def _bound_mean_difference_ci(lower_ci, upper_ci):
    """Bound mean difference and normalized mean difference CI.

    Since the plausible range of mean difference and normalized mean
    difference is [-1, 1], bound the confidence interval to this range.
    """
    lower_ci = lower_ci if lower_ci > -1 else -1
    upper_ci = upper_ci if upper_ci < 1 else 1
    return lower_ci, upper_ci