PRC Statistical Analysis & Software 2 — Questions and Answers
Question 1: A researcher wants to compare the means of three independent groups. Which statistical test is most appropriate?
- Independent samples t-test
- One-way ANOVA (Correct answer)
- Chi-square test
- Paired t-test
Correct answer: One-way ANOVA
One-way ANOVA is designed to compare means across three or more independent groups simultaneously, avoiding inflated Type I error from multiple t-tests.
Question 2: In SPSS, which procedure would you use to assess whether a variable is normally distributed?
- Frequencies with histogram
- Explore with Shapiro-Wilk test (Correct answer)
- Crosstabs
- Reliability Analysis
Correct answer: Explore with Shapiro-Wilk test
The Explore procedure in SPSS provides the Shapiro-Wilk and Kolmogorov-Smirnov normality tests along with Q-Q plots.
Question 3: Which effect size measure is typically reported alongside a one-way ANOVA result?
- Cohen's d
- Cramér's V
- Eta squared (η²) (Correct answer)
- Odds ratio
Correct answer: Eta squared (η²)
Eta squared (η²) measures the proportion of total variance in the dependent variable attributable to the factor, making it the standard effect size for ANOVA.
Question 4: A Pearson r of −0.72 between study hours and exam errors indicates:
- A weak positive relationship
- A strong negative relationship (Correct answer)
- No meaningful relationship
- A perfect inverse relationship
Correct answer: A strong negative relationship
A correlation of −0.72 reflects a strong negative relationship, meaning more study hours are associated with fewer errors.
Question 5: In R, what does the function `lm(y ~ x, data = df)` produce?
- A logistic regression model
- A simple linear regression model (Correct answer)
- A correlation matrix
- A frequency table
Correct answer: A simple linear regression model
The `lm()` function fits a linear model; `y ~ x` specifies y as the outcome and x as the predictor.
Question 6: Which assumption must be met for Pearson's correlation to be valid?
- Both variables must be nominal
- Both variables must be measured on interval or ratio scales (Correct answer)
- One variable must be dichotomous
- The sample size must exceed 500
Correct answer: Both variables must be measured on interval or ratio scales
Pearson's r requires both variables to be continuous (interval or ratio level) and assumes a linear, bivariate normal relationship.
Question 7: Post-hoc tests after a significant ANOVA are used to:
- Increase statistical power
- Determine which specific group means differ (Correct answer)
- Correct for non-normality
- Reduce sample size requirements
Correct answer: Determine which specific group means differ
Post-hoc tests (e.g., Tukey's HSD, Bonferroni) identify which pair-wise group differences are statistically significant after a significant omnibus F-test.
PRC Statistical Analysis & Software 2
A researcher wants to compare the means of three independent groups.
Which statistical test is most appropriate?