Sample Size Calculator

Sample Size Calculator

90% (Z = 1.645) 95% (Z = 1.96) 99% (Z = 2.576)

Recommended Sample Size:

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Understanding Sample Size Calculation

In research and statistics, determining the correct sample size is crucial for ensuring that your results are representative of the larger population. A sample size that is too small may lead to unreliable results, while a sample size that is too large may waste resources and time.

Key Terms Defined

• Confidence Level: Indicates how sure you are that the actual population follows the findings of your sample. Common choices are 95% or 99%.
• Margin of Error: Also known as the confidence interval. This is the amount of "wiggle room" you allow for your results. For example, if you have a 5% margin of error and 60% of your sample answers "Yes," you can be confident that between 55% and 65% of the total population would answer "Yes."
• Population Size: The total number of people or items in the group you are studying. If you are surveying a city of 50,000, that is your population size.
• Population Proportion: The expected percentage of the population that has a certain characteristic. If you are unsure, using 50% (0.50) is the most conservative estimate and ensures a large enough sample size.

The Formula We Use

This calculator utilizes Cochran's formula for large populations and adjusts it for finite populations:

n₀ = (Z² * p * (1-p)) / e²

Where:

• Z is the Z-score based on the confidence level.
• p is the population proportion.
• e is the margin of error (as a decimal).

Realistic Example

Suppose you want to survey a university with 5,000 students to find out how many use the library. You want a 95% confidence level and a 5% margin of error. Assuming a 50% proportion for the most conservative result:

1. Infinite sample size calculation: (1.96² * 0.5 * 0.5) / 0.05² = 384.16
2. Adjusting for the 5,000 population: 384.16 / (1 + (384.16 – 1) / 5000) = 356.66
3. Result: You would need a sample size of 357 students.

function calculateSampleSize() { var z = parseFloat(document.getElementById("confidence").value); var e = parseFloat(document.getElementById("marginOfError").value) / 100; var p = parseFloat(document.getElementById("proportion").value) / 100; var popSizeInput = document.getElementById("population").value; var N = popSizeInput !== "" ? parseFloat(popSizeInput) : null; if (isNaN(e) || e = 1) { alert("Please enter a valid Margin of Error (between 0 and 100)."); return; } if (isNaN(p) || p = 1) { alert("Please enter a valid Population Proportion (between 0 and 100)."); return; } // Cochran's formula for sample size var n0 = (Math.pow(z, 2) * p * (1 – p)) / Math.pow(e, 2); var finalN; if (N !== null && !isNaN(N) && N > 0) { // Adjust for finite population finalN = n0 / (1 + ((n0 – 1) / N)); } else { finalN = n0; } var result = Math.ceil(finalN); document.getElementById("sampleResult").innerText = result.toLocaleString(); document.getElementById("result-box").style.display = "block"; var interpretationText = "With a " + (document.getElementById("confidence").options[document.getElementById("confidence").selectedIndex].text.split(' ')[0]) + " confidence level and a " + (e * 100).toFixed(1) + "% margin of error, you need at least " + result.toLocaleString() + " responses."; document.getElementById("interpretation").innerText = interpretationText; }