I have sample data which I would like to compute a confidence interval for, assuming a normal distribution.
I have found and installed the numpy and scipy packages and have gotten numpy to return a mean and standard deviation (numpy.mean(data) with data being a list). Any advice on getting a sample confidence interval would be much appreciated.
import numpy as np import scipy as sp import scipy.stats def mean_confidence_interval(data, confidence=0.95): a = 1.0*np.array(data) n = len(a) m, se = np.mean(a), scipy.stats.sem(a) h = se * sp.stats.t._ppf((1+confidence)/2., n-1) return m, m-h, m+h you can calculate like this way.
Here a shortened version of shasan's code, calculating the 95% confidence interval of the mean of array a:
import numpy as np, scipy.stats as st st.t.interval(0.95, len(a)-1, loc=np.mean(a), scale=st.sem(a)) But using StatsModels' tconfint_mean is arguably even nicer:
import statsmodels.stats.api as sms sms.DescrStatsW(a).tconfint_mean() The underlying assumptions for both are that the sample (array a) was drawn independently from a normal distribution with unknown standard deviation (see MathWorld or Wikipedia).
For large sample size n, the sample mean is normally distributed, and one can calculate its confidence interval using st.norm.interval() (as suggested in Jaime's comment). But the above solutions are correct also for small n, where st.norm.interval() gives confidence intervals that are too narrow (i.e., "fake confidence"). See my answer to a similar question for more details (and one of Russ's comments here).
Here an example where the correct options give (essentially) identical confidence intervals:
In [9]: a = range(10,14) In [10]: mean_confidence_interval(a) Out[10]: (11.5, 9.4457397432391215, 13.554260256760879) In [11]: st.t.interval(0.95, len(a)-1, loc=np.mean(a), scale=st.sem(a)) Out[11]: (9.4457397432391215, 13.554260256760879) In [12]: sms.DescrStatsW(a).tconfint_mean() Out[12]: (9.4457397432391197, 13.55426025676088) And finally, the incorrect result using st.norm.interval():
In [13]: st.norm.interval(0.95, loc=np.mean(a), scale=st.sem(a)) Out[13]: (10.23484868811834, 12.76515131188166) Start with looking up the z-value for your desired confidence interval from a look-up table. The confidence interval is then mean +/- z*sigma, where sigma is the estimated standard deviation of your sample mean, given by sigma = s / sqrt(n), where s is the standard deviation computed from your sample data and n is your sample size.