What are the common misconceptions about statistical power you should avoid?

1. Equating power with sample size while larger sample sizes generally increase power, other factors like effect size and significance level also play crucial roles. 2. Ignoring effect size, power analysis should consider the magnitude of the effect being studied, as larger effects require smaller sample sizes for detection.

A few widespread fallacies about statistical power can cause you to stumble more quickly than an anomalous data point. First of all, don't let the notion that bigger is always better deceive you. Power can be increased by greater sample numbers, but this isn't the only element at work. Second, resist the temptation to believe that p-values are the gold standard for power indicators. They're not the complete tale, but they're crucial. Lastly, keep in mind that power is not a supernatural force capable of amplifying a weak influence into a strong one. It functions more like a magnifying glass in that it can make things visible to you but cannot generate anything from nothing.

A prevalent misconception about statistical power is the belief that high statistical power guarantees the detection of a true effect. High statistical power does indeed improve the probability of correctly rejecting a false null hypothesis, but it doesn't ensure that all true effects will be detected. Factors such as effect size, sample size, and significance criteria all influence power. Thus, while high statistical power is essential for reducing the risk of Type II errors, where a true effect goes undetected, it is not foolproof. Understanding its limitations is crucial for correctly interpreting study results and setting realistic expectations for research outcomes.

A common misconception is confusing statistical power with significance. Power relates to the likelihood of detecting an effect if it truly exists, focusing on avoiding Type II errors (failing to detect a true effect). Significance, on the other hand, deals with determining whether an observed effect is unlikely to have occurred by chance, primarily concerned with Type I errors (false positives). High power does not imply that an effect is significant, nor does a significant result necessarily indicate that the study was sufficiently powered. Understanding this distinction is essential for properly designing studies and interpreting their results accurately.

This is somewhat of an easy mistake to make. Ultimately, power helps you to determine whether you will be able to find (detect) unique and useful effects from your statistical model(s). Statistical significance is what most people associate with the p-value: will said effects be due to chance or not? Before you engage in an experiment, project, study, etc. you should engage in power analysis. This will help you to determine the smallest sample size that you can get away with. You may worry about significance later on in your task. However, you can determine/estimate what you believe is an appropriate statistical significance, power, and effect size(s) before the power analysis. Remember, statistics is a science. Studies can vary a lot.

In the context of DOEs, there are indeed many ways to increase power than just increasing sample size (fortunately). In explorative studies, it is often a good strategy to accept to increase your "type 1" error risk to increase power. But outside of this type of "statistical game", if I had to name only one, I'd say the way we treat the experimental Noise. Blocking or Split Plot experiments for example.

A common misconception about statistical power is that increasing the sample size is the only way to increase a study's power. While it is generally true that larger sample sizes can enhance power, they are not the only factor. Power also depends on the effect size (the magnitude of the difference being measured) and the significance level set for the study. Sometimes, even with a large sample size, if the effect size is very small, the power might still be insufficient to detect a significant effect. It's important to balance all these factors — sample size, effect size, and significance level — when designing studies.

A freequent misconception is the rigid adherence to the 0.8 standard for statistical power, which suggests that a study should have at least 80% power to be considered adequately powered. While this benchmark is useful as a general guideline, it is not universally applicable across all research. Different studies might require different power levels depending on the context, the potential impact of the findings, and the feasibility of obtaining large sample sizes. Relying solely on this standard without considering the specific needs and constraints of your research can lead to unnecessary oversampling or underpowered studies in cases where different thresholds might be more appropriate.

Consider researchers testing a new blood pressure medication. They run a trial with 100 participants and find a significant reduction in blood pressure for the drug group compared to the placebo. Post-trial, they perform a post-hoc power analysis using the observed effect size from their results. This analysis shows high power, seemingly validating their findings. However, this approach is flawed because the observed effect size can be misleading if it's unusually large due to small sample size or data variability. Ideally, power analysis should be conducted before the study to determine necessary sample size and avoid misleading confidence in the results.