quotient_se.py

from scipy import stats
import numpy as np


def interval_zscore(alpha=0.95):
    """
    Return a zscore corresponding with a confidence interval
    (e.g., for alpha=0.95, returns 1.96)

    :param: alpha: float, the width of the confidence interval, default is 0.95
    """
    return stats.norm.ppf(1 - (1 - alpha) * 0.5)


def quotient_se(mean_a, mean_b, std_a, std_b, n_a, n_b):
    """Returns the standard error of the ratio of two means
    """
    sem_a = std_a / np.sqrt(n_a)
    sem_b = std_b / np.sqrt(n_b)
    q = mean_a / mean_b

    std_err_q = q * np.sqrt(
        ((sem_a**2)/(mean_a**2))+((sem_b**2)/(mean_b**2))
    )
    
    return std_err_q