Correlation – Pearson and Spearman - Question Bank

1. If the ranks of two variables are perfectly reversed (highest rank for one corresponds to lowest for the other), Spearman's rho will be:
A) 0
B) 1
C) -1
D) 0.5
2. Which correlation coefficient is generally considered more robust to non-normality and outliers?
A) Pearson's r
B) Spearman's rho
C) R-squared
D) P-value
3. When calculating Pearson's r, if one of the variables has zero variance (all values are the same), the correlation coefficient will be:
A) 1
B) -1
C) 0
D) Undefined
4. What is the term for a correlation that appears to exist between two variables but is actually due to the influence of a third, unmeasured variable?
A) Spurious correlation
B) Pearson correlation
C) Spearman correlation
D) Positive correlation
5. A researcher finds a strong positive correlation between ice cream sales and drowning incidents. What is the most likely interpretation?
A) Eating ice cream causes people to drown.
B) Drowning causes people to buy ice cream.
C) There is a confounding variable (e.g., hot weather) influencing both.
D) The correlation is purely coincidental and meaningless.
6. Spearman's rho is a non-parametric measure, meaning it does not rely on assumptions about:
A) The direction of the relationship.
B) The strength of the relationship.
C) The distribution of the data (e.g., normality).
D) The type of variables.
7. If the Pearson correlation coefficient is 0.8, the coefficient of determination (r-squared) is:
A) 0.64
B) 0.8
C) 1.6
D) 0.16
8. Which of the following is a graphical method to visualize the relationship between two variables?
A) Histogram
B) Box plot
C) Scatterplot
D) Bar chart
9. A correlation matrix displays:
A) The means of multiple variables.
B) The standard deviations of multiple variables.
C) The pairwise correlation coefficients between multiple variables.
D) The regression coefficients between multiple variables.
10. What is the primary purpose of hypothesis testing in correlation analysis?
A) To calculate the correlation coefficient.
B) To determine if the observed correlation in the sample is likely to exist in the population.
C) To establish causation.
D) To transform the data into ranks.
11. When would you choose Kendall's tau correlation over Spearman's rho?
A) When dealing with very large datasets and many tied ranks.
B) When the relationship is strictly linear.
C) When the data is continuous.
D) When the sample size is very small.
12. If Pearson's r is calculated on data that is not normally distributed, the p-value may be:
A) Accurate
B) Underestimated
C) Overestimated
D) Unreliable
13. The null hypothesis for a correlation test typically states:
A) There is a significant correlation between the variables.
B) There is no significant correlation between the variables.
C) There is a positive correlation between the variables.
D) There is a negative correlation between the variables.
14. A monotonic relationship means that as one variable increases, the other variable:
A) Increases linearly.
B) Decreases linearly.
C) Either consistently increases or consistently decreases, but not necessarily at a constant rate.
D) Stays the same.
15. Which type of variable is most suitable for Pearson correlation?
A) Nominal
B) Ordinal
C) Interval/Ratio
D) Dichotomous
16. The formula for Spearman's rho involves calculating the difference between the ranks of paired observations and then:
A) Multiplying these differences by the number of pairs.
B) Summing the squares of these differences and applying a specific formula.
C) Averaging these differences.
D) Taking the absolute value of these differences.
17. A correlation coefficient of 0.05 between hours of sleep and exam performance would indicate:
A) A very strong positive linear relationship.
B) A very weak positive linear relationship.
C) A very strong negative linear relationship.
D) A very weak negative linear relationship.
18. Which of the following statements about correlation is TRUE?
A) Correlation implies causation.
B) Correlation does not imply causation.
C) Causation implies correlation.
D) Both B and C are true.
19. Spearman's rho is less affected by outliers than Pearson's r because:
A) It uses raw data values.
B) It transforms the data into ranks, which compresses the range of values.
C) It only considers the sign of the relationship.
D) It is only applicable to small sample sizes.
20. Pearson's correlation coefficient is derived from:
A) The sum of squared ranks.
B) The covariance of the two variables divided by the product of their standard deviations.
C) The difference between the highest and lowest values.
D) The proportion of shared variance.
21. Which of the following correlation coefficients indicates the strongest linear relationship?
A) 0.3
B) -0.7
C) 0.8
D) -0.9
22. If the ranks of two variables are identical for all data points, what will be the value of Spearman's rho?
A) 0
B) 1
C) -1
D) Undefined
23. A scatterplot showing a clear upward trend from left to right, but with a noticeable curve, might suggest:
A) A strong Pearson correlation.
B) A strong Spearman correlation.
C) A weak Pearson correlation but potentially a strong Spearman correlation.
D) No correlation.
24. What does the coefficient of determination (r-squared) represent?
A) The strength of the correlation.
B) The proportion of variance in one variable that is predictable from the other variable.
C) The p-value of the correlation test.
D) The slope of the regression line.
25. The primary difference between Pearson's r and Spearman's rho lies in:
A) The range of values they can take.
