The default for the covariate parameter is NULL and if no covariate is specified it returns a data frame containing 5 variables, named as "Pearson","Spearman","p", "adj-p","logratio"
and the data frame is ordered based on the column "p" which is the p-value obtained from the Log-Ratio Test. If there is a covariate, then the output is a dataframe containing 13 variables for all the genes,named as
"adjPearson","adjSpearman","pPearson","Pearson", "Spearman", "pAdjR", "CovEffect1", "adjPeffect1", "CovEffect2", "adjPeffect2", "rawP1", "rawP2","logratio" and sorted based on "rawP1" and "pPearson" which are
p-value corresponding to the effect of the fingerprint feature on the gene expression data as obtained from the t-table after fitting the model using gls and the p-value obtained from the Log-Ratio Test, respectively.
In the first case without any covariate it calls the nullcov function inside it, otherwise the non_nullcov function is called to do the analysis.