def get_ci(mean, cl, sd):
  loc = stats.norm.ppf(1 - cl/2)
  rng_val = stats.norm.cdf(loc - mean/sd)

  lwr_bnd = value - rng_val
  upr_bnd = value + rng_val 

  return_val = (lwr_bnd, upr_bnd)

This function takes three parameters which are the following:

mean --> It is the mean
cl --> Confidence Level
sd --> Standard Deviation

Can someone explain how this function is working as for example if we are calculating 95% confidence interval, why can't we just return (-2*sd+mean,2*sd+mean)?


1 Answer 1


The CI is defined as the interval which contains your mean with a $\alpha$% of probability.

Given that you are using a model which its subjacent assumption is normality (amongst others), the interval is to be obtained comparing the probability in the context of a normal distribution.

The function stats.norm.cdf returns the probability of $loc - \frac{mean}{sd}$ being zero.

The value returned is the $(\bar{X} - Z_{\alpha}\sigma,\bar{X} + Z_{\alpha}\sigma)$.

We can't return $(-2 sd+mean,2 sd+mean)$ because it would not be general in terms of probability, we use tables which say $0.95 \rightarrow 2$ because we (humans) cannot calculate the number for every probability, but the stats.norm.cdf function can.

$Z_{\alpha}$ is difficult for us to have all the possible values (what if we need 90%, 95%, 99%, 99.9% or 70% probability?)

  • 1
    $\begingroup$ I would confirm your understanding of confidence intervals, because what you write is incorrect. See www3.nd.edu/~rwilliam/stats1/x23.pdf for more, especially: "If we drew 100 samples of the same size, we would get 100 different sample means and 100 different confidence intervals. We expect that in 95 of those samples the population parameter will lie within the estimated 95% confidence interval, in the other 5 the 95% confidence interval will not include the true value of the population parameter." It's wrong to say the interval contains some mean with some probability. $\endgroup$
    – Alex L
    Apr 30, 2019 at 16:20

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