Calculating Statistical Sample Size

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Statistical Sample Size Calculator

90% 95% 98% 99%
Leave at 50% if unknown (maximum variability).
Leave blank for large/unknown populations.

Recommended Sample Size

Understanding Statistical Sample Size

In statistics, determining the correct sample size is critical for the validity of your research or survey. If your sample size is too small, you may fail to detect important effects or patterns. If it is too large, you waste time and resources. This calculator uses standard formulas (including Cochran's Formula and the Finite Population Correction) to determine how many responses you need for statistically significant results.

Key Statistical Terms

  • Confidence Level: Indicates how confident you are that the actual population follows the same pattern as your sample. A 95% confidence level is the industry standard, meaning if you ran the study 100 times, 95 times the results would fall within the margin of error.
  • Margin of Error: Also known as the "Confidence Interval." This is the percentage amount that your results might differ from the real population value. For example, if 60% of your sample likes a product and you have a 5% margin of error, the real value is likely between 55% and 65%.
  • Population Proportion: The expected percentage of the population that has a certain attribute. When in doubt, use 50% (0.50), as this provides the most conservative (largest) sample size estimate.
  • Population Size: The total number of people in the group you are studying. If you are surveying the entire world or an extremely large group, you can leave this blank to use the infinite population formula.

The Calculation Formula

For an infinite population, the formula is:

n = (Z² * P * (1 – P)) / e²

Where:

  • n = Sample size
  • Z = Z-score (related to confidence level)
  • P = Population proportion
  • e = Margin of error

Example Calculation

Imagine you want to survey a city of 10,000 people (Population Size) to see if they support a new park. You want a 95% Confidence Level (Z = 1.96) and a 5% Margin of Error. Assuming a 50% Proportion:

  1. Calculate for infinite: (1.96² * 0.5 * 0.5) / 0.05² = 384.16
  2. Apply finite correction: 384.16 / (1 + (384.16 – 1) / 10,000)
  3. Result: Approximately 370 participants.
function calculateSampleSize() { var z = parseFloat(document.getElementById('confidenceLevel').value); var marginError = parseFloat(document.getElementById('marginOfError').value) / 100; var proportion = parseFloat(document.getElementById('populationProportion').value) / 100; var population = document.getElementById('totalPopulation').value; var resultDiv = document.getElementById('sampleResult'); var explanationDiv = document.getElementById('calculationExplanation'); var container = document.getElementById('resultContainer'); if (isNaN(marginError) || marginError = 1) { alert("Please enter a valid Margin of Error between 0.1 and 99."); return; } if (isNaN(proportion) || proportion = 1) { alert("Please enter a valid Population Proportion between 1 and 99."); return; } // Standard Cochran's Formula for infinite population var n0 = (Math.pow(z, 2) * proportion * (1 – proportion)) / Math.pow(marginError, 2); var finalN = n0; // Apply Finite Population Correction if population is provided if (population && population !== "" && !isNaN(population)) { var N = parseInt(population); if (N > 0) { finalN = n0 / (1 + ((n0 – 1) / N)); } } // Sample size must be a whole number, always round up var roundedResult = Math.ceil(finalN); resultDiv.innerHTML = roundedResult.toLocaleString(); var confText = document.getElementById('confidenceLevel').options[document.getElementById('confidenceLevel').selectedIndex].text; explanationDiv.innerHTML = "To achieve a " + confText + " confidence level with a +/-" + (marginError * 100).toFixed(1) + "% margin of error, you need " + roundedResult.toLocaleString() + " survey respondents."; container.style.display = 'block'; }

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