1. The coefficient of correlation measures:
A. Causal relationship between two variables
B. Linear relationship between two variables
C. Average of two scores
D. Variability in one variable only
Answer: B. Linear relationship between two variables
Explanation: The coefficient of correlation indicates the strength and direction of a linear relationship between two variables.
2. The value of the correlation coefficient always lies between:
A. –1 and 1
B. 0 and 1
C. –∞ and +∞
D. –0.5 and 0.5
Answer: A. –1 and 1
Explanation: Correlation coefficients range from –1 (perfect negative) to +1 (perfect positive). A value of 0 indicates no correlation.
3. Spearman’s rank correlation is denoted by:
A. r
B. ρ (rho)
C. β
D. σ
Answer: B. ρ (rho)
Explanation: Spearman’s rank correlation is symbolized by the Greek letter ρ (rho), used for non-parametric data.
4. Pearson’s product moment correlation coefficient is denoted by:
A. r
B. ρ
C. α
D. M
Answer: A. r
Explanation: Pearson’s correlation coefficient, applicable to interval/ratio data, is represented by “r”.
5. Spearman’s Rank Correlation method is preferred when:
A. Data is normally distributed
B. Data is nominal
C. Data is in ranks or ordinal
D. Variables are unrelated
Answer: C. Data is in ranks or ordinal
Explanation: Spearman’s ρ is used when data is ranked or not measured on a true numerical scale.
6. Pearson’s correlation coefficient is suitable when:
A. The data is qualitative
B. The data is categorical
C. The data is quantitative and continuous
D. The data is nominal
Answer: C. The data is quantitative and continuous
Explanation: Pearson’s method is applicable when both variables are continuous and measured on an interval or ratio scale.
7. A correlation coefficient of –0.87 indicates:
A. No correlation
B. Weak positive correlation
C. Strong negative correlation
D. Moderate correlation
Answer: C. Strong negative correlation
Explanation: Values close to –1 indicate a strong negative linear relationship between variables.
8. A correlation of 0 implies:
A. Perfect relationship
B. No linear relationship
C. High variability
D. Variables are dependent
Answer: B. No linear relationship
Explanation: A zero correlation means there is no linear relationship between the two variables, though other types may exist.
9. The formula for Spearman’s rank correlation (ρ) is:
Explanation: This is the correct formula when there are no tied ranks.
10. In the Spearman formula, D represents:
A. Difference in standard deviations
B. Difference between means
C. Difference between ranks
D. Difference in scores
Answer: C. Difference between ranks
Explanation: In Spearman’s method, D is the difference between ranks of corresponding values in two variables.
11. The product moment correlation formula includes which statistical values?
A. Standard scores
B. Standard deviation and means
C. Ranks
D. Percentiles
Answer: B. Standard deviation and means
Explanation: Pearson’s formula uses deviations from the mean and standard deviation to calculate the relationship.
12. If r = +1, it implies:
A. A strong negative correlation
B. No relationship
C. A perfect positive correlation
D. High variability
Answer: C. A perfect positive correlation
Explanation: r = +1 indicates that an increase in one variable corresponds to a proportional increase in the other.
13. Which condition is not necessary for Pearson’s correlation method?
A. Linearity
B. Ordinal data
C. Continuous variables
D. Homoscedasticity
Answer: B. Ordinal data
Explanation: Pearson’s r requires interval or ratio scale data, not ordinal.
14. In Pearson’s method, if the scatter plot shows a downward trend, the correlation is:
A. Positive
B. Negative
C. Zero
D. Perfect
Answer: B. Negative
Explanation: A downward slope in a scatterplot indicates a negative correlation between the variables.
15. Which correlation method is most appropriate for data with ranks and tied values?
A. Pearson’s method
B. Regression
C. Spearman’s method (adjusted for ties)
D. Z-score method
Answer: C. Spearman’s method (adjusted for ties)
Explanation: Spearman’s method can accommodate ties using rank average or correction formulas.
