Week 6: Correlation

Question 1

What does correlation measure in comparison to linear regression?

Answer 1

Linear regression estimates the best fit of a straight line. While correlation measures the strength of the linear association

Question 2

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

Answer 2

-1 to 1

Question 3

What does r = 0 signify in correlation?

Answer 3

There is no linear correlation between the variables

Question 4

How are strength levels of correlation categorised?

Answer 4

• Very strong ± 0.90 to ± 1
• Strong ± 0.70 to ± 0.89
• Moderate ± 0.40 to ± 0.69
• Weak ± 0.10 to ± 0.39
• No or very weak ± 0 to ± 0.09

Question 5

What does the coefficient of determination (R2) indicate?

Answer 5

The amount of variance shared between two variables. By multiplying R2, we can get a percentage of the variability explained by the predictor

Question 6

How is R2 calculated?

Answer 6

By squaring the coefficient (r)

Question 7

What is H0 in correlation hypothesis testing?

Answer 7

There is no correlation between the variables (r = 0)

Question 8

Key assumptions for Pearson correlation

Answer 8

1. Random sample
2. Continuous data
3. Paired sample data
4. Independence of observations
5. Approximate normal distribution
6. Linear association
7. Absence of outliers

Question 9

What alternatives exist if Pearson correlation assumptions are violated?

Answer 9

Use non-parametric methods like Spearman Rank correlation or Kendall’s tau

Question 10

How does Spearman Rank correlation differ from Pearson correlation?

Answer 10

It assesses monotonic relationships (whether linear or not), ranking values instead of using the original measurements - used if data are measured on an ordinal scale

Question 11

Why is visual inspection of data important before calculating correlation?

Answer 11

To confirm linearity and check for the presence of outliers - if there are outliers, can we justify removing them?

Question 12

Why is correlation not equivalent to causation?

Answer 12

Correlation only indicates a statistical relationship, not a cause-effect link

Question 13

What does a strong positive Pearson correlation coefficient (e.g., r = 0.76) suggest?

Answer 13

A strong positive linear relationship between two variables

Question 14

How should missing data in paired samples be handled when calculating r?

Answer 14

Use complete case analysis (only cases with data on x and y considered), but be aware of potential biases

Question 15

What the main visual check to perform before calculating Pearson correlation?

Answer 15

Ensure the data appears linear in a scatter plot?

Question 16

When is Spearman’s rank correlation preferable over Pearson?

Answer 16

When data are not normally distributed or the relationship is monotonic but not linear

Question 17

What value is sufficient for hypothesis testing?

Answer 17

The estimate of r is often enough

Question 18

Name characteristic of correlation

Answer 18

• Independent on units of measure
• Symmetric (e.g., f for weight and plasma ~ r for plasma and weight)
• Independent on scale (e.g., r between body weight in kg and plasma volume in litres is the same as r between body weight in g and plasma volume in ml)
• If r = 0, there is no linear relation but could still be other relationships