What are the best practices for selecting a sample size in experimental design?

Effect size is particularly important. A real but small effect can only ever show up as a significant difference in a large experiment, but equally a small experiment can be enough to allow a very large effect to show up as a significant difference. For example, to become licensed a new pesticide for aquaculture must clear almost 100% of parasites and so will be obvious, whereas to be cost effective a replacement ingredient for an aquaculture feed might only need to cause a tiny increase in growth per day that will only be detectable if allowed to accumulate like compound interest. In the first case a small direct test is appropriate whereas in the second a six month trial might be required.

In the realm of experimental design, the nature of your experiment significantly shapes the ideal sample size. In randomized controlled trials (RCTs), factors like effect size, statistical power, and significance level play pivotal roles. A larger sample enhances the test's power and accuracy but amplifies costs and complexity. Conversely, qualitative or exploratory experiments thrive on flexibility, opting for an iterative approach until reaching a saturation point where novel insights cease to emerge. Balancing precision with practicality defines the art of choosing the right sample size for meaningful results.

The study design and sampling method influence the sample size. Outcome measures also influence the sample size, such as the significance level of your study (p = .05). It is important to consider the feasibility of recruiting a particular sample size, and design the experiment with this in mind.

The purpose behind your experiment guides the requisite sample size. In pilot or feasibility experiments, the focus isn't on quantity but on obtaining enough data to gauge intervention practicality and identify potential issues. Such trials aid in estimating effect size, shaping the groundwork for larger endeavors. Conversely, confirmatory or hypothesis-testing experiments demand ample participants to uphold findings' validity and generalizability, guarding against misleading positives or negatives. Precision in sample size aligns with the overarching goal, be it exploratory insights or robust, conclusive results.

The constraints within your experiment introduce a pragmatic dimension to sample size considerations. Limited resources—be it budget, time, or access to participants—may necessitate compromises in size or design. Optimizing becomes key, employing strategies like leveraging existing data, embracing stratified or cluster sampling, adopting adaptive or sequential designs, or integrating Bayesian methods. Yet, a caveat lies in acknowledging potential trade-offs: heightened bias, diminished precision, or increased complexity. Navigating these constraints requires a delicate balance, ensuring methodological adjustments don't compromise the integrity of your study.

Additionally, ethical considerations play a crucial role in determining the appropriate sample size for your experiment. Ensuring the well-being and rights of participants is paramount. Striking a balance between obtaining sufficient data and safeguarding ethical standards is essential. Ethical scrutiny is especially pertinent in experiments with vulnerable populations or those involving interventions that may have potential risks. A thoughtful approach to ethical considerations further enriches the holistic perspective on selecting the right sample size for a scientifically robust and ethically sound experiment.