16. The square of the correlation coefficient (r²) indicates:
A. The error in prediction
B. The percentage of shared variance
C. Standard deviation
D. Median difference
Answer: B. The percentage of shared variance
Explanation: r² tells us how much of the variance in one variable is explained by the other variable.
17. What does r = 0.95 imply?
A. Weak positive relation
B. Moderate correlation
C. Strong positive correlation
D. No correlation
Answer: C. Strong positive correlation
Explanation: Values close to +1 imply a strong positive linear relationship.
18. When two variables move in opposite directions, their correlation is:
A. Positive
B. Negative
C. Zero
D. Undefined
Answer: B. Negative
Explanation: A negative correlation indicates that as one variable increases, the other decreases.
19. Which of the following is not a use of correlation in education?
A. Predicting student success
B. Establishing cause-effect
C. Comparing achievement and interest
D. Validating test items
Answer: B. Establishing cause-effect
Explanation: Correlation only indicates association, not causation.
20. A perfect correlation occurs when:
A. r = 0
B. r = +1 or –1
C. r = 0.5
D. Variables are unrelated
Answer: B. r = +1 or –1
Explanation: These are the maximum and minimum possible values of correlation, indicating perfect positive or negative linear relationships.
21. A perfect negative correlation is represented by:
A. r = 0
B. r = +1
C. r = –1
D. r = –0.5
Answer: C. r = –1
Explanation: An r value of –1 indicates a perfect negative linear relationship—when one variable increases, the other decreases in exact proportion.
22. A scatter diagram with points close to a straight line going from bottom left to top right indicates:
A. Weak negative correlation
B. No correlation
C. Strong positive correlation
D. Strong negative correlation
Answer: C. Strong positive correlation
Explanation: When the points on a scatter plot align along a rising straight line, it suggests a strong positive relationship.
23. Which of the following is a non-parametric method of correlation?
A. Pearson’s r
B. Spearman’s ρ
C. Regression
D. Coefficient of determination
Answer: B. Spearman’s ρ
Explanation: Spearman’s rank correlation is a non-parametric method that does not assume normality of the data.
24. In Spearman’s formula, if all ranks are the same (no variation), then the correlation will be:
A. 1
B. 0
C. –1
D. Undefined
Answer: D. Undefined
Explanation: If all ranks are identical, there’s no variability; correlation becomes mathematically undefined (division by zero in variance).
25. Which of the following statements is true about correlation and causation?
A. Correlation always implies causation
B. Causation always implies correlation
C. Correlation may suggest causation but doesn’t prove it
D. There’s no relation between them
Answer: C. Correlation may suggest causation but doesn’t prove it
Explanation: Correlation only indicates association. Causal relationships require experimental or longitudinal studies.
26. If the correlation between height and weight is r = 0.90, it suggests:
A. Height and weight are unrelated
B. Tall people are always heavier
C. Strong positive linear relationship
D. No variance in data
Answer: C. Strong positive linear relationship
Explanation: r = 0.90 means as height increases, weight tends to increase—strong association, but not determinism.
27. The assumption of linearity is necessary for which method?
A. Spearman’s rank correlation
B. Chi-square test
C. Pearson’s product moment correlation
D. Sign test
Answer: C. Pearson’s product moment correlation
Explanation: Pearson’s method assumes a linear relationship between variables.
28. Which graph is best suited to visualize correlation between two variables?
A. Bar graph
B. Histogram
C. Pie chart
D. Scatter plot
Answer: D. Scatter plot
Explanation: A scatter plot displays paired data points and visually shows the direction and strength of correlation.
29. Which of the following can distort the value of Pearson’s correlation coefficient?
A. Homogeneous data
B. Large sample size
C. Outliers
D. Standardization
Answer: C. Outliers
Explanation: Outliers can disproportionately affect the magnitude and direction of Pearson’s r, making the correlation misleading.
30. If the ranks are tied in Spearman’s method, what adjustment is necessary?
A. Use raw scores
B. Ignore the ties
C. Assign average ranks
D. Replace with percentiles
Answer: C. Assign average ranks
Explanation: When tied ranks occur, each tied value is assigned the average of the ranks they occupy.
