Hypothesis Testing and Errors

Question 1

Q: What is the goal of inferential statistics?

Answer 1

A: To make inferences about a population based on data from a sample.

Question 2

Q: What is the goal of hypothesis testing?

Answer 2

A: To determine the likelihood that a sample statistic would be selected if the hypothesis about a population parameter were true.

Question 3

Q: What is the null hypothesis (H0​)?

Answer 3

A: A statement that there is no effect, no difference, or no relationship.

Question 4

Q: What is the alternative hypothesis (H1​)?

Answer 4

A: A statement that something other than the null hypothesis is true. This is often the research hypothesis.

Question 5

Q: What is the overall strategy of hypothesis testing?

Answer 5

A: To try and reject the null hypothesis (H0​) in order to support the alternative hypothesis (H1​).

Question 6

Q: What is the significance level (𝛼)?

Answer 6

A: A pre-determined threshold, typically set at 0.05 or 0.01, that defines the region of rejection for the null hypothesis.

Question 7

Q: What is the population distribution?

Answer 7

A: The true distribution from which samples are drawn, which is usually unknown.

Question 8

Q: What is the sample distribution?

Answer 8

A: The distribution of data collected from a sample.

Question 9

Q: What is the sampling distribution?

Answer 9

A: The probability distribution of a sample statistic across repeated samples of the same size. It describes the sample-to-sample variability of the statistic.

Question 10

Q: What is the Central Limit Theorem (CLT)?

Answer 10

A: For a large enough sample size (n), the sampling distribution of the mean is approximately normal, regardless of the population’s shape.

Question 11

Q: What is the Standard Error (SE)?

Answer 11

A: The standard deviation of the sampling distribution. A smaller SE means less sampling variation and a more accurate estimate of the population mean (𝜇).

Question 12

Q: What is a Type I error?

Answer 12

A: Rejecting the null hypothesis (H0​) when it is actually true. The probability is equal to alpha (𝛼).

Question 13

Q: What is a Type II error?

Answer 13

A: Not rejecting the null hypothesis (H0​) when it is actually false. The probability is equal to beta (𝛽).

Question 14

Q: What is Power?

Answer 14

A: The probability of correctly rejecting the null hypothesis (H0​) when it is false. Power is equal to 1−𝛽.

Question 15

Q: What factors increase statistical power?

Answer 15

A: An increase in effect size, alpha (𝛼), or sample size (n) will increase power.

Question 16

Q: What is the difference between statistical significance and practical (clinical) significance?

Answer 16

A: Statistical significance determines if an effect is unlikely due to chance, while practical significance measures how large the effect is in the population.

Question 17

Q: What are two common ways to measure effect size?

Answer 17

A: Mean difference (e.g., Cohen’s d) and variance explained (e.g., R2).

Question 18

Q: What are the general guidelines for interpreting Cohen’s d?

Answer 18

A: Small effect is 0.2, medium is 0.5, and large is 0.8.

Question 19

Q: When would you use a one-sample test?

Answer 19

A: When using a sample to infer whether a population parameter equals a specific value.

Question 20

Q: When would you use an independent-samples t-test?

Answer 20

A: To compare the means from two independent groups.

Question 21

Q: What are the key assumptions for an independent-samples t-test?

Answer 21

A: Independence of observations and homogeneity of variance.

Question 22

Q: When would you use a dependent (paired) samples t-test?

Answer 22

A: When the two sets of scores are not independent, such as in repeated measures designs or matched-pair studies.