def METHOD_NAME(population_1, population_2, window_size, critical_quantile):
    """
    Computes the equivalence test to show that mean 2 - window_size/2 < mean 1 < mean 2 + window_size/2
    Inputs:
        - population_1, np.array 1D: an array of 1 dimension with the observations of 1st group
        - population_2, np.array 1D: an array of 1 dimension with the observations of 2nd group
        - threshold, float: small value that determines the maximal difference that can be between means
        - quantile, float: the level of significance, is the 1-q quantile of the distribution
    Output, bool: True if the null is rejected and False if there is not enough evidence
    """
    population_2_up = population_2 + window_size / 2.0
    population_2_low = population_2 - window_size / 2.0
    if np.array_equal(population_1, population_2):
        p_value_low, p_value_up = 0.0, 0.0
    else:
        p_value_up = stats.wilcoxon(population_1, population_2_up, alternative="less")[1]
        p_value_low = stats.wilcoxon(population_1, population_2_low, alternative="greater")[1]
    test_up = p_value_up < critical_quantile
    test_low = p_value_low < critical_quantile
    if test_low and test_up:
        print("null hypothesis rejected at a level of significance", critical_quantile)
        return True, max(p_value_low, p_value_up)
    else:
        print("not enough evidence to reject null hypothesis")
        return False, max(p_value_low, p_value_up)