Recommend you look at the relationship between the common denominators of different p-values. Best wishes David Booth

The p-value is a statistical measure that indicates the evidence against the null hypothesis. In the context of analyzing gene ontology (GO) terms, the p-value is commonly calculated to assess the enrichment or over-representation of specific GO terms within a set of genes.

When you plot a barplot showing multiple GO terms, the p-value for each term is typically calculated independently based on the statistical test used (e.g., Fisher's exact test, hypergeometric test). The p-value reflects the probability of observing the observed level of enrichment (or deviation from the null hypothesis) or a more extreme result, assuming the null hypothesis is true.

The p-value calculation considers the specific GO term of interest and the background set of genes used for comparison. The background set can vary depending on the analysis and may include all genes in the genome, a subset of genes, or a customized gene list. The choice of the background set can influence the p-value calculation.

Now, regarding the impact of the number of GO terms plotted on the p-values in a barplot, it's important to understand the concept of multiple hypothesis testing. When you test multiple hypotheses simultaneously (such as multiple GO terms), the likelihood of obtaining false positive results by chance alone increases. This is known as the multiple testing problem.

To address this issue, statistical adjustments, such as the Bonferroni correction or the false discovery rate (FDR) correction, are commonly applied to control the family-wise error rate or the false discovery rate, respectively. These adjustments help reduce the probability of false positives when multiple hypotheses are tested simultaneously.

Therefore, when you plot a larger number of GO terms, and especially if you have not corrected for multiple testing, the p-values may appear lower (more significant) than they would be if you had applied a correction. This is because, without correction, you are more likely to observe small p-values by chance alone.

In summary, the p-values for each GO term in a barplot may change according to the number of GO terms plotted due to the issue of multiple hypothesis testing. Applying appropriate correction methods can help control the false positive rate and provide a more accurate assessment of the significance of each GO term.

The behavior you observed in the assignment of p-values when plotting different numbers of GO terms using the clusterProfiler package could be due to multiple testing corrections.

In gene enrichment analysis, multiple testing correction is often applied to simultaneously address the issue of conducting multiple statistical tests. When you perform enrichment analysis with cluster profile, it calculates p-values for each gene ontology (GO) term based on statistical tests (e.g., hypergeometric test). However, when you have multiple GO terms, each test increases the chance of obtaining false positives by chance alone.

To account for this multiple testing issue, the clusterProfiler package applies a correction method to adjust the p-values. It commonly uses the Benjamini-Hochberg (BH) or false discovery rate (FDR) correction, which controls the expected proportion of false positives among all rejected hypotheses.

When you plot the data, the cluster profile likely applies the multiple testing correction by default, and the adjusted p-values (also known as q-values) are used for visualization instead of the original unadjusted p-values. The correction adjusts the p-values based on the number of tests performed, which can result in different rankings and significance levels for the GO terms as the number of terms changes.

In summary, the change in p-values and their ordering when plotting different numbers of GO terms using clusterProfiler is likely due to the application of multiple testing correction, which adjusts the p-values to control the false discovery rate

David Eugene Booth, thank you for your quick reply!

Ma'Mon Abu Hammad Thank you so much for taking the time to answer my question, especially for your clarity and completeness!

I would like to add some important information to this question.

In fact, the problem I understood I was facing wasn't really a problem, but just a misinterpretation.

This was not made explicit at that time, but I did the enrichment analysis only once and with this result several plots were generated, just by changing the number of GO terms presented. Thus, the multiple hypothesis testing problem did not occur.

Considering that the enrichment result is the same, the p-value and adjusted p-value do not change, what does change is the legend gradient, considering an extremely large range of adjusted p-values (from 10^-40 to 10^-2 in the complete results set).

Therefore, in works like this, it is very common to use "transformed" adjusted p-values, for example negative logarithm (-log10) – this will transform the almost infinitely small values into numbers that are easier to work with and visualize.

Anyway, the point discussed by Ma'Mon Abu Hammad is actually valid in cases where, for example, the enrichment analysis is repeated several times with a different number of genes in the set.

Again, thanks for everyone's help!