31. In educational testing, correlation is useful to:
A. Measure reliability
B. Reduce curriculum load
C. Assess students’ creativity
D. Predict future performance
Answer: D. Predict future performance
Explanation: Correlation helps in predicting performance based on related variables like IQ and achievement.
32. If r = 0.00 in a large sample, the implication is:
A. No relationship exists
B. Data are biased
C. Strong nonlinear relationship
D. Strong linear relationship
Answer: A. No relationship exists
Explanation: r = 0 means no linear relationship, although a nonlinear pattern might still exist.
33. The formula for Pearson’s r (simplified) is:
Explanation: This formula standardizes the covariance by dividing by the product of standard deviations.
34. Which of the following does not affect the magnitude of correlation?
A. Measurement error
B. Outliers
C. Unit of measurement
D. Homogeneity of sample
Answer: C. Unit of measurement
Explanation: Correlation is a standardized measure; it is not influenced by the units of measurement.
35. In SPSS, the Pearson correlation output includes all except:
A. Correlation coefficient
B. Significance value (p-value)
C. Mean and SD
D. Regression slope
Answer: D. Regression slope
Explanation: Regression slope is part of regression analysis, not correlation output.
36. A Pearson’s r of –0.30 would be interpreted as:
A. Strong negative correlation
B. Moderate negative correlation
C. Weak negative correlation
D. No correlation
Answer: C. Weak negative correlation
Explanation: Values from –0.1 to –0.3 indicate a weak negative linear relationship.
37. The main purpose of correlation in psychological and educational studies is:
A. Establishing norms
B. Proving causality
C. Studying relationships among variables
D. Standardizing tests
Answer: C. Studying relationships among variables
Explanation: Correlation shows how two variables move together, which is essential in educational research.
38. Which of the following is not a graphical way to examine correlation?
A. Scatter diagram
B. Box plot
C. Line graph (for time series)
D. Correlation matrix
Answer: D. Correlation matrix
Explanation: A correlation matrix is a tabular (not graphical) representation of correlation values among multiple variables.
39. Which of these is true about the sign of the correlation coefficient?
A. It tells strength only
B. It indicates strength and significance
C. It shows direction of relationship
D. It shows causal relationship
Answer: C. It shows direction of relationship
Explanation: A positive sign shows that variables increase together; a negative sign shows that one increases as the other decreases.
40. The correlation coefficient can be best described as a measure of:
A. Agreement
B. Consistency
C. Relationship
D. Difference
Answer: C. Relationship
Explanation: The coefficient of correlation quantifies the degree of relationship between two variables.
41. A correlation coefficient of +0.75 indicates:
A. A weak relationship
B. A strong positive linear relationship
C. No relationship
D. A curvilinear relationship
Answer: B. A strong positive linear relationship
Explanation: Coefficients above 0.70 generally indicate a strong positive relationship between variables.
42. If Pearson’s r between Test A and Test B is 0.00, this means:
A. The scores are identical
B. One variable caused the other
C. No linear relationship exists
D. Scores are unrelated in any form
Answer: C. No linear relationship exists
Explanation: An r value of 0 implies no linear relation. There may still be a non-linear relationship.
43. A researcher finds r = –0.88 between study time and error rate. The best interpretation is:
A. Longer study time increases errors
B. Longer study time decreases errors
C. No relationship
D. Errors increase regardless of study time
Answer: B. Longer study time decreases errors
Explanation: A strong negative correlation means as study time increases, error rate decreases.
44. Pearson’s correlation requires that both variables be:
A. Ordinal
B. Nominal
C. Interval or ratio
D. Binary
Answer: C. Interval or ratio
Explanation: Pearson’s method assumes continuous, normally distributed variables on interval/ratio scale.
45. What is the coefficient of determination if r = 0.60?
A. 0.60
B. 0.36
C. 1.20
D. 0.06
Answer: B. 0.36
Explanation: Coefficient of determination = r² = 0.60² = 0.36. This means 36% of the variance is shared.
