How do you compute the confidence interval for Pearson's r in Python?

Question

In Python, I know how to calculate r and associated p-value using scipy.stats.pearsonr, but I'm unable to find a way to calculate the confidence interval of r. How is this done? Thanks for any help :)

Answer 1

According to [1], calculation of confidence interval directly with Pearson r is complicated due to the fact that it is not normally distributed. The following steps are needed:

1. Convert r to z',
2. Calculate the z' confidence interval. The sampling distribution of z' is approximately normally distributed and has standard error of 1/sqrt(n-3).
3. Convert the confidence interval back to r.

Here are some sample codes:

def r_to_z(r):
    return math.log((1 + r) / (1 - r)) / 2.0

def z_to_r(z):
    e = math.exp(2 * z)
    return((e - 1) / (e + 1))

def r_confidence_interval(r, alpha, n):
    z = r_to_z(r)
    se = 1.0 / math.sqrt(n - 3)
    z_crit = stats.norm.ppf(1 - alpha/2)  # 2-tailed z critical value

    lo = z - z_crit * se
    hi = z + z_crit * se

    # Return a sequence
    return (z_to_r(lo), z_to_r(hi))

Reference:

1. http://onlinestatbook.com/2/estimation/correlation_ci.html