I have gone through the deseq2 paper where it tells that its not a simple logfold change of numerator by denominator ,its shrunken LFC which it calculates the maths behind it kind of im trying to understand in simple manner or layman term as i have to give some explanation why rna seq and RTqpcr are not similar...

I have 4 control and 4 test sample respectively all the counts are normalized used deseq2 default 

    gene baseMean log2FoldChange lfcSE stat pvalue padj	nH4	nH3	nH2	nH1	C4	C3	C2	C1
    ENSG00000112773.13	1156.5575015292	2.52671958320643	0.330914786026763	7.63555963619613	2.25E-14	5.31E-12	326.344363070055	316.430980291062	369.993520743799	241.523773415627	1626.54796885324	3322.42939303791	1321.51219870859	1727.67781411328

   

so how come the log2foldchange or logfoldchange is low.?even though there is a big difference between my sample labelled as H vs C which are stem cells and C's are progenitor cells ? 


Another data point ,i have used lfcMLE for logfold change which says "“unshrunken” log2 fold
changes (for a simple comparison, the ratio of the mean normalized counts in the two groups"

  

>      gene baseMean log2FoldChange lfcMLE lfcSE stat pvalue padj SO_7660_BR_02 SO_7660_BR_03 SO_7660_BR_04 SO_7660_BR_06
>     
>     797.414 2.972936 3.976479 0.1360428 21.85294 7.288395e-106 1.204553e-101  113.6162 75.41853 1320.512 1680.109

    log2foldchange = 2.972936
    lfcMLE   = 3.976479

there is difference log2foldchange and lfcMLE somehow its still less as compared to qPCR ...





The fold-change is barely shrunken for these samples, the naive fold-change is ~6.4 and the shrunken fold-change is ~5.8. So I don't know why you think the log2FC is particularly low. The thing with the naive fold-change is that it will be innately unreliable due to the low number of samples and high variability, which is why it's shrunken toward 0 with a normally distributed prior.

The general idea behind shrinking p-values is that fold-changes will generally be overestimated given the actual variance in the samples and the typical miniscule number of samples. So lowly expressed genes are strongly pulled toward 0 while more highly expressed genes are less strongly pulled toward 0.

Regarding a discordance with your qPCR data, without at least knowing what the fold-change was it's impossible for us to judge how actually different the two values are. In general there's good (though not perfect) concordance between the two technologies, with qPCR generally being less sensitive/more variable.