RA Statistical Analysis and Interpretation 2 — Questions and Answers
Question 1: A chi-square test of independence is most appropriate when a researcher wants to:
- Compare means across three or more groups
- Examine the relationship between two categorical variables (Correct answer)
- Measure the strength of a linear relationship between two continuous variables
- Determine if a single sample mean differs from a known population mean
Correct answer: Examine the relationship between two categorical variables
The chi-square test of independence assesses whether two categorical (nominal or ordinal) variables are statistically associated or independent of each other.
Question 2: What is the primary purpose of a one-way ANOVA?
- To compare the variances of two populations
- To compare means across three or more independent groups simultaneously (Correct answer)
- To assess correlation between two continuous variables
- To test whether a sample comes from a normal distribution
Correct answer: To compare means across three or more independent groups simultaneously
ANOVA (Analysis of Variance) tests whether there are statistically significant differences among the means of three or more independent groups without inflating the Type I error rate.
Question 3: A Pearson correlation coefficient of -0.85 between two variables indicates:
- A weak positive linear relationship
- No meaningful relationship
- A strong negative linear relationship (Correct answer)
- A strong positive linear relationship
Correct answer: A strong negative linear relationship
A Pearson r close to -1 indicates a strong negative linear relationship, meaning as one variable increases, the other tends to decrease proportionally.
Question 4: What is the key difference between parametric and non-parametric statistical tests?
- Parametric tests are always more accurate than non-parametric tests
- Parametric tests assume the data meets certain distribution assumptions; non-parametric tests do not (Correct answer)
- Non-parametric tests can only be used with categorical data
- Parametric tests are used only for small samples
Correct answer: Parametric tests assume the data meets certain distribution assumptions; non-parametric tests do not
Parametric tests assume the underlying population follows a specific distribution (typically normal), while non-parametric tests make fewer assumptions and are suitable when data violates these assumptions.
Question 5: In research, statistical power refers to:
- The probability of making a Type I error
- The probability of correctly detecting a true effect when one exists (Correct answer)
- The sample size required to run a study
- The magnitude of the observed effect
Correct answer: The probability of correctly detecting a true effect when one exists
Statistical power (1 - β) is the probability that a test will correctly reject a false null hypothesis, meaning it will detect a true effect when it actually exists.
Question 6: In a research study, the null hypothesis typically states that:
- The researcher's predicted effect exists
- There is no effect, difference, or relationship between variables (Correct answer)
- The sample data is not representative of the population
- The study design is flawed
Correct answer: There is no effect, difference, or relationship between variables
The null hypothesis (Hâ‚€) is the default assumption of no effect, no difference, or no relationship, which the researcher attempts to disprove with evidence.
Question 7: When should a paired (dependent) samples t-test be used instead of an independent samples t-test?
- When comparing more than two groups
- When the same participants are measured twice or are matched across conditions (Correct answer)
- When the data is not normally distributed
- When the sample size is very large
Correct answer: When the same participants are measured twice or are matched across conditions
A paired t-test is used when two sets of measurements come from the same participants (e.g., pre- and post-test) or from matched pairs, because the measurements within each pair are related.
RA Statistical Analysis and Interpretation 2
A chi-square test of independence is most appropriate when a researcher wants to: