Sample size calculation is the cornerstone of statistical analysis.

To start things off, let's align on what we're talking about when we say "sample size." In the simplest terms, sample size refers to the number of observations or individuals included in a sample. It's the group of folks whose behavior you're scrutinizing in an experiment or a study.

Why does sample size matter, you ask? Well, it's directly tied to the reliability and accuracy of your results. The golden rule is: the larger your sample size, the more reliable and valid your results are likely to be.

Think of it as casting a wider net to catch more fish—the bigger the net, the more fish you’ll likely catch, and the more accurate your understanding of the fish population.

See also: How the 2008 Obama campaign set the standard for modern email sample size practices still used today.

Factors influencing sample size

Now that we're on the same page about what sample size is, let's delve into the nitty-gritty of what determines it. Some of the usual factors include total population size, the level of precision you're after, and the statistical power of the test being used.

Larger sample sizes are usually recommended when the population you're studying is relatively small, or when you're chasing high precision. It’s kind of like using a magnifying glass for a detailed examination—you’re trying to get as close to the truth as possible, so you want more data to inform your decisions.

Calculating sample size isn't a one-size-fits-all formula. Instead, it's a carefully balanced equation of multiple factors that are evaluated before any study or experiment is carried out. Once the sample size is determined, then it's "ready, set, go!" for your study or experiment.

Deep dive: Calculating sample sizes for A/B tests.

The balancing act of choosing sample size

If you're a data scientist in a software company, your primary concern when choosing the sample size is ensuring the experiment delivers reliable, actionable insights. You're constantly juggling a handful of metrics: the level of precision desired, the anticipated effect size, the statistical power of the experiment, and real-world limitations like the size of the population and participant availability.

The desired precision level refers to how accurately the experiment can measure the effect being studied. If you're gunning for spot-on precision, you're looking at a larger sample size. However, if you're okay with a bit of leeway, a smaller sample size might suffice.

Anticipated effect size is essentially the magnitude of the effect you're studying. If it's a larger effect, you can get by with a smaller sample size, while a smaller effect will require a larger sample size.

Statistical power, the probability that your experiment will detect an effect if there is one to be found, is another key piece of this puzzle. The higher the statistical power you want, the larger your sample size needs to be.

Real-world limitations also come into play. If your user base is limited, or participant availability is constrained, you may need a larger sample size to achieve your desired precision level and statistical power.

Statistical significance calculator

Statsig's sample size calculator is a quick way to determine which size is optimal to achieve minimum detectable effect.

Use the calculator

Juggling small audiences

If your user base is small, it's a bit like playing chess on a small board—you have to plan your moves even more carefully. You might need to increase your sample size and adjust the statistical power of your experiment to ensure the accuracy and reliability of your results.

With fewer users, you have fewer potential participants for your sample, which can impact the reliability and accuracy of your findings. Additionally, you might need to adjust the statistical power of your experiment to compensate for the small audience size. It’s all about making the most of what you’ve got.

Wrapping up

In the grand scheme of statistical analysis, sample size might seem like a small cog in a large machine. But underestimate it at your own peril. It’s the responsibility of data scientists to ensure they're harnessing the power of sample size to create experiments and analyses that deliver reliable, actionable insights.

Remember, it's all about understanding your audience, knowing your goals, and being aware of the limits of your resources. So here's to embracing the power of sample size in our statistical analyses, and to the ever-evolving journey of discovery it brings!