Lecture 3

Question 1

What is a correlation?

Answer 1

A relationship between variable A and B. It is the easiest way of quantifying a relationship between 2 numeric variables

Question 2

Are correlations useful?

Answer 2

Not particularly useful so we follow them up with regression

Question 3

What is the value of a perfect positive relationship?

Answer 3

r=1

Question 4

What does r=0 mean?

Answer 4

A complete absence of a relationship

Question 5

What is the value of a perfect negative relationship?

Answer 5

r=-1

Question 6

Name the two features of the correlation

Answer 6

Direction and magnitude

Question 7

What does it mean if there is a weak relationship?

Answer 7

Someone’s performance on the Y variable is not determined by their performance on X, and there must be other variables involved

Question 8

What should you always do first?

Answer 8

Visualise the data. Knowing a mean and SD doesn’t give you much unless you visualise the points, you need to plot data to see the distribution of the data

Question 9

Name the different types of scatterplot and what they look like, and would you use r?

Answer 9

1. Normal - linear, yes.
2. Curvilinear - semi-circle shape, r would underestimate the strength of the relationship because it only measures linear relationships
3. A perfect relationship between X and Y - all point lie on a straight line except one outlier, r would underestimate the strength of the relationship
4. No relationship - vertical line with an extreme outlier, r would lead to an overestimation

Question 10

Why do outliers pose a big threat when the sample is small?

Answer 10

Because they exert a strong influence on the results - can influence the value and interpretation of the correlation. Need to plot your data to see if there are any point which don’t lie with the rest of your data set

Question 11

What would qualify as at outlier?

Answer 11

There is no absolute definition, but in general, a score that is more than 3SDs from the mean would qualify as an outlier

Question 12

What do z-scores do?

Answer 12

Convert individuals’ scores on a variable to standard scores which are normally distributed with a mean of 0 and SD of 1. Need to standardise the score to understand where it falls on the distribution

Question 13

When are deviation products positive/negative, respectively?

Answer 13

When X and Y scores are both above the mean/both below the mean OR when X and Y scores are not both above the mean/below the mean

Question 14

How can the correlation between X and Y can be obtained?

Answer 14

• Multiplying each individual’s z-score on X by their z-score on Y
• Summing these products
• Dividing this sum by N or by N-1

Question 15

Why do we have to do n-1?

Answer 15

If not, we have an over-estimated correlation

Question 16

What is r a measure of?

Answer 16

The strength of the linear association between 2 variables

Question 17

How do you compare the magnitude of correlations?

Answer 17

Calculate the proportion of shared or common variance

Question 18

What is a better way of looking at the strength of a correlation?

Answer 18

R^2