Given several measurements of a single quantity, determine the average value of the measurements, the standard deviation of the measurements and the 95% confidence interval for the average.
This is a recipe for computing the confidence interval. The strategy is:
- compute the average
- Compute the standard deviation of your data
- Define the confidence interval, e.g. 95% = 0.95
- compute the student-t multiplier. This is a function of the confidence
interval you specify, and the number of data points you have minus 1. You subtract 1 because one degree of freedom is lost from calculating the average. The confidence interval is defined as ybar +- T_multiplier*std/sqrt(n).
import numpy as np from scipy.stats.distributions import t y = [8.1, 8.0, 8.1] ybar = np.mean(y) s = np.std(y) ci = 0.95 alpha = 1.0 - ci n = len(y) T_multiplier = t.ppf(1-alpha/2.0, n-1) ci95 = T_multiplier * s / np.sqrt(n-1) print [ybar - ci95, ybar + ci95]
We are 95% certain the next measurement will fall in the interval above.
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