Understanding Type 2 Errors in Hypothesis Testing | How to Detect the Undetected

Type 2 error

In hypothesis testing, a type 2 error occurs when we fail to reject a null hypothesis that is actually false

In hypothesis testing, a type 2 error occurs when we fail to reject a null hypothesis that is actually false. It is also known as a “false negative” error.

To understand type 2 errors, let’s first review the basics of hypothesis testing. In hypothesis testing, we have a null hypothesis (H0) and an alternative hypothesis (Ha), representing two conflicting statements about a population parameter. We collect sample data and use it to make an inference about the population parameter.

When conducting hypothesis testing, we set a significance level (α), which determines the probability of making a type 1 error. If the p-value (the probability of obtaining our observed data, assuming the null hypothesis is true) is less than the significance level, we reject the null hypothesis in favor of the alternative hypothesis.

However, if the p-value is greater than the significance level, we fail to reject the null hypothesis. This is where a type 2 error can occur. It means that we failed to reject the null hypothesis, even though the alternative hypothesis is correct.

To put it simply, a type 2 error occurs when we miss detecting a difference or effect that actually exists. It can happen when the sample size is too small, leading to insufficient statistical power. In other words, we have a higher chance of making a type 2 error when our study lacks the ability to detect a true difference.

In practical terms, let’s consider an example. Imagine a pharmaceutical company testing a new drug to lower blood pressure. The null hypothesis states that the drug has no effect on blood pressure, while the alternative hypothesis suggests that the drug does have an effect. If the company fails to reject the null hypothesis and concludes that their drug has no effect on blood pressure (when it actually does), they commit a type 2 error.

To minimize the probability of type 2 errors, researchers can increase the sample size or adjust the significance level. However, it’s essential to strike a balance between avoiding type 2 errors and controlling type 1 errors (rejecting a null hypothesis that is actually true). This trade-off is inherent in statistical hypothesis testing.

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