Independent-sample t-test

A/B Testing in R

Lauryn Burleigh

Data Scientist

Independent t-test in A/B design

  • Significance in difference of means
  • Null hypothesis:
    • Cheese and Pepperoni pizza are eaten in the same amount of time (no difference)
A/B Testing in R

Assumptions

  • Dependent variable:
    • Interval or ratio
    • Equal intervals
  • Random samples
  • Normal distribution
  • Similar group variances
library(ggplot2)
ggplot(pizza, aes(x = Time, 
                  fill = Topping)) +
       geom_histogram() + 
       facet_grid(Topping~.)

Two normally distributed histograms. Pepperoni in pink with a mean of 8 and Cheese in blue with a mean of 6.2.

A/B Testing in R

Sample size

library(pwr)
pwr.t.test(d = 0.73, power = 0.80, 
           sig.level = 0.05, 
           type = "two.sample", 
           alternative = "two.sided")

  Two-sample t test power calculation 

              n = 30.44799
              d = 0.73
      sig.level = 0.05
          power = 0.8
    alternative = two.sided

NOTE: n is number in *each* group
A/B Testing in R

Assessing variances

  • Group variances equal
  • Levene's test

Not significant (p > 0.05) = variances equal

If significant (p < 0.05) = variances not equal

library(car)
leveneTest(Time ~ Topping, 
           data = Pizza)

Levene's Test for Homogeneity of Variance
         Df F value Pr(>F)
group   1  0.1457 0.7031
A/B Testing in R

Test

t.test(Time ~ Topping, data = Pizza, 
       paired = FALSE, 
       alternative = "two.sided", 
       var.equal = TRUE)

    Two Sample t-test
data:  Time by Topping
t = 2.3811, df = 198, p-value = 0.01821
alternative hypothesis: true difference 
in means between group Pepperoni and 
group Cheese is not equal to 0
95 percent confidence interval:
 0.0599370 0.6377601
A/B Testing in R

Cohen's d

  • Cohen's d: t-test effect size
    • Standardized measure of differences between means
  • Small: 0.2
  • Medium: 0.5
  • Large: 0.8
library(effectsize)
cohens_d(Time ~ Topping, data = Pizza)

Cohen's d |       95% CI
<----------------------
0.34      | [0.06, 0.62]
A/B Testing in R

Power

library(pwr)

pwr.t.test(n = 1000, 
           sig.level = 0.0182, 
           d = 0.34, 
           type = "two.sample")

  Two-sample t test power calculation 
              n = 100
              d = 0.34
      sig.level = 0.0182
          power = 0.510256
    alternative = two.sided
NOTE: n is number in *each* group
  • Ideal power to accept results: 0.8
    • Probability of error: 20%
    • 100 - 80 = 20
A/B Testing in R

Let's practice!

A/B Testing in R

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