Module 12, Correlation

Question 1

What is correlation?

Answer 1

correlation describes the relationship between two variables (bivariate relationship)

Question 2

Key Assumptions (4)

Answer 2

1) ratio or interval scale of measurement
- pearson product movement correlation

2) both variables are continuous
- although there might be exceptions for some types of correlations (bi-serial)
- if you met assumption one you automatically met assumption 2

3) each variable is more or less normally distributed (examine the shapiro-wilk’s test (frequency does not differ from normal distribution), if you reject it then you look histograms, modality, symmetry and variability)

4) linear relationship between variables (scatter plot each dot represents intersection between two variables which each dot being one person) - suggests that the best way to represent a relationship is through a straight line
- if it is curvilinear it is violating the assumption (first diagram assumption is met, 2 and 3rd is not met)

Question 3

Positive Relationship (scatter plot)

Answer 3

positive r value
- in a positive relationship as one variables increases in value the other variables increases in value
- there is no casual direction of the relationship rather just looking at association between two variables
- it does not matter what is on your x or y axis the pattern of the relationship will hold
- regression line also called line of best fit - in a positive relationship the line is fitted to the dots (moves from left to right in an extending manner) - we can identify outliers by seeing what dots are far away from the regression line

Question 4

Negative Relationship

Answer 4

negative r value
- regression line goes downward from left to right (the dots are going downward - as you jump further you have a lower sprint time or if you cannot jump as far you are not as fast with a higher sprint time)
◦ bigger values do not always mean better (you want to have smaller time with sprinting)

Question 5

No Relationship

Answer 5

straight flat line
r value of 0

Question 6

Correlation Coefficient (r)

Answer 6

• quantifies relationships between sets of scores (in order for somebody to be included in correlation they needed to be included in both variables)
• indicates the strength (effect size - r acts as an effect size) and direction (positive, negative) of the linear relationship
• range from: +1 to -1 (needs to be within this range) - 0 indicates that there is no relationship
• as you move towards -1 or +1 the relationship becomes stronger
• if the relationship becomes stronger the dots are going to be more clustered around the regression line and the regression line becomes steeper
• a perfect positive relationship is 1 (all the dots are on the line) and a perfect negative relationship is going to have value of -1

positive: one variable increases as the other increases
negative: one variables increases as the other decreases

Question 7

r2 as an Effect Size

Answer 7

the square of Pearson product-moment correlation coefficient (r)
- shows shared variance between the variables

Question 8

Interpreting r2

Answer 8

small effect is .01
medium effect is .09
large effect is .25

Question 9

Null and Alternative Hypotheses

Answer 9

H0: ρ = 0 (always stated as equal to 0 because that implies that there is no relationship)
H1: ρ ≠ 0