Hi Phillip
Paired testing is similar (or equal) as introducing an extra subject covariate in the linear model. However, the way we prefer do it in Omics Playground is to correct for the pairing effect using limma, ComBat or one of the unsupervised bath correction methods (NPM, SVA or RUV). Batch correction is closely related to adding subject covariate in ANOVA. It also uses linear regression, but it explicitly subtracts the pair/subject induced variation and gives you the residuals as a corrected matrix.
To correct for the pairing effect using limma or ComBat, you need to add a column in your sample information (samples.csv) file that denotes the subject/patient ID. So if the first two samples come from patient A, and sample 3-4 from patient B, you would add a colum: c(A,A,B,B). Be sure that conditions (e.g. treated and control) exists is all subjects. If you use NPM, SVA or RUV, they should 'automagically' remove the pairing effect for you. It is not 'odd' to get no significance if you do not correct or do explicit paired testing. In many real world data from patients there is considerable patient specific variation even in the baseline and correction is needed.
Best
Ivo