MRA Statistical Techniques & Data Interpretation 3 — Questions and Answers
Question 1: Which statistical test would be most appropriate to compare the means of two independent groups?
- Paired t-test
- Independent samples t-test (Correct answer)
- One-way ANOVA
- Wilcoxon signed-rank test
Correct answer: Independent samples t-test
The independent samples t-test is designed to compare the means of two separate, unrelated groups.
Question 2: In factor analysis, what does a factor loading of 0.75 represent?
- 75% of respondents chose that factor
- The correlation between the observed variable and the underlying factor (Correct answer)
- The eigenvalue of the factor
- The number of items loaded on that factor
Correct answer: The correlation between the observed variable and the underlying factor
Factor loadings are correlations between individual items and the underlying latent factor; 0.75 indicates a strong relationship.
Question 3: A normal distribution has a mean of 100 and a standard deviation of 15. Approximately what percentage of scores fall between 85 and 115?
- 50%
- 68% (Correct answer)
- 95%
- 99.7%
Correct answer: 68%
According to the empirical rule (68-95-99.7), approximately 68% of data falls within one standard deviation of the mean.
Question 4: What is the primary purpose of a Box-and-Whisker plot in data analysis?
- To display the frequency distribution of a categorical variable
- To show the five-number summary and identify outliers in a dataset (Correct answer)
- To plot the correlation between two continuous variables
- To display time-series trends
Correct answer: To show the five-number summary and identify outliers in a dataset
A box plot visualizes the median, quartiles, and potential outliers, providing a compact summary of the data distribution.
Question 5: A marketing analyst notices that ice cream sales and drowning incidents both rise in summer. This relationship is best described as:
- Causal — ice cream causes drowning
- Spurious correlation due to a confounding variable (heat/season) (Correct answer)
- A statistically significant finding that requires intervention
- Negative correlation
Correct answer: Spurious correlation due to a confounding variable (heat/season)
Both variables are driven by a third variable (warm weather/summer), making their correlation spurious rather than causal.
Question 6: In cluster analysis, what does the 'elbow method' help a researcher determine?
- The statistical significance of cluster differences
- The optimal number of clusters in the data (Correct answer)
- Whether clusters are normally distributed
- The internal reliability of each cluster
Correct answer: The optimal number of clusters in the data
The elbow method plots within-cluster variance against number of clusters and identifies the point where adding more clusters yields diminishing returns.
Question 7: What does a z-score of +2.5 tell you about a data point?
- The data point is 2.5 units above the median
- The data point is 2.5 standard deviations above the mean (Correct answer)
- The data point has a 2.5% probability of occurring
- The data point is in the 2.5th percentile
Correct answer: The data point is 2.5 standard deviations above the mean
A z-score measures how many standard deviations a value is above (+) or below (−) the population or sample mean.
MRA Statistical Techniques & Data Interpretation 3
Which statistical test would be most appropriate to compare the means of two independent groups?