# Sample Size Calculator

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When conducting research, determining the appropriate sample size is crucial to obtaining accurate and reliable results. A sample size that is too small may lead to insufficient data and unreliable conclusions, while an excessively large sample size may waste resources and time. That's where the sample size calculator comes in. This tool allows you to quickly and easily calculate the optimal sample size for your research project, ensuring that your findings are both accurate and reliable.

## How to use the Sample Size Calculator?

Our sample size calculator is designed to be user-friendly and straightforward. To use the calculator, you'll need to input the following information:

1. Confidence Level: The confidence level represents the degree of certainty you want in your results. It is usually expressed as a percentage, with common values being 90%, 95%, or 99%. In the calculator, input the desired confidence level as a decimal (e.g., 0.95 for 95%).
2. Margin of Error: The margin of error indicates the range within which the true population value is likely to fall. It is expressed as a percentage, with smaller values indicating more precise results. In the calculator, input the desired margin of error as a decimal (e.g., 0.05 for 5%).
3. Population Size: If you're studying a finite population, you can input the size of the population to apply the finite population correction. If you're studying an infinite population or don't know the size of the population, enter a very high value such as 100000.

After entering the necessary information, click the "Calculate Sample Size" button. The calculator will then display the optimal sample size for your research project. This sample size will ensure that your results are accurate and reliable, given the confidence level and margin of error you specified.

## Sample Size Calculator

Sample Size Calculator

``` function calculateSampleSize() { const confidenceInput = document.getElementById('confidence'); const marginInput = document.getElementById('margin'); const populationInput = document.getElementById('population'); const output = document.getElementById('output'); const confidence = parseFloat(confidenceInput.value); const margin = parseFloat(marginInput.value); const population = parseInt(populationInput.value); if (isNaN(confidence) || isNaN(margin) || isNaN(population)) { alert('Please enter valid values for confidence level, margin of error and population size.'); return; } const z = getZScore(confidence); const sampleSize = calculateSampleSizeForProportion(z, margin, population); output.innerHTML = ` <p>Sample Size: \${Math.ceil(sampleSize)}</p> `; } function getZScore(confidence) { const alpha = 1 - confidence; const criticalProbability = 1 - alpha / 2; const z = -1 * Math.abs((Math.sqrt(2) * erfinv(2 * criticalProbability - 1)).toFixed(2)); return z; } function calculateSampleSizeForProportion(z, margin, population) { const p = 0.5; // Worst-case scenario (maximum uncertainty) const q = 1 - p; const numerator = (z * z) * p * q; const denominator = margin * margin; let sampleSize = numerator / denominator; // Finite population correction if (population !== Infinity) { sampleSize = sampleSize / (1 + ((sampleSize - 1) / population)); } return sampleSize; } function erfinv(x) { let w, p; w = -Math.log((1 - x) * (1 + x)); if (w < 5) { w = w - 2.5; p = 2.81022636e-08; p = 3.43273939e-07 + p * w; p = -3.5233877e-06 + p * w; p = -4.39150654e-06 + p * w; p = 0.00021858087 + p * w; p = -0.00125372503 + p * w; p = -0.00417768164 + p * w; p = 0.246640727 + p * w; p = 1.50140941 + p * w; } else { w = Math.sqrt(w) - 3; p = -0.000200214257; p = 0.000100950558 + p * w; p = 0.00134934322 + p * w; p = -0.00367342844 + p * w; p = 0.00573950773 + p * w; p = -0.0076224613 + p * w; p = 0.00943887047 + p * w; p = 1.00167406 + p * w; p = 2.83297682 + p * w; } return p * x; } ```

## Conclusion

The sample size calculator is a valuable tool for researchers, helping you to determine the appropriate sample size for your research project. By using this calculator, you can ensure that your findings are accurate, reliable, and supported by sufficient data. So, go ahead and give our sample size calculator a try – it's an essential resource for any researcher.

Posted on April 7, 2023 by  Quality Gurus

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