30. Hypothesis Testing

Question 1

What is the process of hypothesis testing?

Answer 1

Deciding whether findings reflect chance or real effects at a given level of probability

If results do not represent chance effects, they are considered statistically significant.

Question 2

What are the two types of hypotheses in hypothesis testing?

Answer 2

• Null hypothesis (H0)
• Alternative hypothesis (HA)

H0 claims differences are due to chance, while HA asserts that results are significant.

Question 3

What is the conventional alpha level used in hypothesis testing?

Answer 3

0.05

If p < 0.05, H0 can be rejected; if p ≥ 0.05, results are not significant.

Question 4

What does a Type I error represent?

Answer 4

Incorrectly rejecting H0 when it is true

Also known as a ‘false alarm’; probability represented by α.

Question 5

What does a Type II error represent?

Answer 5

Incorrectly retaining H0 when HA is true

Referred to as a ‘miss’; probability represented by β.

Question 6

What is the relationship between Type I error (α) and Type II error (β)?

Answer 6

Inversely related

As α decreases, β increases, meaning stronger evidence is needed to reject H0.

Question 7

What is a directional hypothesis (HA)?

Answer 7

Predicts a specific direction of change

Should be based on prior evidence and decided before data collection to avoid bias.

Question 8

What is a non-directional hypothesis (HA)?

Answer 8

Predicts a change but does not specify direction

It allows for the possibility of change in either direction.

Question 9

What is the critical value in hypothesis testing?

Answer 9

Threshold that determines the rejection region for H0

Influenced by whether HA is directional (one-tailed) or non-directional (two-tailed).

Question 10

What is the effect of a larger sample size (n) on hypothesis testing?

Answer 10

More likely to reject H0

A larger sample size reduces the standard error of the mean, leading to a larger test statistic.

Question 11

What happens when a more demanding decision level (smaller α) is used?

Answer 11

Less likely to reject H0

A smaller α requires stronger evidence to reject the null hypothesis.

Question 12

What is the probability of Type I error when α is set to 0.05?

Answer 12

Less than 1 in 20

For α=0.01, the probability of making a Type I error is less than 1 in 100.

Question 13

What are some ways to minimize Type II error (β)?

Answer 13

• Increase sample size (n)
• Reduce measurement variability (SX)
• Use directional HA based on previous evidence
• Set less demanding α

A larger α reduces the risk of missing a true effect.

Question 14

What is the practical limit for α in hypothesis testing?

Answer 14

Should not be set too low (e.g., 0.001)

Setting α too low reduces Type I errors but increases Type II errors, potentially overlooking real effects.