Power Analysis Calculator

Power Analysis & Sample Size Calculator

Small: 0.2 | Medium: 0.5 | Large: 0.8
0.01 (1%) 0.05 (5%) 0.10 (10%) Standard threshold for Type I Error.
0.80 (80%) 0.85 (85%) 0.90 (90%) 0.95 (95%) Probability of avoiding Type II Error.
Use 1.0 for equal group sizes.

Calculation Results

Group 1 Size

0

Group 2 Size

0

Total Sample Size Required

0

Understanding Power Analysis in Research

Power analysis is a critical statistical procedure performed during the design phase of a study. It allows researchers to determine the minimum sample size required to detect an effect of a given size with a specific degree of confidence. Conducting a power analysis ensures that your study is adequately powered to avoid "Type II errors"—the failure to detect an effect that actually exists.

Key Components of the Calculation

  • Effect Size (Cohen's d): This represents the magnitude of the difference you expect to find between your groups. A d of 0.2 is considered small, 0.5 medium, and 0.8 large.
  • Significance Level (Alpha): The probability of rejecting the null hypothesis when it is actually true (Type I error). Typically set at 0.05.
  • Statistical Power: The probability that the test correctly rejects the null hypothesis when the alternative hypothesis is true. Most behavioral science research aims for a power of 0.80 or higher.
  • Allocation Ratio: The ratio of the number of participants in group two compared to group one. For most clinical trials or experiments, this is 1.0 (equal sizes).

Example Calculation

Imagine you are testing a new teaching method. You expect a Medium Effect Size (0.5). You set your Alpha at 0.05 and desire a Power of 0.80. Using this calculator, you would find that you need approximately 64 participants per group, for a total sample size of 128 students. This ensures that if the new method truly works as expected, you have an 80% chance of proving it statistically.

Why Sample Size Matters

Studies with sample sizes that are too small often lead to "underpowered" results, where important findings are missed. Conversely, unnecessarily large samples can be a waste of resources, funding, and participant time. A precise power analysis strikes the perfect balance between scientific rigor and operational efficiency.

function calculatePower() { var d = parseFloat(document.getElementById('effectSize').value); var alpha = parseFloat(document.getElementById('alpha').value); var power = parseFloat(document.getElementById('power').value); var k = parseFloat(document.getElementById('ratio').value); var resultsDiv = document.getElementById('results'); if (isNaN(d) || d <= 0 || isNaN(k) || k <= 0) { alert("Please enter valid positive numbers for Effect Size and Ratio."); return; } // Z-score approximations for Alpha (Two-tailed) var zAlpha; if (alpha == 0.01) zAlpha = 2.576; else if (alpha == 0.05) zAlpha = 1.960; else if (alpha == 0.10) zAlpha = 1.645; else zAlpha = 1.960; // Z-score approximations for Power (One-tailed Z-beta) var zBeta; if (power == 0.80) zBeta = 0.842; else if (power == 0.85) zBeta = 1.036; else if (power == 0.90) zBeta = 1.282; else if (power == 0.95) zBeta = 1.645; else zBeta = 0.842; // Standard formula for sample size per group (n1) for comparison of two means // n1 = ( (k+1)/k ) * (zAlpha + zBeta)^2 / d^2 var n1 = ((k + 1) / k) * Math.pow((zAlpha + zBeta) / d, 2); // Finalize numbers var finalN1 = Math.ceil(n1); var finalN2 = Math.ceil(finalN1 * k); var totalN = finalN1 + finalN2; // Display results document.getElementById('n1Result').innerHTML = finalN1; document.getElementById('n2Result').innerHTML = finalN2; document.getElementById('totalNResult').innerHTML = totalN; resultsDiv.style.display = 'block'; }

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