def _check_improve_clusters(new_tstat_mean: float, mean_redo_tstat: float,
    old_cluster: tuple, new_cluster: tuple) ->tuple:
    """
    Checks cluster improvement condition based on t-statistic.
    :param new_tstat_mean: (float) t-statistics
    :param mean_redo_tstat: (float) average t-statistcs for cluster improvement
    :param old_cluster: (tuple) old cluster correlation matrix, optimized clusters, silh scores
    :param new_cluster: (tuple) new cluster correlation matrix, optimized clusters, silh scores
    :return: (tuple) cluster
    """
    if new_tstat_mean > mean_redo_tstat:
        return old_cluster
    return new_cluster
