def pc_anova(self, covariates, num_pc=5):
        """ 
        Calculate one-way ANOVA between the first num_pc prinicipal components
        and known covariates. The size and index of covariates determines
        whether u or v is used.
    
        Parameters
        ----------
        covariates : pandas.DataFrame
            Dataframe of covariates whose index corresponds to the index of
            either u or v. 
    
        num_pc : int
            Number of principal components to correlate with.
    
        Returns
        -------
        anova : pandas.Panel
            Panel with F-values and p-values.
    
        """
        from scipy.stats import f_oneway
        if (covariates.shape[0] == self.u.shape[0] and 
            len(set(covariates.index) & set(self.u.index)) == self.u.shape[0]):
            mat = self.u
        elif (covariates.shape[0] == self.v.shape[0] and 
            len(set(covariates.index) & set(self.v.index)) == self.v.shape[0]):
            mat = self.v
        anova = pd.Panel(items=['fvalue', 'pvalue'],
                         major_axis=covariates.columns,
                         minor_axis=mat.columns[0:num_pc])
        for i in anova.major_axis:
            for j in anova.minor_axis:
                t = [mat[j][covariates[i] == x] for x in set(covariates[i])]
                f, p = f_oneway(*t)
                anova.ix['fvalue', i, j] = f 
                anova.ix['pvalue', i, j] = p 
        return anova