CRS Statistical Analysis & Software 3 — Questions and Answers
Question 1: What is the primary purpose of a Q-Q plot in statistical analysis?
- To display bivariate relationships between two continuous variables
- To assess whether data follow a particular theoretical distribution (Correct answer)
- To compare means across multiple groups
- To visualize the distribution of categorical variables
Correct answer: To assess whether data follow a particular theoretical distribution
A Q-Q (quantile-quantile) plot compares the quantiles of observed data to the quantiles of a theoretical distribution, most commonly the normal distribution.
Question 2: In factor analysis, what does 'communality' represent for a given variable?
- The proportion of variance in a variable explained by all extracted factors (Correct answer)
- The correlation between a variable and a single factor
- The eigenvalue associated with a factor
- The percentage of total variance explained by the factor solution
Correct answer: The proportion of variance in a variable explained by all extracted factors
Communality is the proportion of a variable's variance that is accounted for by the retained factors in a factor analysis solution.
Question 3: Which non-parametric test is the appropriate alternative to the independent-samples t-test?
- Wilcoxon Signed-Rank Test
- Mann-Whitney U Test (Correct answer)
- Kruskal-Wallis Test
- Friedman Test
Correct answer: Mann-Whitney U Test
The Mann-Whitney U test compares the distributions of two independent groups when normality assumptions cannot be met.
Question 4: In multiple regression, what does the Variance Inflation Factor (VIF) measure?
- The proportion of variance explained by each predictor independently
- The degree to which a predictor variable is collinear with other predictors (Correct answer)
- The amount of variance in the outcome unexplained by the model
- The inflation of standard errors due to small sample size
Correct answer: The degree to which a predictor variable is collinear with other predictors
VIF quantifies how much the variance of a regression coefficient is inflated due to multicollinearity with other predictors in the model.
Question 5: When using SPSS to run a reliability analysis, under which menu option would a researcher find Cronbach's alpha?
- Analyze > Scale > Reliability Analysis (Correct answer)
- Analyze > Descriptive Statistics > Frequencies
- Analyze > Dimension Reduction > Factor
- Analyze > Compare Means > One-Sample T Test
Correct answer: Analyze > Scale > Reliability Analysis
Cronbach's alpha is computed via Analyze > Scale > Reliability Analysis in SPSS, where the researcher specifies the items to be assessed.
Question 6: What does a negative skewness value indicate about a distribution?
- The distribution is symmetric
- The tail extends further to the right
- The tail extends further to the left (Correct answer)
- The distribution is bimodal
Correct answer: The tail extends further to the left
Negative skewness indicates the distribution has a longer left tail, with most scores clustered at the higher end of the scale.
Question 7: In structural equation modeling (SEM), what does the CFI (Comparative Fit Index) measure?
- The ratio of chi-square to degrees of freedom
- How much better the hypothesized model fits compared to a null model (Correct answer)
- The absolute difference between observed and model-implied correlations
- The penalty for model complexity
Correct answer: How much better the hypothesized model fits compared to a null model
CFI compares the fit of the hypothesized model to a null (independence) model, with values above 0.95 indicating good fit.
CRS Statistical Analysis & Software 3
What is the primary purpose of a Q-Q plot in statistical analysis?