There is no test telling you what is "truely" the case - e.g. if a gene is "truely" differentially expressed or if it is "truely" not differentially expressed.

Tests compare observations to a statistical model under which the likelihood of observations can be derived. If the probability of observations being at least "as extreme" as the actual observations under this statistical model is very low, the statistical model is thought to be unsuited to "explain" the actual observations - the model and the actual observations do not fit (well) together. Typically, the model is formulated as a restricted version of a more general model that should (ideally) be able to explain the data (well) in any case, but may explain the data considerably worse in its restricted form. For instance, the t-test is based on the unrestricted model that the mean difference is approximately normal distributed, with no restictions on variance and mean (expectation). The restiction applied if to keep the mean fixed at some chosen value (often zero, but any other value would work, too). This restriction is often called the "null hypothesis", and the only purpose of the test is to see if the observed data are (already) sufficient to clearly see that it does not fit well to the model with this restriction (in which caes on "rejects" the null hypothesis and dares to interpret the sample statistic (the observed mean difference) with respect to the null hypothesis (it is either larger or smaller).

At no point the test tries to say that the unknown true mean difference (the expected difference) is zero (or equal to the chosen value of the null hypothesis) or that it is different to that value. The purpose is to weight the evidence of the observations against the choosen null hypothesis, and when this evidence is considered sufficiently strong, then one dares to interpret the estimated value w.r.t to the chosen fixed hypothesized value.

If you choose zero as null hypothesis, a test may allow you to distinguish "up-regulated" from "down-regulated" genes (and to remain inconclusive where you were unable to reject the null hypothesis).

If you choose, say, a log fold-change of 1, a test may allow you to distinguish genes that are up-regulated by more than a factor of two by those that are up-regulated by less than a factor of two (including genes that are down-regulated).

If you choose, say, a log fold-change of -1, a test may allow you to distinguish genes that are down-regulated by more than a factor of two by those that are down-regulated by less than a factor of two (including genes that are up-regulated).

A smart way is to look at the test results for all possible hypotheses you could test: this a a confidence interval. The 95% confidence interval is the interval of hypotheses that you can not reject at a 5% level of significance. This means that your data is statistically (sufficiently) incompatible with all hypotheses outside this interval. If such an interval for the log fold-change is completely, say, between -0.5 and +0.5, then the observed data are sufficiently incompatibel with all hypotheses < -0.5 and > +0.5. You still don't know if it is regulated and you dont know if it is up- or down-regulated. But the data are sufficiently incompatible with any strong regulation in either direction. If you think that a log fold-change of 0.5 is still possibly biologically relevant, you are free to choose more stringent limits, like ±0.1 or so.

The problem in screening assays is that you need to control for an accumulation of "false positives". There are many methods to adjust p-values for multiple testing. It is not that clear or you are less flexible in adjusting confidence intervals in a similar way. One simple method is to apply a Bonferroni correction (if you do 20000 tests, use a nominal alpha of 0.05/20000 = 0.0000025 instead of 0.05 to construct the confidence intervals). This method is very conservative.

I don't think that there is a way to reliably identify genes that are not (or not much, not relevantly) regulated without having lots and lots and lots and even more data (what very typically is not the case!).

Good luck anyway.

Chat-GPT really is a jabber-box. Context must be critically reworked by a person knowing the topic. Answers like the one posted by Rana above are not only not useful but also potentially misleading, not to say wrong. But most relevantly, it has nothing to do with a scientific interaction of researchers.

From a purely practical perspective, RNAseq data can give you expression for a HUGE number of genes, so you can really afford to be quite selective in your criteria.

Your traditional volcano plot tells you two things: how much the expression differs between samples, and the statistical confidence of that change. Stuff down the bottom can suggest large fold changes (spreading out along the X-axis) but often these changes are sufficiently variable as to be low confidence (hence they're at the bottom).

Alternatively, they could be very low abundance (few reads), which also makes statistical assessment challenging.

You can ignore all these (and you should).

You can also have genes near the midline toward the top: these are genes that vary only a little between groups, but sufficiently consistently to be assigned high statistical confidence of being "different". A gene that increases expression by ~10% in every single sample from one group might be assigned a high -log(p.adj), but this might not be of biological relevance because that's still a very modest change.

What this means, however, is that right in the centre, down at the 'base' of the volcano, there are a large collection of genes that have almost no difference in expression, and thus have crappy p.adj values because they're not different.

Sort your data based on these, and then filter based on abundance: from a list of some 20-40,000 genes, it shouldn't be too hard to find ten genes that are robustly expressed but that also do not differ whatsoever between groups. Probably you'll find a bunch of things people use as reference genes (HPRT1, RPL13a, RPS9, etc), because people pick reference genes for exactly this reason.

I agree with Jochens statement "There is no test telling you what is "truely" the case - e.g. if a gene is "truely" differentially expressed or if it is "truely" not differentially expressed." Are you sure you (just) need a software to show you all of this? What about the before the software/stats part? Has the experimental design been appropriately tailored to the conditions you described. From reading your situation, do you have many biological replicates, heck even technical replicates. And you sequenced these samples to an appropriate depth? I've dealt with data with high variance for gene expression and protein expression. If that's what shows up, then that's what it is. That's also interesting in itself. In my PhD thesis, I've had female cohorts that showed high variance in relative gene expression for select genes which was in contrast to males (no cross-sex comparisons were made). We're not here to prove something has to be significant or not significant. If it's not significant, then so be it, so long as my experimental design was robust (to the best of our knowledge at that time), we move on. Sadly there is too much of an emphasis placed on "significant results" which I think many of us find unhealthy.