Karl Pearson’s coefficient of correlation MCQs With Answer

Karl Pearson’s coefficient of correlation MCQs With Answer

by

Introduction: Karl Pearson’s coefficient of correlation, commonly called Pearson correlation or r, is a fundamental biostatistics tool for B.Pharm students studying relationships between continuous variables in pharmacology and pharmaceutical research. This correlation coefficient quantifies the strength and direction of linear association, ranging from -1 to +1, and is widely used in pharmacokinetics, assay validation, dose–response analysis, and clinical data interpretation. Key concepts include covariance, standardization, hypothesis testing for rho, assumptions (linearity, normality, homoscedasticity), sensitivity to outliers, and difference from Spearman rank correlation. Mastery of Pearson’s r helps in data analysis, result interpretation, and designing sound experiments. Now let’s test your knowledge with 30 MCQs on this topic.

Q1. What is the formula for Karl Pearson’s coefficient of correlation (r) between two variables X and Y?

  • r = covariance(X,Y) / (SD(X) * SD(Y))
  • r = covariance(X,Y) * (SD(X) + SD(Y))
  • r = mean(XY) – mean(X) – mean(Y)
  • r = (sum of ranks of X)(sum of ranks of Y)

Correct Answer: r = covariance(X,Y) / (SD(X) * SD(Y))

Q2. Which of the following best describes the range of Pearson’s correlation coefficient r?

  • 0 to 1
  • -1 to 1
  • -∞ to +∞
  • -0.5 to +0.5

Correct Answer: -1 to 1

Q3. If r = -0.85 for drug dose vs adverse event score, what does this indicate?

  • Strong positive linear relationship
  • Strong negative linear relationship
  • No linear relationship
  • Perfect positive correlation

Correct Answer: Strong negative linear relationship

Q4. Which assumption is NOT required for valid interpretation of Pearson’s r?

  • Both variables are continuous and measured on interval or ratio scales
  • The relationship between variables is linear
  • Both variables are categorical with more than two levels
  • Homoscedasticity (constant variance of Y across X)

Correct Answer: Both variables are categorical with more than two levels

Q5. How does a single strong outlier typically affect Pearson’s correlation?

  • It has no effect on r
  • It can substantially distort r, either inflating or deflating it
  • It always reduces r towards zero
  • It converts r into Spearman’s rho

Correct Answer: It can substantially distort r, either inflating or deflating it

Q6. For a sample size n, the test statistic to test H0: rho = 0 uses which distribution?

  • Z-distribution with n degrees
  • t-distribution with n-1 degrees
  • t-distribution with n-2 degrees
  • Chi-square distribution with 1 degree

Correct Answer: t-distribution with n-2 degrees

Q7. Which equation gives the t-statistic for testing significance of r?

  • t = r * sqrt(n-1) / sqrt(1-r^2)
  • t = r * sqrt(n-2) / sqrt(1-r^2)
  • t = r / (1-r^2)
  • t = (r^2) * (n-2)

Correct Answer: t = r * sqrt(n-2) / sqrt(1-r^2)

Q8. If covariance(X,Y) = 20, SD(X) = 4 and SD(Y) = 5, what is r?

  • 0.5
  • 1.0
  • 0.8
  • 0.2

Correct Answer: 1.0

Q9. Which statement about r-squared (r2) is true?

  • r2 equals the proportion of variance in Y explained by X in a linear model
  • r2 is always negative when r is negative
  • r2 is a measure of causal effect size irrespective of model
  • r2 can exceed 1 for small samples

Correct Answer: r2 equals the proportion of variance in Y explained by X in a linear model

Q10. What is the effect on r if all X values are multiplied by a positive constant and a constant is added?

  • r remains unchanged
  • r becomes zero
  • r doubles
  • r changes sign

Correct Answer: r remains unchanged

Q11. Which of the following is a major limitation of Pearson’s correlation in pharmaceutical data?

  • It cannot detect linear relationships
  • It only measures linear association and misses nonlinear relationships
  • It can only be applied to categorical variables
  • It always implies causation

Correct Answer: It only measures linear association and misses nonlinear relationships

Q12. Which symbol usually denotes population Pearson correlation?

  • r (lowercase)
  • R-squared
  • ρ (rho)
  • σ (sigma)

Correct Answer: ρ (rho)

Q13. When comparing Pearson and Spearman correlation, which is true?

  • Pearson measures monotonic relationship; Spearman measures only linear relationship
  • Pearson requires ranked data; Spearman requires interval data
  • Pearson is sensitive to outliers; Spearman is less sensitive as it uses ranks
  • Both are identical for all datasets

Correct Answer: Pearson is sensitive to outliers; Spearman is less sensitive as it uses ranks

Q14. In pharmacokinetics, Pearson’s r can help assess the relationship between which pairs?

  • Dose and patient height
  • Plasma concentration and drug effect (pharmacodynamic response)
  • Manufacturer name and tablet color
  • Study ID and enrollment date

Correct Answer: Plasma concentration and drug effect (pharmacodynamic response)

Q15. If r = 0, which conclusion is correct?

