Pearson’s Correlation

Question 1

Correlations vs Scatterplots

Answer 1

Scatterplots allow us to visualize our data
Observe relationships between 2 variables

Correlations quantify relationships
How much of a relationship (strength)
The likelihood of finding the observed relationship in the sample, if there was no relationship in the population (significance)

Question 2

Correlation: explaining variability

Answer 2

How much of a relationship?
Correlations measure how much of the variance in one variable can be explained by another variable
In other words: how much of the variance is explained by our model

Any variance not explained by our model is explained by other variables

Can determine whether our model explains a meaningful amount of variance

Question 3

Variance explained by our model

Answer 3

Line through all data points
Smallest distance = “Line of best fit”
Uses “least squares” method

smaller distance = bigger effect

Models the relationship
(remember models are simplified versions of reality)

Question 4

a perfect model

Answer 4

If our data were perfectly linear:
Data would all lie on the line of best fit
We could work out one variable as long as we know the other
(we will cover this in more detail in term 2)

Question 5

Correlation – Effect Size

Answer 5

Correlation coefficient = size of the effect
No relationship: r = 0
Perfect relationship: r = +1 or r = -1
Pearson’s r

Question 6

How much of a relationship?

Answer 6

Correlations measure how much of the variance in one variable can be explained by another variable

Hypothesis: there will be a positive relationship between hunger levels and time since last meal

Question 7

Variance Explained

Answer 7

Precisely how much variance in our data is explained by our model?

Squaring the correlation coefficient (r) tells us this

Can convert this to percentage (%)

Question 8

Pearson’s r = 1

Answer 8

100% of the variance in hunger levels is explained by the amount of time since the last meal

Question 9

Pearson’s r = .89

Answer 9

79% of the variance in hunger levels is explained by the amount of time since the last meal

Question 10

Pearson’s r = -.08

Answer 10

<1% of the variance in hunger levels is explained by the amount of time since the last meal

Question 11

Statistical Significance

Answer 11

The likelihood of observing this relationship, if there’s no real relationship in the world
We tend to use 𝛼 = .05 in Psychology
Reject the null hypothesis if there is less than 5% likelihood
In other words: how likely is it that there really is a relationship in the population?

A bigger sample size is better able to reveal if the relationship is real
but significant relationships aren’t the same as strong relationships

Question 12

Correlation – Summary

Answer 12

Correlations in a nutshell
Used to measure the strength of relationship between two variables
Tells us how much of the variance in one variable is explained by another variable
correlation coefficient (r) is the size of the effect in our sample
Value between 0 and +/- 1
+ values are positive relationships
- values are negative relationships
0 means no relationship
Squaring the correlation coefficient reveals what proportion of the variance is explained by the model
p-value is the likelihood of observing this relationship if there’s no real relationship in the population
Making an inference from our sample to the population

Question 13

correlations in r

Answer 13

Formatting your data
Each participant on a separate row
Each variable in a separate column
Meaningful variable (column) labels

Save as .csv

Import into your R workspace
I’ll call my data “df”

Correlation Functions
You need 1 function to calculate Pearson’s correlation in R:
cor.test()