Inferential Statistics

Question 1

How do you perform hypothesis testing?

Answer 1

It involves setting up a null and alternative hypothesis, choosing a significance level, calculating the test statistic, and making a decision based on the comparison of the statistic with a critical value.

Question 2

What are confidence intervals and what do they represent?

Answer 2

They estimate the range within which a population parameter lies with a certain level of confidence.

Question 3

What is a Type I error in hypothesis testing?

Answer 3

The error of rejecting a true null hypothesis.

Question 4

What is a Type II error in hypothesis testing?

Answer 4

The error of failing to reject a false null hypothesis.

Question 5

Define power analysis in the context of statistical testing.

Answer 5

It refers to the probability that a statistical test will detect an effect when there is one.

Question 6

What assumptions do you need to check before performing a t-test?

Answer 6

Normality of data, equal variance, and independence of observations.

Question 7

How do you determine which type of t-test to use?

Answer 7

Based on the number of samples and whether the samples are independent or paired.

Question 8

What is the difference between a one-tailed and a two-tailed test?

Answer 8

A one-tailed test looks for an effect in one direction, a two-tailed test in both directions.

Question 9

What factors influence the width of a confidence interval?

Answer 9

Sample size, variability in the data, and confidence level.

Question 10

How do sample size and variability affect statistical power?

Answer 10

Larger sample sizes and lower variability increase power.

Question 11

What is the null hypothesis in a statistical test?

Answer 11

The hypothesis that there is no effect or no difference.

Question 12

What is an alternative hypothesis?

Answer 12

It proposes that there is an effect or a difference.

Question 13

Why is the significance level often set at 0.05?

Answer 13

It controls the acceptable rate of Type I error.

Question 14

What is the p-value and how do you interpret it?

Answer 14

It measures the probability of observing the test results under the null hypothesis.

Question 15

How does one reduce the likelihood of committing a Type I error?

Answer 15

By setting a more stringent significance level.

Question 16

What are the consequences of a Type II error?

Answer 16

It might result in missing a genuine effect or difference.

Question 17

How do you calculate the power of a test?

Answer 17

By the inverse relationship between beta (risk of Type II error) and power.

Question 18

What role does effect size play in hypothesis testing?

Answer 18

It quantifies the size of the effect and is crucial for determining the test’s sensitivity.

Question 19

How can increasing the sample size affect the outcomes of a test?

Answer 19

Increases the power and precision of the test results.

Question 20

Why is random sampling important in hypothesis testing?

Answer 20

To ensure the generalizability of the results.

Question 21

What are the ethical considerations in hypothesis testing?

Answer 21

Maintaining transparency, avoiding manipulation of data and respecting participant rights.

Question 22

How does bias affect the results of hypothesis testing?

Answer 22

It can lead to erroneous conclusions and reduce the reliability of the test results.

Question 23

What is the central limit theorem and why is it important in statistics?

Answer 23

It states that the sample means will approximate a normal distribution as the sample size increases, regardless of the population’s distribution.

Question 24

How do you choose between using a parametric and a non-parametric test?

Answer 24

Parametric tests assume underlying statistical distributions; non-parametric do not, making them suitable for non-normal data.

Question 25

Why might a researcher use a two-tailed test instead of a one-tailed test?

Answer 25

To avoid directionality in testing hypotheses, providing a more conservative test.

Question 26

What strategies can be used to increase the power of a statistical test?

Answer 26

Improving the study design, increasing the sample size, or using more precise measurements.

Question 27

How does the choice of significance level affect the results of a test?

Answer 27

A lower level reduces Type I errors but increases the chance of Type II errors.

Question 28

What is the difference between statistical significance and clinical significance?

Answer 28

Statistical significance may indicate a mathematically detected difference, but it might not be meaningful in practical terms.

Question 29

How do you interpret confidence intervals that do not include zero?

Answer 29

They suggest a significant effect or difference (as zero is not within the interval).

Question 30

What are common mistakes made during hypothesis testing?

Answer 30

Ignoring assumptions of the test, misinterpreting p-values, or overlooking necessary data transformations.

Question 31

What is the benefit of reporting confidence intervals along with p-values?

Answer 31

They provide a range of plausible values for the parameter and more information than a single p-value.

Question 32

How do you handle multiple comparisons in statistical analysis?

Answer 32

Adjusting significance levels or using statistical methods to control for family-wise error rate.

Question 33

What is the Bonferroni correction and when should it be used?

Answer 33

A method to adjust the significance threshold when multiple comparisons are made, to control the family-wise error rate.

Question 34

What is the role of replication in hypothesis testing?

Answer 34

Increases confidence in the results by demonstrating reproducibility.

Question 35

Why is pre-registration important in hypothesis trials?

Answer 35

To minimize biases and confirmatory biases in conducting the research.

Question 36

What is the consequence of p-hacking?

Answer 36

Leads to an inflated Type I error rate, questioning the reliability of findings.

Question 37

How do you determine if your test results are robust?

Answer 37

By performing robustness checks such as rerunning the tests with different assumptions or subsets of data.

Question 38

What are the limitations of the p-value?

Answer 38

It does not provide information about the magnitude or importance of an effect.

Question 39

What factors should be considered when setting the sample size for a study?

Answer 39

Considering the expected effect size, desired power, and the level of acceptable error.

Question 40

How can researchers ensure the integrity of their hypothesis testing process?

Answer 40

By adhering to predefined protocols, documenting all decisions made during the research, and conducting peer reviews.