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Sample Size Calculator

Leave blank for infinite population

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How to use the Sample Size Optimization: Precision vs. Cost

Determining the correct Sample Size is the first step in any rigorous research or survey. Collecting too much data is a waste of resources (time and money), while collecting too little leads to underpowered studies that may fail to detect important effects even when they truly exist.

📉 Diminishing Returns

Accuracy doesn't scale linearly with sample size. To cut your Margin of Error in half, you actually need to quadruple your sample size. This represents a law of diminishing returns where researchers must balance the cost of acquisition against the necessity of extreme precision.

🔋 Statistical Power

In medical research, Power Analysis acts as a safeguard. It ensures that a clinical trial has enough participants to prove a drug's efficacy with statistical certainty. A "low powered" study is one of the leading causes of the Replication Crisis in social sciences.

The Formula

n = (z² × p × [1-p]) / e²

The Finite Population Correction

If the population you are studying is relatively small (e.g., employees at a specific company), you can use the Finite Population Correction (FPC). This mathematical adjustment reduces the required sample size because each individual response represents a larger proportion of the whole, increasing your study's overall efficiency.

Frequently Asked Questions

Frequently Asked Questions

What is "Non-Response Bias"?

Even with a perfect sample size, your results can be skewed if the people who *don't* respond are different from those who *do*. For example, a survey about digital literacy might miss the very people who struggle with technology, leading to misleadingly high scores.

Why is 0.5 used for expected proportion?

When you don't know the expected result of a survey, using **0.5 (50%)** is the "safest" choice. It yields the **maximum possible sample size**, ensuring that your survey is adequately powered regardless of how the population actually feels.

What is the relationship between Margin of Error and Sample Size?

They are inversely proportional. To **halve** your margin of error (e.g., from 4% to 2%), you need to **quadruple** your sample size. This is why extremely high-precision surveys require significantly larger budgets and more participants.