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pythonstatistics
VanTan
VanTan

Reputation: 657

Python Mann-Whitney confidence interval

I have two datasets (Pandas Series) - ds1 and ds2 - for which I want to calculate 95% confidence interval for difference in mean (if normal) or median (for non-normal).

For difference in mean, I calculate t test statistic and CI as such:

import statsmodels.api as sm
tstat, p_value, dof = sm.stats.ttest_ind(ds1, ds2)
CI = sm.stats.CompareMeans.from_data(ds1, ds2).tconfint_diff()

for median, I do:

from scipy.stats import mannwhitneyu
U_stat, p_value = mannwhitneyu(ds1, ds2, True, "two-sided")

How do I to calculate CI for difference in median?

Upvotes: 1

Views: 2701

Answers (1)

VanTan
VanTan

Reputation: 657

I came across a paper (Calculating confidence intervals for some non-parametric analyses by MICHAEL J CAMPBELL, MARTIN J GARDNER) that gave CI formula.

Based on that:

from scipy.stats import norm

ct1 = ds1.count()  #items in dataset 1
ct2 = ds2.count()  #items in dataset 2
alpha = 0.05       #95% confidence interval
N = norm.ppf(1 - alpha/2) # percent point function - inverse of cdf

# The confidence interval for the difference between the two population
# medians is derived through these nxm differences.
diffs = sorted([i-j for i in ds1 for j in ds2])

# For an approximate 100(1-a)% confidence interval first calculate K:
k = int(round(ct1*ct2/2 - (N * (ct1*ct2*(ct1+ct2+1)/12)**0.5)))

# The Kth smallest to the Kth largest of the n x m differences 
# ct1 and ct2 should be > ~20
CI = (diffs[k], diffs[len(diffs)-k])

Upvotes: 4

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