Significat P-value but low Log2 Fold Change I'm using Volcano plot to investegate the abundace of cells in two groups: responders vs non-responders for certain cancer drug. We are trying to see if certain cells are more abundant among one of the groups. The data behind this is cell type enrichment analysis, and p values calculated with Wilcoxon test.
The volcano-plot is showing many significant cells, however many of them are statisticaly significant with unsignificant log fold change (LFC). What could be the reason for that? why are those datapoints (cells) significant although the LFC is relatively low?
Does this indicade that I have noise in the data?
If it helps, here is the code:
### Volcano-Plot: Complete response (CR) vs all other responses for the drug

p=c()

for (i in 1:nrow(scores.batch)){
  p[i] = wilcox.test(scores.batch[i,metadata$CR=='1'],scores.batch[i,metadata$CR=='0'])$p.value
}
p.adj = p.adjust(p,method='fdr') 

lfc = log2(rowMeans(scores.batch[,metadata$CR=='1'])/rowMeans(scores.batch[,metadata$CR=='0']))

set.seed(42)
DF = data.frame(lfc, p, labels= rownames(scores.batch))
EnhancedVolcano(toptable = DF, lab=DF$labels,x='lfc',y='p',pCutoff = 0.5,
                FCcutoff = 0.25, ylim = c(0,5), xlim = c(-1,2), drawConnectors = TRUE)

And this is the plot I got - focus on the blue dots in the middle:


If you have enough cases, almost any difference (however small) can end up "statistically significant." That's why volcano plots are helpful: they display both the statistical (p-value) and the practical (e.g., fold-change) differences at once.
Remember that your Wilcoxon-Mann-Whitney significance test and the fold change measure different things. The Wilcoxon test

is a nonparametric test of the null hypothesis that, for randomly selected values X and Y from two populations, the probability of X being greater than Y is equal to the probability of Y being greater than X.

If the null hypothesis fails "significantly," it doesn't say anything about how much the values of Y differ in magnitude from those of X.
For practical significance, you specified a cutoff of 0.25 for the log2 fold-change in your plot. That's only about a 19% change in fold change (2^0.25). Think about whether that really is of practical significance in your field.
One more thought: you took mean values on the original scale for each group, then took the log of the ratio of their means to get the log-fold-change. Sometimes it makes more sense to calculate the means for each group in the log scale, and then take the difference in mean-log values between the groups to get the log-fold-change. That depends on the nature of your data. That alternate approach makes sense if the original data tend to have errors proportional to their values rather than constant-magnitude errors.
