“highly significant”

The resulting network showed a highly significant interaction among the proteins (p value < 1.0e −16 ).

In sharp contrast, the STRING analysis found a highly significant connection enrichment in the MSI-H overexpressed proteins ( Fig. 3 B ; p -Value < 10 −16 ).

The difference in the maximum likelihood (ML) values for the GTR + Γ and JC models was very large (Δln L = 14757.9) and highly significant ( P < 10 −16 ).

For a random protein set of comparable size, the expected number of edges was 8, whereas the observed network contained 44 interactions, resulting in a highly significant PPI enrichment p -value < 1.0 × 10 −16 .

The correlation between the distance of GO groups in the 0.001 cutoff co-evolution network (that is, their evolutionary distance) and their distance in the corresponding GO ontology network (that is, their functional distance) is highly significant: 0.38 for cellular component, 0.16 for biological process and 0.43 for molecular function (all three with P -values <10 -16 ; a similar trend is observed using the 0.01 cutoff network).

The overall PPI enrichment was highly significant ( p -value < 1.0e-16).

Again, the correlation between the P values of the 1000 top variants for the classical and mixed-effect Cox models was highly significant ( r = 0.97, Spearman P value < 10 −16 (Supplementary Fig. 4b )).

The highly significant protein–protein interaction network ( p < 1.0E-16) was created with 378 nodes, 810 edges, 4.29 average node degree, and 0.357 average local clustering coefficient ( Figure 13A ).

All were highly significant ( p < 10 –16 for all chromosomes after Bonferroni correction), with over 96% of the variation in the F5 position being explained by the F2 position for every chromosome tested ( Figure 2 ).

Again, this is highly significant ( P < 10 -16 , Wilcox rank test).

PPI enrichment analysis was highly significant (P < 1.0e-16; Fig 5B ), indicating that the observed interaction density was greater than expected by chance and suggesting coordinated involvement of these genes in bladder cancer–related pathways.

It further confirmed that the association of clock PRRs with flowering control genes was not random and connected with a highly significant value of p < 1 × 10 −16 .

The correlation between RNA-seq fold changes computed on the data from day 2 versus that from day 4 was highly significant (r = 0.50, P<10 −16 , Figure S2A ).

The perfect association of the haplotype was highly significant (p<10 −16 ).

To validate the biological significance of this manually compiled pathway, we applied STRING protein–protein interaction enrichment analysis, which confirmed highly significant interaction for the RORC consensus pathway (expected number of edges: 11, observed number of edges: 83, enrichment p < 10 −16 ).

The C > A mutations observed were associated with highly significant sequence-selectivity, being marked by an excess at CpCpT (NGCII082, odds ratio (OR) = 3.2, P -value < 10 -16 , χ 2 test) or TpCpA sites (NGCII092, OR = 1.7, P -value < 10 -16 , χ 2 test) and extensions of these motifs (Materials and methods; Note 6 and Figure S6 in Additional file 1 and Table S14 in Additional file 6 ).

However, larger differences were observed between organs that were highly significant ( P < 10 −16 for all four targets).

In other words, organisms sampled from a defined skin habitat were more similar to each other in 16S sequence than expected for a global background; this enrichment was statistically highly significant (p<<10 −16 , one-sided Mann-Whitney-U test, see Table S1 ).

There is a highly significant correlation between F ST and A ancestry difference between the lowland and highland samples (Spearman's ρ = 0.26, P < 10 −16 ).

We found a strong and highly significant correlation between CpG O/E estimates in ortholog genes in S. mimosarum and S. dumicola (Pearson’s rho = 0.78 (0.77–0.79), p < 10 −16 ) ( Figure S9 ).

As reported in the Results section, the resulting network showed a highly significant protein–protein interaction enrichment ( p -value = 1 × 10−16), indicating that the observed interactions are far more frequent than expected for a random set of proteins of comparable size.

These results show that all four topological measures provide highly significant ( p -value < 1e-16) enrichment in pathogen targets, with betweenness and clustering coefficient displaying highest enrichment, thereby demonstrating the added value of incorporating PPI data into inferred networks for a generalizable approach to identify target regulatory nodes within networks.

One-way analysis of variance (ANOVA) using the cluster size as the factor variable found that both results are highly significant ( P < 10 −16 ).

In comparison, full-field static flashes were represented by waveforms that were 147 ± 4% and 115 ± 2% of the full-field motion responses in the two populations; this difference in the ratio between responses to stationary flashes and full-field motion was highly significant ( p < 10 −16 , Fig. 2e ).

This highly significant directionality ( P < 10 -16 ) is not expected by models of statistical positioning, but suggests instead that Isw1-dependent shifts reflect its function during elongation [ 15 ].