Type II Error Calculator Online

In the realm of statistics, understanding the impact of errors is crucial for data analysis. A Type II error, also known as a false negative, occurs when a statistical test fails to reject a false null hypothesis. This kind of error can have significant consequences in various fields, from scientific research to business analytics. The Type II Error Calculator is a tool designed to help users estimate the probability of committing a Type II error, based on specific input parameters related to their data set and hypothesis testing approach.

Formula of Type II Error Calculator

The formula for calculating statistical power, which is inversely related to the probability of a Type II error, is fundamental in statistical hypothesis testing. Here’s a simplified breakdown of the formula used in the context of testing means, where the assumption is that data follows a normal distribution:

Statistical Power Formula:

Power = 1 – beta = P((X̄ – μ) / (σ / √n) > Z(1 – α) – (μ – μ0) / (σ / √n))

Where:

• X̄ is the sample mean.
• μ is the true population mean.
• μ0 is the mean under the null hypothesis.
• σ is the standard deviation of the population.
• n is the sample size.
• Z(1 – α) is the 1 – alpha quantile of the standard normal distribution.

To calculate β (the probability of a Type II error), you subtract the power from 1:

β = 1−Power

Table of Statistical Power Values

Below is a table providing general values for statistical power given common levels of alpha, sample sizes, and effect sizes. This table allows users to estimate the probability of a Type II error without detailed calculations:

Effect Size	Sample Size	Alpha Level	Power
Small	30	0.05	0.12
Medium	30	0.05	0.56
Large	30	0.05	0.88
Small	100	0.05	0.34
Medium	100	0.05	0.80
Large	100	0.05	0.98

These values provide a quick reference for researchers or analysts to assess the adequacy of their study’s design in terms of its statistical power.

Example of Type II Error Calculator

Let’s consider an example to illustrate the use of the Type II Error Calculator:

Suppose a pharmaceutical company is testing a new drug to lower blood pressure. The null hypothesis (H0) states that the drug has no effect, while the alternative hypothesis (H1) suggests that the drug does lower blood pressure. The company conducts a clinical trial with a sample size of 100 patients.

After analyzing the data, the statistical power of the test is found to be 0.80, indicating an 80% chance of correctly rejecting the null hypothesis if it is false. Therefore, the probability of committing a Type II error (beta) is 0.20 or 20%.

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