learn about in the next section. We will then look at some example sample size calculations for \(t\)-tests and the two-sample test of proportions.

These notes have been prepared by Amanda J. Shaker. The copyright for the material in these notes resides with the author named above, with the Department of Mathematics and Statistics and with La Trobe University. Copyright in this work is vested in La Trobe University including all La Trobe University branding and naming. Unless otherwise stated, material within this work is licensed under a Creative Commons Attribution-Non Commercial-Non Derivatives License CC BY-NC-ND