Types of Errors

Whenever you make a decision in hypothesis testing based on sample data, there's always some chance of getting it wrong. Statisticians classify these mistakes into two types - Type I and Type II errors.

Type I Error (False Positive)

Rejecting the null hypothesis when it is actually true - concluding there's an effect or difference when there really isn't one. The probability of a Type I error is denoted by alpha (α), the significance level you chose for the test.

Type II Error (False Negative)

Failing to reject the null hypothesis when it is actually false - missing a real effect or difference that does exist. The probability of a Type II error is denoted by beta (β).

A Simple Table

	H0 is actually True	H0 is actually False
Reject H0	Type I Error (α)	Correct Decision
Fail to Reject H0	Correct Decision	Type II Error (β)

A Real-World Analogy

In a medical test for a disease: a Type I error is telling a healthy patient they have the disease, while a Type II error is telling a sick patient they're healthy. Both carry real consequences, but often of very different severity.

Statistical Power

The power of a test is the probability of correctly rejecting a false null hypothesis, calculated as 1 - β. Higher power means a better chance of detecting a real effect when one truly exists.

There's an inherent trade-off between the two error types - reducing the chance of a Type I error (by lowering alpha) generally increases the chance of a Type II error, unless you also increase your sample size.

You've Completed This Section

This wraps up the foundations of probability distributions and hypothesis testing - from discrete and continuous distributions, through the Central Limit Theorem, to the null and alternate hypothesis, critical value and p-value methods, and the types of errors that can occur along the way. These concepts form the statistical toolkit behind rigorous, evidence-based decision-making in Data Science.