ANOVA-Tests

Hypothesentests in Python

James Chapman

Curriculum Manager, DataCamp

Arbeitszufriedenheit: 5 Kategorien

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
Hypothesentests in Python

Mehrere Verteilungen visualisieren

Unterscheidet sich das durchschnittliche Jahresgehalt je nach Zufriedenheitsstufe?

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

Boxplot der Vergütungsverteilung für alle 5 Kategorien. „Sehr zufrieden“ wirkt etwas höher, aber es ist schwer zu sagen.

Hypothesentests in Python

Varianzanalyse (ANOVA)

  • Ein Test auf Unterschiede zwischen Gruppen
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 $< \alpha$
  • Mindestens zwei Kategorien haben signifikant unterschiedliche Vergütung
Hypothesentests in Python

Paarweise Tests

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

 

Setze das Signifikanzniveau auf $\alpha = 0.2$.

Hypothesentests in Python

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]
Hypothesentests in Python

Wenn die Anzahl der Gruppen steigt ...

Streudiagramm: Anzahl der Paare vs. Anzahl der Gruppen. Mit mehr Gruppen steigt die Anzahl der Paare quadratisch.

Streudiagramm: Wahrscheinlichkeit für mind. 1 signifikantes Ergebnis vs. Anzahl der Gruppen. Mit mehr Gruppen steigt die Wahrscheinlichkeit.

Hypothesentests in Python

Bonferroni-Korrektur

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]
Hypothesentests in Python

Weitere Methoden

padjust : string

Methode zur Testung und Anpassung der p-Werte.

  • 'none': keine Korrektur [Standard]
  • 'bonf': Bonferroni-Einkorrektur
  • 'sidak': Šidák-Einkorrektur
  • 'holm': schrittweises Verfahren mit Bonferroni-Anpassung
  • 'fdr_bh': Benjamini/Hochberg-FDR-Korrektur
  • 'fdr_by': Benjamini/Yekutieli-FDR-Korrektur
Hypothesentests in Python

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Hypothesentests in Python

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