Failing to reject a false null hypothesis, meaning a real difference is not found, is known as?

Failing to reject a false null hypothesis, meaning a real difference is not found, is known as?

• A. Type II error
• B. Type I error
• C. Sampling error
• D. Instrumentation error

Answer: (A)

The concept being tested is Type II error: failing to reject a false null hypothesis, meaning there is a real difference or effect, but the study does not show it. This is also called a false negative. When the null hypothesis is actually false but the test concludes there is no effect, you miss the finding. Think of the two types of errors in hypothesis testing: Type I error is a false alarm—rejecting a true null. Type II error is missing a real effect—failing to reject a false null. Type II error arises when the study lacks enough evidence to detect the true difference, which can happen with small sample sizes, high variability, or a small effect size. The probability of this error is beta, and power (1 minus beta) reflects how likely you are to detect a real effect. To reduce Type II error, you can increase sample size, use more precise measurements to reduce noise, or design the study to have greater sensitivity to the expected effect. In contrast, sampling error and instrumentation error describe different issues: sampling error is the natural variability from selecting a subset of the population, and instrumentation error refers to measurement inaccuracies.

The concept being tested is Type II error: failing to reject a false null hypothesis, meaning there is a real difference or effect, but the study does not show it. This is also called a false negative. When the null hypothesis is actually false but the test concludes there is no effect, you miss the finding.

Think of the two types of errors in hypothesis testing: Type I error is a false alarm—rejecting a true null. Type II error is missing a real effect—failing to reject a false null. Type II error arises when the study lacks enough evidence to detect the true difference, which can happen with small sample sizes, high variability, or a small effect size. The probability of this error is beta, and power (1 minus beta) reflects how likely you are to detect a real effect.

To reduce Type II error, you can increase sample size, use more precise measurements to reduce noise, or design the study to have greater sensitivity to the expected effect. In contrast, sampling error and instrumentation error describe different issues: sampling error is the natural variability from selecting a subset of the population, and instrumentation error refers to measurement inaccuracies.