Uji t sampel independen

Pengujian A/B di R

Lauryn Burleigh

Data Scientist

Uji t independen dalam desain A/B

  • Signifikansi beda rata-rata
  • Hipotesis nol:
    • Pizza Cheese dan Pepperoni dimakan dalam waktu sama (tidak ada beda)
Pengujian A/B di R

Asumsi

  • Variabel dependen:
    • Interval atau rasio
    • Jarak antarnilai sama
  • Sampel acak
  • Distribusi normal
  • Varian grup serupa
library(ggplot2)
ggplot(pizza, aes(x = Time, 
                  fill = Topping)) +
       geom_histogram() + 
       facet_grid(Topping~.)

Dua histogram berdistribusi normal. Pepperoni berwarna merah muda dengan mean 8 dan Cheese berwarna biru dengan mean 6,2.

Pengujian A/B di R

Ukuran sampel

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
Pengujian A/B di R

Menilai varian

  • Varian grup sama
  • Uji Levene

Tidak signifikan (p > 0,05) = varian sama

Jika signifikan (p < 0,05) = varian tidak sama

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
Pengujian A/B di R

Uji

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
Pengujian A/B di R

Cohen's d

  • Cohen's d: ukuran efek uji t
    • Ukuran baku beda rata-rata
  • Kecil: 0,2
  • Sedang: 0,5
  • Besar: 0,8
library(effectsize)
cohens_d(Time ~ Topping, data = Pizza)

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

Daya (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
  • Daya ideal untuk menerima hasil: 0,8
    • Probabilitas galat: 20%
    • 100 - 80 = 20
Pengujian A/B di R

Ayo berlatih!

Pengujian A/B di R

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