LEC 10 Correlation

Question 1

Correlation definition (3)

Answer 1

• the quantification of the degree to which 2 random variables (continuous or ordinal) are related
• variables must be numerical
• provided that the relationship is linear
  (check scatter plot to check for potential linear relationship)

Question 2

Scatter plot

Answer 2

• plot y against x

- useful for visually examining whether a relationship exists between 2 numerical variables

Question 3

Correlation coefficient

Answer 3

• quantitative measure of the strength and direction of a linear relationship between 2 variables

Question 4

Types of correlation coefficient (2)

& the type of data analysed

Answer 4

1. Pearson product-moment correlation coefficient
   - continuous normally distributed variables
   - r
2. Spearman rank correlation coefficient
   - continuous non-normally distributed variables
   - ordinal
   - less sensitive to outlying values as it uses rank > definite values
   - rs

Question 5

Are r and rs dimensionless?

Answer 5

Yes, no units

Question 6

Range of possible r and rs values

Answer 6

-1 to 1

Question 7

What does the sign of r and rs indicates?

Answer 7

The direction of the linear relationship between the 2 variables

Question 8

What does the magnitude of r and rs indicates?

Answer 8

The strength of the linear relationship between the 2 variables

<0.5 : weak
0.5-0.7 : strong
>= 0.7 : very strong

Question 9

If r/rs = 0?

Answer 9

• means no linear correlation
• DOES NOT mean no correlation cos it can be other non-linear correlation (eg curve)
• check scatter plot for relationship

Question 10

If r/rs = 1

Answer 10

Perfect positive correlation

Question 11

If r/rs = -1

Answer 11

Perfect negative correlation
OR
Perfect inverse correlation

Question 12

If r/rs > 0 (positive)

Answer 12

• means positive correlation

- both variables tend to increase together

Question 13

If r/rs < 0 (negative)

Answer 13

• means negative/inverse correlation

- one variable increases as the other decreases

Question 14

Potential misuse of the correlation coefficient (3)

Answer 14

1. If correlation coefficient = 0, does not mean no relationship, only mean no LINEAR relationship
2. If strong correlation coefficient, does not necessarily imply “linearity” as some parts of the graph might be non-linear
3. Does not imply causation (cause-and-effect relationship)

Question 15

Statistical test for correlation if BOTH data is :

• continuous
• normally distributed

Answer 15

Pearson product-moment correlation

(parametric test)

To test the null hypothesis that there is no correlation between the 2 numerical variables

Question 16

Pearson product-moment correlation assumptions (3)

Answer 16

1. The x and y values are independent
2. The pairs of observations are randomly selected
3. For Pearson product-moment correlation, the underlying populations of BOTH variables are normally distributed

Question 17

Pearson product-moment correlation hypothesis

Answer 17

Ho :
- There is no correlation between the 2 variables

H1 :

• There is a correlation between the 2 variables (two-tailed)
• There is a positive correlation between the 2 variables (one-tailed)
• There is a negative correlation between the 2 variables (one-tailed)

Question 18

Spearman Rank correlation assumptions (2)

Answer 18

1. The x and y values are independent

2. The pairs observed are randomly selected

Question 19

Spearman Rank correlation process

Answer 19

Involves ranking the values of x and y

Question 20

Correlation coefficient and p-value

Answer 20

Correlation =/ p-value

Question 21

What if your data is :
- 1 continuous normally distributed
- 1 ordinal / continuous non-normally distributed
OR
- both are ordinal / continuous non-normally distributed
?

Answer 21

Use Spearman Rank correlation

Question 22

Correlation assumption (1)

Answer 22

Linear relationship between the 2 variables

Question 23

Can you perform correlation analysis if scatter plot shows non-linear relationship?

Answer 23

No.

Correlation analysis assumes linear relationship between the 2 variables.

Question 24

If statistical report shows p = 0.000

Answer 24

p < 0.0005

Question 25

Advantage of Spearman Rank Correlation

Answer 25

Less sensitive to outlying values as compared to Pearson Product Moment Correlation
- use ranks rather than the actual values