B) The type of relationship they measure (linear vs. monotonic).
C) Their sensitivity to sample size.
D) Their calculation method (using raw scores vs. ranks).
26. When is it generally advisable to use Spearman's rho instead of Pearson's r?
A) When both variables are perfectly normally distributed.
B) When the relationship between variables is expected to be linear and continuous.
C) When there are outliers that might unduly influence Pearson's r, or when data is ordinal.
D) When the sample size is very large.
27. Which of the following is NOT a type of correlation coefficient?
A) Pearson's r
B) Spearman's rho
C) Kendall's tau
D) Student's t
28. If two variables have a strong positive Pearson correlation, what can be inferred?
A) One variable causes the other.
B) As one variable increases, the other tends to increase linearly.
C) As one variable increases, the other tends to decrease.
D) There is no relationship between the variables.
29. Spearman's rho is a measure of:
A) Linear association.
B) Non-linear association.
C) Monotonic association.
D) Causal association.
30. Pearson's r is sensitive to which type of data?
A) Nominal data
B) Ordinal data
C) Interval or Ratio data
D) Categorical data
31. What does a Spearman's rho of -0.75 suggest?
A) A weak positive monotonic relationship between the ranks of the variables.
B) A strong negative monotonic relationship between the ranks of the variables.
C) No monotonic relationship between the ranks of the variables.
D) A moderate positive monotonic relationship between the ranks of the variables.
32. Which scenario would be most appropriate for using Spearman's rank correlation?
A) Measuring the relationship between height and weight (both continuous).
B) Measuring the relationship between students' exam scores and study hours (both continuous).
C) Measuring the relationship between a doctor's rating of pain severity (ordinal) and a patient's reported pain level (ordinal).
D) Measuring the relationship between temperature and ice cream sales (both continuous).
33. A perfect positive rank correlation using Spearman's rho would result in a value of:
A) 0
B) 0.5
C) 1
D) -1
34. If a dataset has tied ranks, how is Spearman's rho typically calculated?
A) Ties are ignored.
B) A special formula is used that accounts for ties.
C) The average rank is assigned to tied values.
D) The data is discarded.
35. Spearman's correlation coefficient measures the strength and direction of the relationship between:
A) The actual values of two continuous variables.
B) The ranks of two variables.
C) The frequencies of two categorical variables.
D) The means of two groups.
36. What is a key advantage of Spearman's correlation over Pearson's correlation?
A) It is more sensitive to outliers.
B) It does not require the data to be normally distributed.
C) It can only be used for interval data.
D) It measures non-linear relationships directly.
37. Spearman's correlation works by calculating the Pearson correlation coefficient on:
A) The original raw scores of the variables.
B) The ranks of the data for each variable.
C) The logarithms of the variables.
D) The differences between the variables.
38. Spearman's correlation is used when:
A) Variables are continuous and normally distributed.
B) The relationship is strictly linear.
C) Data is ordinal or when the assumption of normality for Pearson's r is violated.
D) Causation needs to be established.
39. Spearman's rank correlation coefficient is denoted by:
A) r
B) rho (ρ)
C) beta (β)
D) gamma (γ)
40. What is a common assumption for using Pearson's correlation coefficient?
A) The data must be ordinal.
B) The variables must be normally distributed.
C) The sample size must be small.
D) The relationship must be non-linear.
41. The formula for Pearson's r involves:
A) The sum of squared differences between ranks.
B) The product of deviations from the mean for each variable.
C) The proportion of variance explained.
D) The ratio of means.
42. Which statistical test is used to calculate Pearson's correlation coefficient?
A) T-test
B) ANOVA
C) Z-test
D) None of the above (it's a formula)
43. What does a Pearson correlation coefficient of 0 indicate?
A) A perfect positive linear relationship.
B) A perfect negative linear relationship.
C) No linear relationship between the variables.
D) A weak positive linear relationship.
44. Pearson's correlation coefficient is most appropriate when the relationship between variables is:
A) Non-linear and ordinal.
B) Linear and interval/ratio.
C) Non-linear and nominal.
D) Linear and ordinal.
45. Pearson's correlation coefficient is also known as:
A) Rank correlation coefficient
B) Product-moment correlation coefficient
C) Kendall's tau
D) Chi-squared coefficient
46. What is the range of possible values for a Pearson correlation coefficient (r)?
A) 0 to 1
B) -1 to 0
C) -1 to 1
D) 0 to infinity
47. A correlation coefficient of -0.95 suggests:
A) A weak positive linear relationship.
B) A strong negative linear relationship.
C) No linear relationship.
D) A moderate positive linear relationship.
48. Which type of correlation indicates that as one variable increases, the other variable also increases?
A) Negative correlation
B) Zero correlation
C) Positive correlation
D) Spurious correlation
49. What does correlation analysis aim to measure?
A) The causal relationship between two variables.
B) The strength and direction of the linear relationship between two variables.
C) The difference in means between two groups.
D) The probability of an event occurring.
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