def bootstrap_test(higher, lower, n=100000):
    xs = higher
    ys = lower
    m = np.mean(xs) - np.mean(ys)
    zs = np.concatenate((xs,ys))
    boots = np.random.choice(ys, size=(n,len(zs)))
    return np.sum(np.mean(boots[:,0:len(xs)], 1) - np.mean(boots[:,len(xs)+1:], 1) > m)

# test whether the mean of the array `higher` is higher than the mean of the array `lower`
def bootstrap_pvalue(higher, lower, n=100000):
    return bootstrap_test(higher, lower, n=100000) / n