Type I and Type II Errors
In the previous lesson, we learned how hypothesis testing works and how decisions are made using sample data.
Every decision involves some level of risk. In hypothesis testing, this risk appears in the form of Type I and Type II errors.
Why Errors Occur in Hypothesis Testing
Hypothesis testing is based on samples, not the entire population. Because samples vary, decisions based on them are never perfect.
As a result, two kinds of mistakes are possible:
- Rejecting a true null hypothesis
- Failing to reject a false null hypothesis
Type I Error
A Type I error occurs when we reject the null hypothesis even though it is actually true.
In simple words:
Type I Error = False alarm
Example
A company tests whether a machine is producing defective items.
- H₀: The machine is working correctly
- H₁: The machine is defective
If we conclude the machine is defective when it is actually working fine, we have made a Type I error.
Type II Error
A Type II error occurs when we fail to reject the null hypothesis even though it is false.
In simple words:
Type II Error = Missed detection
Example
Using the same machine example:
If the machine is actually defective but we conclude it is working fine, we have made a Type II error.
Summary of Errors
| Decision | Reality: H₀ True | Reality: H₀ False |
|---|---|---|
| Reject H₀ | Type I Error | Correct Decision |
| Fail to Reject H₀ | Correct Decision | Type II Error |
Probability of Errors
The probability of making a Type I error is denoted by α (the significance level).
The probability of making a Type II error is denoted by β.
Lowering α reduces the chance of Type I error, but may increase the chance of Type II error.
Real-World Interpretation
- Type I Error → Rejecting an innocent person (false positive)
- Type II Error → Letting a guilty person go free (false negative)
Different situations prioritize different types of errors.
Balancing Type I and Type II Errors
There is a trade-off between Type I and Type II errors. Reducing one often increases the other.
The goal is to choose an appropriate balance based on context.
Real-World Example
In medical testing:
- Type I error → Diagnosing a healthy person as sick
- Type II error → Missing a disease in a sick person
In such cases, minimizing Type II error is often more important.
Quick Check
Which error occurs when a true null hypothesis is rejected?
Practice Quiz
Question 1:
What kind of error is failing to detect a real effect?
Question 2:
Which symbol represents the probability of a Type I error?
Question 3:
Can both Type I and Type II errors be eliminated completely?
Mini Practice
A fire alarm system is tested.
- Type I error: Alarm rings when there is no fire
- Type II error: Alarm does not ring when there is a fire
Which error is more dangerous in this case?
What’s Next
In the next lesson, we will apply these ideas using One-Sample Z Tests for Means.