46. When interpreting correlation in SPSS, a p-value less than 0.05 indicates:
A. Correlation is insignificant
B. Correlation is significant
C. Correlation is negative
D. Sample size is too small
Answer: B. Correlation is significant
Explanation: A p-value < 0.05 shows the result is statistically significant (not due to chance).
47. A positive Spearman correlation of 0.90 suggests:
A. No relationship
B. Linear relationship
C. Strong monotonic relationship
D. Weak correlation due to ties
Answer: C. Strong monotonic relationship
Explanation: Spearman’s ρ measures monotonic (increasing or decreasing) trends between ranks.
48. In rank correlation, when ranks are tied, which correction is needed?
A. Normalization
B. Pearson’s adjustment
C. Tie correction factor
D. No correction is needed
Answer: C. Tie correction factor
Explanation: Ties are adjusted in the Spearman formula using a tie correction factor for accuracy.
49. If two variables are uncorrelated, their regression slope is:
A. Zero
B. One
C. Positive
D. Undefined
Answer: A. Zero
Explanation: A correlation of 0 implies no linear relationship, hence a slope of 0 in regression.
50. Correlation is a measure of:
A. Prediction
B. Association
C. Frequency
D. Causation
Answer: B. Association
Explanation: Correlation quantifies the strength and direction of an association between two variables.
51. Which one is not true about Pearson’s correlation?
A. Sensitive to outliers
B. Measures curvilinear relationship
C. Assumes normal distribution
D. Is a parametric test
Answer: B. Measures curvilinear relationship
Explanation: Pearson’s r measures linear relationships only; curvilinear patterns require different methods.
52. The highest possible positive value of Spearman’s rank correlation is:
A. 0
B. 1
C. 10
D. 100
Answer: B. 1
Explanation: Spearman’s rank correlation ranges from –1 to +1.
53. If the value of r is close to zero, it implies:
A. Strong relationship
B. Perfect positive relationship
C. Weak or no linear relationship
D. Strong negative relationship
Answer: C. Weak or no linear relationship
Explanation: The closer r is to 0, the weaker the linear relationship.
54. Which correlation method is appropriate for Likert scale data (ordinal)?
A. Pearson’s correlation
B. Spearman’s rank correlation
C. Regression
D. Chi-square
Answer: B. Spearman’s rank correlation
Explanation: Likert-scale data are ordinal; Spearman’s method is more appropriate than Pearson’s.
55. A correlation of –0.95 indicates:
A. A weak relationship
B. Perfect negative correlation
C. Strong negative correlation
D. Moderate positive correlation
Answer: C. Strong negative correlation
Explanation: A value close to –1 indicates a strong inverse relationship.
56. The primary limitation of correlation is that:
A. It cannot be calculated by hand
B. It only works for small samples
C. It does not imply causation
D. It requires nominal data
Answer: C. It does not imply causation
Explanation: Correlation shows association, not causality.
57. What happens to Pearson’s r when you multiply all X and Y values by 10?
A. r increases
B. r decreases
C. r remains the same
D. r becomes negative
Answer: C. r remains the same
Explanation: Pearson’s r is scale-invariant—it doesn’t change with linear transformations.
58. In educational research, correlation can help in:
A. Diagnosing learning disabilities
B. Predicting future academic performance
C. Teaching moral values
D. Memorizing facts
Answer: B. Predicting future academic performance
Explanation: Correlation helps educators predict performance based on prior scores or variables like IQ.
59. If Spearman’s ρ = +1, it means:
A. All ranks are reversed
B. All ranks are perfectly aligned
C. Data are random
D. There are many tied ranks
Answer: B. All ranks are perfectly aligned
Explanation: A +1 indicates a perfect monotonic (increasing) rank relationship.
60. In product moment correlation, the denominator contains:
A. Means only
B. Sum of squares of X and Y
C. Product of standard deviations of X and Y
D. Median values
Answer: C. Product of standard deviations of X and Y
Explanation: The denominator standardizes the covariance by dividing it by the product of standard deviations of X and Y.
