# Example usage:

# Here is a function I wrote (adapted from the source) which does this:

import numpy as np

import scipy.stats as st

​

def get_correlation_confidence_interval(correl_coeff, sample_size, confidence):

    """

    Description: Function to calculate the confidence interval for a given

                 correlation score and sample size. Adapted from:

                 https://www.statskingdom.com/correlation-confidence-interval-calculator.html

    Inputs: correl_coeff, a Pearson correlation coefficient: [-1, 1]

            sample_size, the number of values that were used in the correlation

            confidence, the desired confidence for the interval. E.g., 95

                means that you want the interval that contains the true

                correlation with 95% confidence.

    Outputs: (lower, upper), a tuple of floats which are the lower and upper

                bounds of the confidence interval, rounded to 4 decimals, e.g.:

                (0.9456, 0.9678)

    """

    # Transform correlation to z scale using the Fisher transformation

    z = np.log((1 + correl_coeff) / (1 - correl_coeff)) / 2

    # Calculate the standard error of the transformed correlation

    standard_err = 1 / np.sqrt(sample_size - 3)

    # Obtain the z statistic for the desired confidence level

    z_stat = st.norm.ppf(1 - ((1 - (confidence * 0.01)) * 0.5))

    # Get the upper and lower bounds of the interval in z space

    lower_z = z - z_stat * standard_err

    upper_z = z + z_stat * standard_err

    # Transform the upper and lower bounds back to correlation scale and limit

    # them to 4 decimals

    lower = format(round((e**(2 * lower_z) - 1) / (e**(2 * lower_z) + 1), 4), '.4f')

    upper = format(round((e**(2 * upper_z) - 1) / (e**(2 * upper_z) + 1), 4), '.4f')

    return (lower, upper)