Type I and Type II Error Calculator

A Type I error (also called a false positive) occurs when you reject the null hypothesis even though it is actually true. The probability of committing a Type I error is equal to the significance level (α) you choose for your test. For example, if α = 0.05, there is a 5% chance of a Type I error.

A Type II error (also called a false negative) occurs when you fail to reject the null hypothesis even though it is actually false. Its probability is denoted by β. Type II errors matter because they mean your study missed a real effect — a significant concern in medical research, quality control, and social sciences where detecting a true difference is critical.

Type I and Type II errors are inversely related when all other factors are held constant. Lowering α (reducing Type I error risk) generally increases β (raises Type II error risk), and vice versa. The only way to reduce both simultaneously is to increase the sample size.

Statistical power (1 - β) is the probability that your test correctly rejects a false null hypothesis. A power of 0.80 (80%) is conventionally considered the minimum acceptable threshold, meaning there is at most a 20% chance of a Type II error. Values above 0.90 are preferred for high-stakes research.

Increasing sample size reduces the standard error of the mean, which narrows the sampling distribution and makes it easier to detect a true effect. This directly lowers β (Type II error) and increases statistical power, without changing α (Type I error), which is fixed by the researcher.

Use a one-tailed test when you have a specific directional hypothesis (e.g., the true mean is greater than the null mean). Use a two-tailed test when you want to detect a difference in either direction. Two-tailed tests are more conservative and are the default in most scientific research.

You need five inputs: the null hypothesis mean (μ₀), the true (alternative) mean (μ₁), the population standard deviation (σ), the sample size (n), and the significance level (α). The calculator uses a Z-test framework, so it is most appropriate when the population standard deviation is known or the sample size is large.

Effect size (Cohen's d) measures the standardized difference between the null and true means. A larger effect size means the two distributions are farther apart, making them easier to distinguish — this increases statistical power and reduces Type II error. Small effect sizes require larger samples to achieve adequate power.