Uji ANOVA

Pengujian Hipotesis dengan Python

James Chapman

Curriculum Manager, DataCamp

Kepuasan kerja: 5 kategori

stack_overflow['job_sat'].value_counts()

Very satisfied           879
Slightly satisfied       680
Slightly dissatisfied    342
Neither                  201
Very dissatisfied        159
Name: job_sat, dtype: int64

Memvisualisasikan banyak distribusi

Apakah rata-rata kompensasi tahunan berbeda menurut tingkat kepuasan kerja?

import seaborn as sns
import matplotlib.pyplot as plt
sns.boxplot(x="converted_comp", 
            y="job_sat", 
            data=stack_overflow)
plt.show()

Box plot distribusi kompensasi untuk 5 kategori. "Very satisfied" terlihat sedikit lebih tinggi, tapi sulit dipastikan.

Analisis varians (ANOVA)

Uji perbedaan antar grup

alpha = 0.2


pingouin.anova(data=stack_overflow,
               dv="converted_comp",
               between="job_sat")

    Source  ddof1  ddof2         F     p-unc       np2
0  job_sat      4   2256  4.480485  0.001315  0.007882

0.001315 $< \alpha$
Setidaknya dua kategori punya kompensasi berbeda signifikan

Uji berpasangan

$\mu_{\text{very dissatisfied}} \neq \mu_{\text{slightly dissatisfied}}$
$\mu_{\text{very dissatisfied}} \neq \mu_{\text{neither}}$
$\mu_{\text{very dissatisfied}} \neq \mu_{\text{slightly satisfied}}$
$\mu_{\text{very dissatisfied}} \neq \mu_{\text{very satisfied}}$
$\mu_{\text{slightly dissatisfied}} \neq \mu_{\text{neither}}$

$\mu_{\text{slightly dissatisfied}} \neq \mu_{\text{slightly satisfied}}$
$\mu_{\text{slightly dissatisfied}} \neq \mu_{\text{very satisfied}}$
$\mu_{\text{neither}} \neq \mu_{\text{slightly satisfied}}$
$\mu_{\text{neither}} \neq \mu_{\text{very satisfied}}$
$\mu_{\text{slightly satisfied}} \neq \mu_{\text{very satisfied}}$

Tetapkan tingkat signifikansi $\alpha = 0.2$.

pairwise_tests()

pingouin.pairwise_tests(data=stack_overflow, 
                        dv="converted_comp", 
                        between="job_sat", 
                        padjust="none")

  Contrast                   A                      B  Paired  Parametric  ...          dof  alternative     p-unc     BF10    hedges
0  job_sat  Slightly satisfied         Very satisfied   False        True  ...  1478.622799    two-sided  0.000064  158.564 -0.192931
1  job_sat  Slightly satisfied                Neither   False        True  ...   258.204546    two-sided  0.484088    0.114 -0.068513
2  job_sat  Slightly satisfied      Very dissatisfied   False        True  ...   187.153329    two-sided  0.215179    0.208 -0.145624
3  job_sat  Slightly satisfied  Slightly dissatisfied   False        True  ...   569.926329    two-sided  0.969491    0.074 -0.002719
4  job_sat      Very satisfied                Neither   False        True  ...   328.326639    two-sided  0.097286    0.337  0.120115
5  job_sat      Very satisfied      Very dissatisfied   False        True  ...   221.666205    two-sided  0.455627    0.126  0.063479
6  job_sat      Very satisfied  Slightly dissatisfied   False        True  ...   821.303063    two-sided  0.002166     7.43  0.173247
7  job_sat             Neither      Very dissatisfied   False        True  ...   321.165726    two-sided  0.585481    0.135 -0.058537
8  job_sat             Neither  Slightly dissatisfied   False        True  ...   367.730081    two-sided  0.547406    0.118  0.055707
9  job_sat   Very dissatisfied  Slightly dissatisfied   False        True  ...   247.570187    two-sided  0.259590    0.197  0.119131

[10 rows x 11 columns]

Saat jumlah grup bertambah...

Plot pencar jumlah pasangan vs. jumlah grup. Saat jumlah grup naik, jumlah pasangan naik kuadratik.

Plot pencar peluang mendapat ≥1 hasil signifikan vs. jumlah grup. Saat jumlah grup naik, peluang punya ≥1 hasil signifikan meningkat.

Koreksi Bonferroni

pingouin.pairwise_tests(data=stack_overflow, 
                        dv="converted_comp", 
                        between="job_sat", 
                        padjust="bonf")

  Contrast                   A                      B   ...     p-unc    p-corr p-adjust     BF10    hedges
0  job_sat  Slightly satisfied         Very satisfied   ...  0.000064  0.000638     bonf  158.564 -0.192931
1  job_sat  Slightly satisfied                Neither   ...  0.484088  1.000000     bonf    0.114 -0.068513
2  job_sat  Slightly satisfied      Very dissatisfied   ...  0.215179  1.000000     bonf    0.208 -0.145624
3  job_sat  Slightly satisfied  Slightly dissatisfied   ...  0.969491  1.000000     bonf    0.074 -0.002719
4  job_sat      Very satisfied                Neither   ...  0.097286  0.972864     bonf    0.337  0.120115
5  job_sat      Very satisfied      Very dissatisfied   ...  0.455627  1.000000     bonf    0.126  0.063479
6  job_sat      Very satisfied  Slightly dissatisfied   ...  0.002166  0.021659     bonf     7.43  0.173247
7  job_sat             Neither      Very dissatisfied   ...  0.585481  1.000000     bonf    0.135 -0.058537
8  job_sat             Neither  Slightly dissatisfied   ...  0.547406  1.000000     bonf    0.118  0.055707
9  job_sat   Very dissatisfied  Slightly dissatisfied   ...  0.259590  1.000000     bonf    0.197  0.119131

[10 rows x 11 columns]

Metode lain

padjust : string

Metode untuk pengujian dan penyesuaian p-value.

'none': tanpa koreksi [default]
'bonf': koreksi Bonferroni satu langkah
'sidak': koreksi Sidak satu langkah
'holm': metode step-down dengan penyesuaian Bonferroni
'fdr_bh': koreksi FDR Benjamini/Hochberg
'fdr_by': koreksi FDR Benjamini/Yekutieli

Ayo berlatih!

Pengujian Hipotesis dengan Python