Type I and Type II Errors in Hypothesis Testing

 In research and statistics, errors can occur when making decisions about hypotheses. These errors are classified as Type I and Type II errors.

 Basic Hypothesis Testing Framework

Hypothesis Type

Meaning

Null Hypothesis (H₀)

Assumes no effect or no difference.

Alternative Hypothesis (H₁ or Ha)

Assumes there is an effect or difference.

When we test a hypothesis, we either:

  • Reject H₀ (accepting Ha), or
  • Fail to reject H₀ (keeping Ha unproven)

 1. Type I Error (False Positive)

Aspect

Description

Definition

Rejecting a true null hypothesis

Interpretation

Concluding an effect exists when it doesn't

Symbol

α (alpha) — level of significance

Example

A pregnancy test says a woman is pregnant when she is not.

Risk Control

Set α (usually 0.05, i.e., 5%) — lower α means lower chance of Type I error

 2. Type II Error (False Negative)

Aspect

Description

Definition

Failing to reject a false null hypothesis

Interpretation

Concluding no effect exists when it actually does

Symbol

β (beta) — probability of Type II error

Example

A pregnancy test fails to detect pregnancy in a pregnant woman

Risk Control

Increase power of the test (Power = 1 – β) by increasing sample size, improving measurement, or using better design

 Comparison Table

Type of Error

What Happens

True State

Consequence

Symbol

Type I

Reject H₀ when H₀ is true

H₀ is true

False alarm

α

Type II

Fail to reject H₀ when H₀ is false

H₁ is true

Missed detection (effect exists, not found)

β

 Graphical Representation (Conceptual)

Reality → H₀ True         H₀ False

           ┌─────────────┬───────────────┐

Decision → │ Don't Reject│ Correct Decision (Power) │

           │    Type I   │     Type II Error       │

           └─────────────┴───────────────┘

 How to Reduce Errors

Error Type

How to Reduce

Type I

Lower the significance level (α)

Type II

Increase sample size, reduce variability, increase effect size, improve test sensitivity

 

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