Correlations

Question 1

What is correlation in statistics?

Answer 1

Correlation measures the strength and direction of a relationship between two continuous variables.

Question 2

What are the key characteristics of correlation?

Answer 2

Strength (weak, moderate, strong).

Direction (positive or negative).

Does not imply causation.

Question 3

What is the range of the correlation coefficient (r)?

Answer 3

The correlation coefficient ranges from -1 to +1.

Question 4

What does a correlation coefficient (r) of +1 mean?

Answer 4

A perfect positive correlation; as one variable increases, the other increases proportionally.

Question 5

What does a correlation coefficient (r) of -1 mean?

Answer 5

A perfect negative correlation; as one variable increases, the other decreases proportionally.

Question 6

What does a correlation coefficient (r) of 0 mean?

Answer 6

No correlation; there is no linear relationship between the variables.

Question 7

What is a positive correlation?

Answer 7

When both variables increase or decrease together (e.g., study time and exam scores).

Question 8

What is a negative correlation?

Answer 8

When one variable increases while the other decreases (e.g., stress and sleep quality).

Question 9

What are the types of correlation?

Answer 9

Pearson’s correlation (linear relationship).

Spearman’s rank correlation (monotonic relationship).

Kendall’s tau correlation (ordinal data).

Question 10

When is Pearson’s correlation used?

Answer 10

When both variables are continuous and the relationship is linear.

Question 11

When is Spearman’s correlation used?

Answer 11

When data are ordinal or not normally distributed, and the relationship is monotonic.

Question 12

What assumptions must be met for Pearson’s correlation?

Answer 12

Continuous variables.

Linearity of the relationship.

No significant outliers.

Normal distribution of data.

Question 13

What is the formula for Pearson’s correlation coefficient?

Answer 13

Sqr of ∑ (X-X)2 ∑(Y-y)2

Question 14

What does a small correlation coefficient indicate?

Answer 14

A weak relationship between the two variables.

Question 15

What are the common benchmarks for interpreting correlation strength?

Answer 15

0.1 - 0.3: Weak
0.3 - 0.5: Moderate
0.5 - 1.0: Strong

Question 16

What is the difference between correlation and causation?

Answer 16

Correlation indicates an association, while causation suggests that one variable directly affects the other.

Question 17

What are common applications of correlation analysis?

Answer 17

Psychology (e.g., anxiety and performance).

Business (e.g., advertising and sales).

Medicine (e.g., exercise and heart rate).

Question 18

How can outliers affect correlation?

Answer 18

Outliers can distort the correlation coefficient, making it weaker or stronger than it actually is.

Question 19

What is the coefficient of determination (r²)?

Answer 19

The proportion of variance in one variable that is explained by the other variable.

Question 20

What does an r² value of 0.64 indicate?

Answer 20

64% of the variance in one variable is explained by the other variable.

Question 21

What is a scatterplot used for in correlation analysis?

Answer 21

To visually assess the relationship and identify patterns or outliers.

Question 22

What are potential pitfalls of correlation analysis?

Answer 22

Ignoring confounding variables.

Misinterpreting correlation as causation.

Relying on linear relationships only.

Question 23

How can correlation be tested for statistical significance?

Answer 23

By using a hypothesis test where the null hypothesis states there is no correlation (𝐻0:𝜌=0)