Introduction to correlations

A/B Testing in R

Lauryn Burleigh

Data Scientist

Correlation in A/B design

Relationship strength and direction
Two variables
Increase or decrease in one variable per unit of the other variable
- Enjoyment correlated with time to eat
Ignore groups

Scatter plot of a positive correlation with time on the x-axis and enjoyment on the y-axis with each point colored either pink if Pepperoni pizza and blue if Cheese pizza.

Correlation in A/B design

Within groups

Scatter plot of a positive correlation with time on the x-axis and enjoyment on the y-axis of only Cheese pizza.

Scatter plot of a positive correlation with time on the x-axis and enjoyment on the y-axis of only Pepperoni pizza.

Correlation

Does NOT imply causation
Increase in drownings & ice cream sales
- NOT causal
- Likely: warm months
Using A/B to deduce causation
- Make and test changes
A/B: cheese and pepperoni
- Enjoyment and time to eat pizza
- Group change - Relationship change
Does not indicate dependency

ggplot(data, aes(x = drownings, 
                 y = icecream)) +
  geom_point()

A scatter plot showing a positive correlation with number of drownings on the x-axis and ice cream sales on the y-axis.

Correlation coefficient

Correlation coefficient (r) - degree of association
- -1 to +1
More extreme values - stronger association
- Better prediction

A scatter plot showing no correlation with points at the same level on the y-axis across the entirety of the x-axis.

A scatter plot showing a negative correlation with points high on the left of the x-axis and decreasing as moving to the right of the x-axis.

A scatter plot showing a positive correlation with points low on the left of the x-axis and increasing as moving to the right of the x-axis.

Correlation values

Proportion of variation in time eating that can be attributed to enjoyment
- R^2

corvalue <- cor(data$time, data$enjoyment)
corvalue

[1]    .73

corvalue^2

[1]        .5329

Correlation limitations

Particularly susceptible to outliers

Correlation coefficients

Not line of best fit
- Regression
Not indication of significance
- Correlation coefficient and sample size for p-value

Image of a positive correlation on a computer with a data point away from the linear correlation at the bottom right labeled as an outlier.

A scatter plot of a positive correlation with a red line of best fit through drownings on the x-axis and ice cream sales on the y-axis.

Let's practice!

A/B Testing in R