Pearson correlation

A/B Testing in R

Lauryn Burleigh

Data Scientist

Pearson correlation assumptions

  • Choosing correlation test: properties of data
  • Pearson correlation
    • Linear
    • Normal distribution

Linear line in graph increasing from bottom left to top right.

Standard normal distribution graph.

A/B Testing in R

Pearson correlation and A/B tests

  • Group A: Cheese pizza
  • Group B: Pepperoni pizza

 

  • Relationship of time to eat pizza and enjoyment

Ignoring groups

  • Null hypothesis - no relationship between time to eat and enjoyment of the pizza

Each group

  • Null hypothesis - no relationship between time to eat and enjoyment of the Cheese pizza
  • Null hypothesis - no relationship between time to eat and enjoyment of the Pepperoni pizza
A/B Testing in R

Determine sample size

  • r expected effect (found with cor())
  • sig.level at which we reject the null
library(pwr)
pwr.r.test(r = 0.3, power = 0.80, 
           sig.level = 0.05)

    approximate correlation power 
 calculation (arctangh transformation) 

              n = 84.07364
              r = 0.3
      sig.level = 0.05
          power = 0.8
    alternative = two.sided
A/B Testing in R

Assessing linearity

ggplot(pizza, aes(x = enjoyment, 
                  y = time)) + 
    geom_point()

Scatter plot of a positive linear relationship between enjoyment on the x-axis and time on the y-axis.

ggplot(pizza, aes(x = enjoyment, 
                  y = time)) + 
    geom_point()

Scatter plot of a positive linear relationship between enjoyment on the x-axis and time on the y-axis, with one cluster of data points at the lower left and a distinctively different cluster at the upper right.

A/B Testing in R

Assessing normality

shapiro.test(pizza$time)

    Shapiro-Wilk normality test
data:  pizza$time
W = 0.98686, p-value = 0.4282
  • Data is normal
shapiro.test(pizza$enjoyment)

    Shapiro-Wilk normality test
data:  pizza$enjoyment
W = 0.98916, p-value = 0.5971
  • Data is normal
A/B Testing in R

Pearson ignoring groups

cor.test(~ time + enjoyment, 
         data = pizza, 
         method = "pearson")

 

Proportion of variance: cor^2

0.30^2

[1] 0.09

Pearson's product-moment correlation

data:  time and enjoyment
t = 22.304, df = 88, p-value = 0.0218
alternative hypothesis: true correlation
is not equal to 0
95 percent confidence interval:
 0.8833166 0.9479256
sample estimates:
      cor 
0.3021878
A/B Testing in R

Pearson within groups

cor.test(~ time + enjoyment, 
         data = pizza, 
         subset = 
             (Topping == "Cheese"),
         method = "pearson")

Pearson's product-moment correlation

data:  Time and Enjoy
t = 11.121, df = 98, p-value < 2.2e-16
alternative hypothesis: true correlation 
is not equal to 0
95 percent confidence interval:
 0.6451710 0.8226595
sample estimates:
     cor 
0.746935
A/B Testing in R

Power analysis

Pearson ignoring groups:

Pearson's product-moment correlation

data:  time and enjoyment
t = 22.304, df = 88, p-value = 0.0218
alternative hypothesis: true 
correlation is not equal to 0
95 percent confidence interval:
 0.8833166 0.9479256
sample estimates:
      cor 
0.3021878

library(pwr)
pwr.r.test(r = 0.302, n = 100, 
           sig.level = 0.022)

     approximate correlation power 
  calculation (arctangh transformation) 

              n = 100
              r = 0.302
      sig.level = 0.022
          power = 0.7853514
    alternative = two.sided
A/B Testing in R

Let's practice!

A/B Testing in R

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