Calculate Statistical Power Sample Size

Statistical Power Sample Size Calculator

Use this calculator to determine the minimum sample size required for each group in a two-sample t-test to achieve a desired statistical power, given a significance level and an expected effect size (Cohen's d).

80% (0.80) 90% (0.90) 95% (0.95)

5% (0.05) 1% (0.01) 10% (0.10)

function calculateSampleSize() { var desiredPower = parseFloat(document.getElementById("desiredPower").value); var significanceLevel = parseFloat(document.getElementById("significanceLevel").value); var effectSize = parseFloat(document.getElementById("effectSize").value); if (isNaN(desiredPower) || isNaN(significanceLevel) || isNaN(effectSize) || effectSize <= 0) { document.getElementById("sampleSizeResult").innerHTML = "Please enter valid positive numbers for all fields, and Effect Size must be greater than 0."; return; } // Z-score lookup table for common values var zAlphaLookup = { "0.01": 2.576, // Two-tailed for alpha=0.01 "0.05": 1.96, // Two-tailed for alpha=0.05 "0.10": 1.645 // Two-tailed for alpha=0.10 }; var zBetaLookup = { "0.80": 0.842, // For power=0.80 "0.90": 1.282, // For power=0.90 "0.95": 1.645 // For power=0.95 }; var zAlpha = zAlphaLookup[significanceLevel.toString()]; var zBeta = zBetaLookup[desiredPower.toString()]; if (!zAlpha || !zBeta) { document.getElementById("sampleSizeResult").innerHTML = "Could not find Z-scores for the selected Power or Significance Level. Please choose from the provided options."; return; } // Formula for sample size per group (n) for a two-sample t-test using Cohen's d // n = ( (Z_alpha/2 + Z_beta)^2 * 2 ) / Cohen's d^2 var numerator = Math.pow((zAlpha + zBeta), 2) * 2; var denominator = Math.pow(effectSize, 2); var sampleSizePerGroup = Math.ceil(numerator / denominator); var totalSampleSize = sampleSizePerGroup * 2; var resultHTML = "

Required Sample Size:

"; resultHTML += "Sample Size per Group: " + sampleSizePerGroup + ""; resultHTML += "Total Sample Size: " + totalSampleSize + ""; document.getElementById("sampleSizeResult").innerHTML = resultHTML; }

Understanding Statistical Power and Sample Size

In statistical hypothesis testing, determining the appropriate sample size is crucial for the validity and reliability of research findings. A sample size that is too small might fail to detect a real effect, leading to a Type II error (false negative), while an unnecessarily large sample size can be a waste of resources and time.

What is Statistical Power?

Statistical power is the probability that a study will correctly reject a false null hypothesis. In simpler terms, it's the probability of finding an effect if there actually is one. Researchers typically aim for a power of 0.80 (80%), meaning there's an 80% chance of detecting a true effect if it exists. Higher power reduces the risk of a Type II error.

What is Significance Level (Alpha)?

The significance level, denoted as alpha (α), is the probability of making a Type I error (false positive). A Type I error occurs when you incorrectly reject a true null hypothesis. Common alpha levels are 0.05 (5%), 0.01 (1%), or 0.10 (10%). An alpha of 0.05 means there's a 5% chance of concluding there's an effect when there isn't one.

What is Effect Size (Cohen's d)?

Effect size quantifies the magnitude of the difference or relationship between variables. It's a standardized measure, meaning it's independent of the units of measurement. For a two-sample t-test, Cohen's d is a commonly used effect size measure. It represents the difference between two means in terms of standard deviations.

• Small Effect Size (d = 0.2): The difference is barely perceptible or trivial.
• Medium Effect Size (d = 0.5): The difference is noticeable and of practical significance.
• Large Effect Size (d = 0.8): The difference is substantial and clearly evident.

Estimating the expected effect size is often the most challenging part of sample size calculation. It can be based on previous research, pilot studies, or theoretical considerations.

How the Calculator Works (Two-Sample T-Test)

This calculator uses the following formula to determine the sample size per group (n) for a two-sample t-test, assuming equal group sizes and variances:

n = ( (Zα/2 + Zβ)2 * 2 ) / d2

• Zα/2: The Z-score corresponding to the chosen significance level (alpha), for a two-tailed test.
• Zβ: The Z-score corresponding to the desired statistical power (1 – beta).
• d: The expected effect size (Cohen's d).

The calculator then rounds up the result to the nearest whole number, as sample sizes must be integers, and multiplies it by two to get the total sample size for both groups.

Example Scenario:

Imagine a researcher wants to compare the effectiveness of two different teaching methods on student test scores. They hypothesize a medium effect size (Cohen's d = 0.5) based on prior literature. They want to achieve 80% statistical power and set their significance level at 0.05.

• Desired Power: 0.80
• Significance Level (Alpha): 0.05
• Expected Effect Size (Cohen's d): 0.5

Using the calculator, the researcher would find that they need approximately 64 students per group, for a total of 128 students, to detect a medium effect with 80% power at a 0.05 significance level.

Why is Sample Size Important?

• Ethical Considerations: Too many participants can expose more individuals than necessary to potential risks, while too few might lead to inconclusive results, wasting participants' time and resources.
• Resource Allocation: Proper sample size planning helps optimize the use of time, money, and personnel.
• Validity of Results: An adequately powered study is more likely to produce statistically significant and meaningful results if an effect truly exists.
• Publication Bias: Studies with insufficient power are more likely to produce non-significant results, which are less likely to be published, contributing to publication bias.

Always consider the practical implications and ethical guidelines when determining your final sample size.