  • Variables are independent in all cases
  • There is no linear relationship, but a nonlinear relationship may exist
  • There is a strong nonlinear relationship
  • r = 0 implies perfect negative correlation

Correct Answer: There is no linear relationship, but a nonlinear relationship may exist

Q16. Which preprocessing step can stabilize Pearson correlation when variables have non-normal distributions?

  • Removing all observations
  • Applying appropriate transformations (log, square root) to variables
  • Converting continuous data to arbitrary categories
  • Multiplying all values by random constants

Correct Answer: Applying appropriate transformations (log, square root) to variables

Q17. In sample data, which statistic is used to estimate population covariance in the numerator of Pearson’s r?

  • Sum of products divided by n
  • Sum of products divided by n-1 (sample covariance)
  • Sum of squares only of X
  • Mean of ranks of Y

Correct Answer: Sum of products divided by n-1 (sample covariance)

Q18. Which scenario is inappropriate for Pearson correlation?

  • Assessing linear association between blood concentration and response
  • Variables measured on ratio scales with linear relation
  • Strongly skewed variables with many outliers without transformation
  • Two approximately normally distributed, continuous measures

Correct Answer: Strongly skewed variables with many outliers without transformation

Q19. If you square Pearson’s r and get 0.49, what does this mean?

  • 49% of variability in one variable is linearly explained by the other
  • r is -0.49
  • There is no relationship between variables
  • The correlation is non-significant regardless of sample size

Correct Answer: 49% of variability in one variable is linearly explained by the other

Q20. Which test would you use to determine whether an observed Pearson r differs significantly from zero?

  • Chi-square goodness-of-fit
  • t-test based on r with n-2 degrees of freedom
  • Z-test for proportions
  • ANOVA F-test without regression context

Correct Answer: t-test based on r with n-2 degrees of freedom

Q21. How does restriction of range in X affect Pearson’s r?

  • It typically inflates r
  • It typically attenuates (reduces) r
  • It converts r to Spearman rho
  • It has no effect on r

Correct Answer: It typically attenuates (reduces) r

Q22. Which of the following interpretations is INCORRECT?

  • r = 0.7 indicates strong positive linear association
  • r = -0.9 indicates a strong inverse linear association
  • High r always implies a causal effect between variables
  • Values near ±1 indicate near-perfect linear relationship

Correct Answer: High r always implies a causal effect between variables

Q23. In a dataset with bivariate normal distribution, what does r = 0 imply?

  • Independence of the two variables
  • Perfect dependence
  • Nonlinear dependence only
  • There is always a hidden confounder

Correct Answer: Independence of the two variables

Q24. Which practice improves reliability of computed Pearson correlation in experimental studies?

  • Use very small sample sizes to avoid variability
  • Increase sample size and ensure representative range of values
  • Exclude all midpoint values
  • Always convert data to ranks before analysis

Correct Answer: Increase sample size and ensure representative range of values

Q25. Which statement correctly compares Pearson r and coefficient of determination in a simple linear regression?

  • r is the square of r-squared
  • r equals the square root of r-squared, preserving sign of slope
  • r and r-squared are unrelated
  • r-squared is always negative when slope is negative

Correct Answer: r equals the square root of r-squared, preserving sign of slope

Q26. In validation of an assay, Pearson’s r between known concentrations and measured responses should be:

  • Close to zero for a valid assay
  • Highly positive (close to +1) if the assay is accurate and linear
  • Highly negative to indicate inverse accuracy
  • Exactly equal to sample size

Correct Answer: Highly positive (close to +1) if the assay is accurate and linear

Q27. Which transformation can change a nonlinear relationship into an approximately linear one allowing Pearson’s r to be meaningful?

  • Log transformation of one or both variables
  • Replacing values with ranks only
  • Random shuffling of data
  • Dropping the smallest and largest 50% of observations

Correct Answer: Log transformation of one or both variables

Q28. When is it more appropriate to use Spearman rank correlation instead of Pearson’s r?

  • When both variables are exactly normally distributed and linear
  • When the relationship is monotonic but not linear or when data contain outliers
  • When you want to measure causation
  • When sample size is exactly two

Correct Answer: When the relationship is monotonic but not linear or when data contain outliers

Q29. Which of the following best expresses r in terms of standardized scores (z-scores)?

  • r is the mean of products of z-scores: r = mean(Zx * Zy)
  • r is the difference between z-scores of X and Y
  • r equals sum of z-scores only of X
  • r equals median of z-scores

Correct Answer: r is the mean of products of z-scores: r = mean(Zx * Zy)

Q30. Which phrase best summarizes responsible use of Pearson’s correlation in pharmacy research?

  • Use r to prove causation between drug and outcome
  • Use r to quantify linear association, check assumptions, report confidence and limitations
  • Always report only r without context
  • Prefer correlation over all other statistical analyses regardless of design

Correct Answer: Use r to quantify linear association, check assumptions, report confidence and limitations

Leave a Comment