ERRORS IN HYPOTHESIS TESTING

Hypothesis

Meaning & Major Types (Research Methodology)

Meaning of Hypothesis

A hypothesis is a tentative, testable statement about the relationship between variables. It is formulated to be verified or rejected through scientific and statistical investigation.

Example:
There is a significant relationship between teaching method and students’ achievement.

Research Hypothesis

A research hypothesis is a predictive statement proposed by the researcher based on theory, observation, or previous studies. It expresses the expected outcome of the study in conceptual terms.

Example:
Use of activity-based learning improves academic achievement of students.

Alternative Hypothesis (H₁ / Hₐ)

An alternative hypothesis states that there is a real effect, difference, or relationship between variables. It is accepted when the null hypothesis is rejected.

Example:
There is a significant difference in achievement between students taught by digital learning and traditional method.

Statistical Hypothesis

A statistical hypothesis is a hypothesis stated in quantitative and statistical terms concerning population parameters. It is tested using statistical tools. It includes Null hypothesis (H₀) and Alternative hypothesis (H₁).

Example:
H₀ : μ₁ = μ₂ (No significant difference between mean scores of two groups)

Directional Hypothesis

A directional hypothesis specifies the direction of the expected relationship or difference between variables, such as higher, lower, more, or less.

Example:
Students taught through smart classroom teaching will score higher than students taught through lecture method.

Non-Directional Hypothesis

A non-directional hypothesis states that a relationship or difference exists between variables but does not indicate the direction of the difference.

Example:
There is a significant difference in academic achievement between rural and urban students.

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Errors in Hypothesis Testing

(Type I Error & Type II Error)

Meaning

In hypothesis testing, errors occur because decisions about a population are made on the basis of sample data. These errors are called Type I error and Type II error.

Type I Error (α Error)

A Type I error occurs when a true null hypothesis (H₀) is rejected incorrectly.
Also called: False Positive

Example:
H₀: New teaching method is not effective.
Reality: Method is not effective.
Decision: Researcher says it is effective.
➜ This is a Type I Error.

Probability: α (usually 0.05 or 0.01)

Type II Error (β Error)

A Type II error occurs when a false null hypothesis (H₀) is accepted incorrectly.
Also called: False Negative

Example:
H₀: New teaching method is not effective.
Reality: Method is effective.
Decision: Researcher says it is not effective.
➜ This is a Type II Error.

Probability: β

Power of Test

Power of a test = 1 − β
It shows the ability of a test to detect a real effect.

Decision Table

Reality / Decision	Accept H₀	Reject H₀
H₀ is True	Correct Decision	Type I Error (α)
H₀ is False	Type II Error (β)	Correct Decision

Diagrammatic View

REALITY vs DECISION

H₀ True → Reject → Type I Error (α)
H₀ False → Accept → Type II Error (β)

MCQs (UGC-NET / CTET)

1. Rejecting a true null hypothesis is called:
Answer: Type I Error

2. Probability of Type II error is denoted by:
Answer: β

3. Power of test is equal to:
Answer: 1 − β

Conclusion (Exam-Ready)

Type I error involves rejecting a true null hypothesis, whereas Type II error involves accepting a false null hypothesis. Both errors are unavoidable but can be controlled by choosing an appropriate level of significance and sample size.

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UGC NET (Education) – MCQs

Errors in Hypothesis Testing

Q1. Rejecting a true null hypothesis is called:

A. Type II error
B. Sampling error
C. Random error
D. Type I error

✔ Answer: D

Q2. Accepting a false null hypothesis is known as:

A. Type I error
B. Type II error
C. Level of significance
D. Standard error

✔ Answer: B

Q3. The probability of committing a Type I error is denoted by:

A. β
B. σ
C. α
D. p

✔ Answer: C

Q4. The probability of committing a Type II error is denoted by:

A. α
B. β
C. z
D. t

✔ Answer: B

Q5. Power of a statistical test is equal to:

A. α
B. β
C. 1 − α
D. 1 − β

✔ Answer: D

Q6. A false positive decision in hypothesis testing refers to:

A. Type II error
B. Type I error
C. True negative
D. Correct decision

✔ Answer: B

Q7. Failing to reject a null hypothesis when it is false is:

A. Type I error
B. Type II error
C. Sampling bias
D. Correct inference

✔ Answer: B

Q8. In hypothesis testing, which hypothesis is tested directly?

A. Research hypothesis
B. Working hypothesis
C. Null hypothesis
D. Statistical hypothesis

✔ Answer: C

Q9. Decreasing the level of significance (α) generally:

A. Decreases β
B. Increases β
C. Increases power
D. Has no effect

✔ Answer: B

Q10. Which of the following is NOT a decision in hypothesis testing?

A. Reject H₀
B. Accept H₀
C. Fail to reject H₀
D. Prove H₁

✔ Answer: D

UGC NET | Research Aptitude | Education