Confidence Interval for t-test (difference between means) in Python

Question

I am looking for a quick way to get the t-test confidence interval in Python for the difference between means. Similar to this in R:

X1 <- rnorm(n = 10, mean = 50, sd = 10) X2 <- rnorm(n = 200, mean = 35, sd = 14) # the scenario is similar to my data  t_res <- t.test(X1, X2, alternative = 'two.sided', var.equal = FALSE)     t_res 

Out:

    Welch Two Sample t-test  data:  X1 and X2 t = 1.6585, df = 10.036, p-value = 0.1281 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval:  -2.539749 17.355816 sample estimates: mean of x mean of y   43.20514  35.79711  

Next:

>> print(c(t_res$conf.int[1], t_res$conf.int[2])) [1] -2.539749 17.355816 

I am not really finding anything similar in either statsmodels or scipy, which is strange, considering the importance of significance intervals in hypothesis testing (and how much criticism the practice of reporting only the p-values recently got).

Answer 1

Here how to use StatsModels' CompareMeans to calculate the confidence interval for the difference between means:

import numpy as np, statsmodels.stats.api as sms  X1, X2 = np.arange(10,21), np.arange(20,26.5,.5)  cm = sms.CompareMeans(sms.DescrStatsW(X1), sms.DescrStatsW(X2)) print cm.tconfint_diff(usevar='unequal') 

Output is

(-10.414599391793885, -5.5854006082061138) 

and matches R:

> X1 <- seq(10,20) > X2 <- seq(20,26,.5) > t.test(X1, X2)      Welch Two Sample t-test  data:  X1 and X2 t = -7.0391, df = 15.58, p-value = 3.247e-06 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval:  -10.414599  -5.585401 sample estimates: mean of x mean of y         15        23