Uji Mann-Whitney U

Pengujian A/B di R

Lauryn Burleigh

Data Scientist

Mann-Whitney U

  • Waktu makan Pizza Keju vs Pepperoni
  • Distribusi tidak normal
  • Nonparametrik
    • Bentuk distribusi tidak diasumsikan
    • Uji Mann-Whitney U

Dua histogram miring ke kiri. Pepperoni berwarna merah muda dengan mean 8 dan Cheese berwarna biru dengan mean 6,2.

Pengujian A/B di R

Asumsi

  • Bentuk distribusi sama
  • Menilai perbedaan median
  • Distribusi normal: mean = median
  • Tidak normal: median lebih tepat
  • Asumsi ekstra: uji lebih kuat
  • H0: tidak ada perbedaan median waktu makan pizza keju dan pepperoni
library(ggplot2)
ggplot(pizza, aes(x = Time, 
                  fill = Topping)) +
       geom_histogram() + 
       facet_grid(Topping~.)

Dua histogram miring ke kiri. 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.2p2n.test(h = 0.40, 
              sig.level = 0.05, 
              power = 0.8, n1 = 100)

    difference of proportion power 
 calculation for binomial distribution
              h = 0.4
             n1 = 100
             n2 = 96.29156
      sig.level = 0.05
          power = 0.8
    alternative = two.sided
NOTE: different sample sizes

pwr.2p2n.test(h = 0.40, 
              sig.level = 0.05, 
              power = 0.8, n1 = 110)

    difference of proportion power 
 calculation for binomial distribution
              h = 0.4
             n1 = 110
             n2 = 88.54092
      sig.level = 0.05
          power = 0.8
    alternative = two.sided
NOTE: different sample sizes
  • Ukuran efek yang diharapkan h: korelasi rank-biserial r
    • Lihat peringkat subjek antar grup
Pengujian A/B di R

Uji

wilcox.test(Time ~ Topping, 
            data = Pizza)
  • y ~ x
    • y: data
    • x: grup
    Wilcoxon rank sum test with 
    continuity correction
data:  Enjoyment by Topping
W = 6051, p-value = 0.01026
alternative hypothesis: true location 
shift is not equal to 0
Pengujian A/B di R

Ukuran efek dan power

Ukuran efek

library(effectsize)
rank_biserial(Time ~ Topping, 
              data = pizza)

r (rank biserial) |         95% CI
<----------------------------------
0.21              | [0.05, 0.36]
  • Kecil: 0.1
  • Sedang: 0.3
  • Besar: 0.5

1 - 0.14 = 0.86 probabilitas galat Tipe II

Analisis daya (power)

library(pwr)
pwr.2p2n.test(h = 0.21, sig.level = 0.01, 
              n1 = 100, n2 = 100)

     difference of proportion power calculation for binomial distribution 

              h = 0.21
             n1 = 100
             n2 = 100
      sig.level = 0.01
          power = 0.1376818
    alternative = two.sided

NOTE: different sample sizes
Pengujian A/B di R

Ayo berlatih!

Pengujian A/B di R

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