Week 3

Question 1

Correlation research

Answer 1

The variables of interest are typically measured and not directly manipulated by the researcher
• Can be used for research questions where it is not possible to manipulate variables
• Cannot be used to infer a cause-effect relationship between the independent and dependent variable
• The distinction between the response and explanatory variable is not always clear
-> determined by the aims of the study
• The correlation measures the strength and direction of the association between two quantitative variables
• The notation is r

Question 2

Y axis scores in correlation

Answer 2

Response variable (y): 
measures the outcome of a study
• We are interested in hazardous drinking, so this is our criterion or response variable
• Sometimes called the dependent variable

Question 3

X axis scores in correlation

Answer 3

Explanatory variable (x): 
proposed to explain changes in the values in the response variable
• We think that stress may influence hazardous drinking, so this is our predictor variable
• Sometimes called the independent variable

Question 4

Scatterplots

Answer 4

Scatterplots are a graphical way to show the association between two variables

• response variable on y axis
• explanatory variable on x axis

Question 5

What to look for in a scatterplot

Answer 5

• Form:
Are there clusters in the scatterplot?

• Direction
Is there a diagonal pattern of a certain direction?

• Strength
Do all individuals closely follow the pattern?

Question 6

Negative association

Answer 6

• depicts a trend from the top left to the bottom right of the scatterplot
• Above average values of one variable tend to be associated with below average values on the other variable.
• As you increase on one variable the other variable decreases

Question 7

Positive association

Answer 7

• shows data in a trend from the bottom left to the top right of the scatterplot
• Above average values of one variable tend to be associated with above average values on the other variable.
• both variables increase together

Question 8

Strength (of clustered data)

Answer 8

• A weak strength relationship will have data quite broadly scattered around a plot, even if there is a slight directional tendency
• With a moderate strength relationship, the data is more tightly clustered
• A strong relationship shows a clear direction as the data is tightly clustered around an imaginary line.

Question 9

Predicting the line of best fit

Answer 9

Scatterplots can be examined further by using the line of best fit
Interpret the line of best fit by asking about:
• Direction: where is the line pointing?
• Strength: how closely do the dots cluster around the line?
• Form: where along the line do the dots lie?
• Deviations: are there any dots that fall far away from the line?

Question 10

What does the R value tell us

Answer 10

It can vary from -1 to +1
• Direction
Negative values indicate a negative association
Positive values indicate a positive association
• Strength
Correlations near zero indicate a weak association
Correlations near -1 or +1 indicate a strong association
*not resistant to outliers

Question 11

Cohen’s conventions for correlations

Answer 11

• R values around 0.1 or negative 0.1 are weak, or small correlations
• R values around 0.3 or -0.3 are moderate or medium correlations
• R values around 0.5 or negative 0.5 are strong, or large.

Question 12

Linear relationships

Answer 12

Pearson’s R is designed to capture linear relationships between variables

Question 13

Non-linear relationships

Answer 13

• Parabolic “curvilinear”

- correlation R value is not resistant to outliers, can not help with non-linear