def _posterior_decision(probabilities, alpha):
    """
    calculate decision based on probabilities and desired significance
    """
    if len(probabilities) == 3:
        # with ROPE
        if probabilities[0] >= 1 - alpha:
            return 'smaller'
        elif probabilities[1] >= 1 - alpha:
            return 'equal'
        elif probabilities[2] >= 1 - alpha:
            return 'larger'
        else:
            return 'inconclusive'
    else:
        # without ROPE (i.e., rope=0)
        if probabilities[0] >= 1 - alpha:
            return 'smaller'
        elif probabilities[1] >= 1 - alpha:
            return 'larger'
        else:
            return 'inconclusive'