Last week I posted a video that provided an introduction to the basic concepts of statistics, namely effect sizes and sampling error. A test statistic like a t-value, is simply the ratio of the effect size over sampling error. This ratio is also known as a signal to noise ratio. The bigger the signal (effect size), the more likely it is that we will notice it in our study. Similarly, the less noise we have (sampling error), the easier it is to observe even small signals.
In this video, I use the basic concepts of effect sizes and sampling error to introduce the concept of statistical power. Statistical power is defined as the percentage of studies that produce a statistically significant result. When alpha is set to .05, it is the expected percentage of p-values with values below .05.
Statistical power is important to avoid type-II errors; that is, there is a meaningful effect, but the study fails to provide evidence for it. While researchers cannot control the magnitude of effects, they can increase power by lowering sampling error. Thus, researchers should carefully think about the magnitude of the expected effect to plan how large their sample has to be to have a good chance to obtain a significant result. Cohen proposed that a study should have at least 80% power. The planning of sample sizes using power calculation is known as a priori power analysis.
The problem with a priori power analysis is that researchers may fool themselves about effect sizes and conduct studies with insufficient sample sizes. In this case, power will be less than 80%. It is therefore useful to estimate the actual power of studies that are being published. In this video, I show that actual power could be estimated by simply computing the percentage of significant results. However, in reality this approach would be misleading because psychology journals discriminant against non-significant results. This is known as publication bias. Empirical studies show that the percentage of significant results for theoretically important tests is over 90% (Sterling, 1959). This does not mean that mean power of psychological studies is over 90%. It merely suggests that publication bias is present. In a follow up video, I will show how it is possible to estimate power when publication bias is present. This video is important to understand what statistical power.