Type-I and Type-II Error, Alpha error, Beta error, Power of Test

This presentation discusses on Type-I and Type- II error. Alpha error, Beta error, Power of Test. etc.

1. Dr Vikramjit Singh
Type –I and
Type-II Error
Page 01

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What Are Type-I and
Type-II Errors?
•Brief introduction to hypothesis testing.
•Definition of Type-I and Type-II Errors.
•Importance in statistical analysis and real-
world decision-making.

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Introduction to Hypothesis Testing
•Hypothesis testing is a statistical method
used to make decisions based on data.
• Involves two hypotheses:
Null Hypothesis (H₀): No effect or no
difference.
Alternative Hypothesis (H₁): There is an
effect or difference.
We use sample data to decide whether to
reject H₀ or fail to reject it.

Significance Level (α) and its role.

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What Are Type-I and Type-II Errors?
Type-I Error (False Positive): Rejecting a true
null hypothesis.


Type-II Error (False Negative):Failing to reject
a false null hypothesis.

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Definition: Rejecting a true null hypothesis.
•Example in Education: Concluding a new teaching
method is effective when it’s not

•Example: A school falsely identifies a student as
needing special education when they don’t.


Definition: Failing to reject a false null hypothesis.

•Example in Education: Concluding a new teaching
method is ineffective when it actually works.
•Example: A school fails to identify a student who actually
needs special education support.
-
Type-I Error (False Positive):
Type-II Error (False Negative):

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Example : Guilty vs. Not Guilty -Courtroom Analogy
Decision Reality (Innocent H₀ True) Reality (Guilty H₀ False)
Convict (Reject H₀) Type-I Error (Innocent
punished)
Correct Decision
Acquit (Fail to reject H₀) Correct Decision Type-II Error (Guilty goes
free)
A court system where a Type-I error means convicting an
innocent person, and a Type-II error means letting a guilty
person go free.

• Null Hypothesis (H₀): Defendant is not guilty.
• Type-I Error: Innocent person is convicted.
• Type-II Error: Guilty person is acquitted.

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Alpha (α) and Beta
(β) Errors
Alpha (α) Error: Probability of making a Type-I error.
•Example: Setting α = 0.05 in a study on
student performance.
• Risk of falsely concluding a new curriculum
improves grades.

Beta (β) Error: Probability of making a Type-II error.
• Example: Failing to detect a true improvement
in student performance due to small sample
size.

Significance level (α): Typically set at 0.05 or 5%,
meaning there is a 5% risk of a Type-I error.

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Power of a Statistical Test
Probability of correctly rejecting a false null
hypothesis (1 - β).
Importance of high power in experiments.
Example: Increasing sample size to improve
power.
Power = 1 - β (probability of correctly
rejecting a false H₀).
A test with high power can detect real
effects better.
Higher power → Lower Type-II Error.
Factors Affecting Power
1. Sample Size: Larger sample → Higher power.
2. Effect Size: Larger difference → Easier to detect.
3. Significance Level (α): Higher α → More power but increased Type-I
error risk.

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Effect of Reducing Alpha (α) on Errors
Lowering α reduces Type-I error but increases
Type-II error.

• Example: In a medical test, reducing α
makes the test stricter, decreasing false
positives but increasing false negatives.
Lowering α reduces Type-I Errors
but increases Type-II Errors.

•Example: Setting α = 0.01 instead
of 0.05 in an educational study.

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Lowering α reduces Type-I Errors but increases Type-II Errors.
Example: Setting α = 0.01 instead of 0.05 in an educational study.

Strategies to Reduce Type-II Errors
Content:
Increasing sample size.
Improving measurement tools.
Example: Using standardized tests in educational research.

Level of Significance & Its Impact on Errors

Lower α (e.g., 0.01) → More conservative test, reduces Type-I error but increases
Type-II error.
Higher α (e.g., 0.10) → More liberal test, increases Type-I error but reduces
Type-II error.

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How to Minimize Both Errors?
•Increase sample size to improve accuracy.
•Choose an optimal significance level (α) based on
the context.
•Improve measurement tools to enhance
precision.
Real-World Example – Medical Testing
Type-I Error: Diagnosing a healthy person with a disease (false positive).
Type-II Error: Failing to diagnose a sick person (false negative).
Balance needed based on disease severity and treatment consequences.
Type-I Error: Falsely failing a student who actually understands the material.
Type-II Error: Passing a student who lacks understanding.
Example in hiring:
Type-I Error: Rejecting a good candidate.
Type-II Error: Hiring an unqualified candidate.

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Recap – Key Takeaways
Type-I Error (False Positive): Rejecting a true null hypothesis.
Type-II Error (False Negative): Failing to reject a false null hypothesis.
Lowering α reduces Type-I errors but increases Type-II errors.
Power of a test helps detect real effects more accurately.

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1. Which error occurs when a true null
hypothesis is rejected?
a) Type-I Error
b) Type-II Error
c) Alpha Error
d) Beta Error

2. If we increase α, what happens to Type-I
error?
a) Increases
b) Decreases
c) Stays the same
d) No effect

3. Which of the following increases the power
of a test?
a) Increasing sample size
b) Reducing effect size
c) Lowering significance level
d) Increasing β

4. A study concludes a new curriculum improves grades, but it
actually doesn’t. What type of error is this?
Options: A) Type-I Error, B) Type-II Error, C) No Error.

5. If α = 0.01 and β = 0.20, what is the power of the test?
Options: A) 0.01, B) 0.20, C) 0.80.

6. In a courtroom, acquitting a guilty person is an example of
which error?
Options: A) Type-I Error, B) Type-II Error, C) No Error.

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Answers
1. a) Type-I Error
2. a) Increases
3. a) Increasing sample size
4. A) Type-I Error
5. C) 0.80.
6. B) Type-II Error

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THANK YOU