“highly significant”

Unusually, ChIP-seq identified highly significant, noncanonical binding of DsdC1 FLAG ( P = 1.98 × 10 −106 ) and DsdC2 FLAG ( P = 2.5 × 10 −74 ) both within the coding sequence and directly downstream of the neuO gene, with only a very modest peak being identified within its promoter region ( Fig. 4 A ).

Using these analytic approaches, we found that each of the eight groups of sex-specific genes listed in SM- Table 3 a-3b are jointly and significantly associated with longevity in one sex ( P = 8.7 × 10 −165 ∼1.5 × 10 −37 ), but not jointly significant in the other sex ( P > 0.05), while PRS-sex interaction effects are highly significant ( P = 5.2 × 10 −106 ∼4.4 × 10 −15 ) (SM- Table 5 ).

S2 ): While only 24,303 (5.7%) of the total 427,350 pairs of enzyme-catalyzed reactions are coregulated, 175 (42.9%) of the 408 fully coupled pairs are coregulated, which is highly significant (hypergeometric test, P value = 4.2 × 10 −105 ).

Despite these differences, mRNA and protein levels displayed a highly significant positive Pearson’s correlation coefficient of 0.35 ( p = 3.6 × 10 −104 Figure 1 a).

Next, based on the z score in the latent factor mixed models (LFMMs), we detected 155 CNVs with |z| scores ≥ 10 ( Supplementary Table S11 ) that were highly significant (3.63 × 10 −6 ≥ p values ≥ 1.34 × 10 −103 ), associated with environmental parameters in 47 old sheep populations.

Among these, MTND2 had highly significant associations across HDL cholesterol, Apolipoprotein A1, LDL and Triglycerides (lowest P = 3.2 × 10 –103 ).

The 212 transcripts reduced in both Caco2 and HUG1N cells depleted of GATA6 represent a highly significant, non-random overlap ( Fig. 4A ; odds ratio 9.0, p <4 × 10 −103 by Fisher exact test) and were enriched for Gene Ontology terms related to the cell cycle, particularly M-phase ( Fig. 4B ).

For example, when considering the 100 top genes most enriched in a cell type, there was a highly significant enrichment in astrocytes (Fold Enrichment (FE) = 1.4e8, p = 4.2e-103), endothelial cells (FE = 1.2e8, p = 2.8e-86), microglia (FE = 1.2e8, p = 2e-86), neurons (FE = 4.2e7, p = 3.7e-30), and oligodendrocytes (FE = 2e8, p = 6.4e-163) across the five data sets.

We also confirmed strong and highly significant associations at the previously described loci, including chromosome 2q24.2 encoding PLA2R1 (rs17831251, OR = 2.25, Meta-analysis P = 4.7 × 10 −103 ) and 6p21.32 encoding HLA-DQA1/DRB1 genes (rs9271573, OR = 2.41, Meta-analysis P = 2.7 × 10 −154 ).

This highly significant overlap ( p -value = 4.3 × 10 − 102 by hypergeometric test, 2.4-fold-enriched) demonstrates that alteration of regulatory complex binding is strongly predictive of a change in gene expression (i.e., 70%; 359 / 510) and suggests possible mechanisms for the observed gene expression effects.

Other highly significant proteins for AD included GFAP ( β = 0.676; FDR-adjusted p = 5.02 × 10 −102 ), p-tau231 ( β = 0.700; FDR-adjusted p = 4.42 × 10 −94 ), NEFL ( β = 0.417; FDR-adjusted p = 1.52 × 10 −48 ) and p-tau181 ( β = 0.483; FDR-adjusted p = 9.25 × 10 −46 ; Supplementary Table 1 ).

Considering the pool sizes ( N = 651 and N = 240 for thapsigargin stimulation and nutrient starvation, respectively), this intersection was found highly significant ( p = 1.44×10 -101 ), thus showing that a strong common transcriptional signature exists for genes upregulated by these two stresses.

Fisher exact test confirmed that the overlap between peaks lost in the IDH mutant tumors is highly significant (p<10 −100 ).

The reduction in likelihood caused by eliminating one of the pause states was highly significant, and cannot be attributed simply to the elimination of two parameters ( p <10 -100 ; likelihood ratio test).

As expected, these region-specific inflammation gene networks (HIP_M18, TCx_M18, PCx_M18, FWM_M13) show highly significant gene overlap (hypergeometric test, p<10 −100 ), despite being generated independently.

All these variables have a statistically highly significant correlation (P~10 −100 ).

We found that the similarity among all pairs of networks was highly significant (hyper-geometric test P -value <10 −100 ), and hence we focused on the F -score as this was a more sensitive measure for comparisons.

Remarkably, of the 1733 proteins in our data set, 62% were elevated significantly in at least one mutant (62% was highly significant in comparison to the null hypothesis in which peptide ratios are randomly assigned to proteins ( p value < 1e-100)), suggesting that the Cdc48 network has a profound impact on the UPS that is greater than has been previously appreciated.

This comparison yielded a highly significant overlap ( P < 1e−100) in 2419 of 3802 DEGs, validating our adopted strategy ( supplemental Figure 1 D).

The likelihood ratio test further indicated that the genetic effect was highly significant (LRT = 1,655.76, df = 1, P < 10 −100 ) ( Kang et al., 2008 ; Yang et al., 2011 ; Visscher et al., 2008 ).

Similarly, when surveying combined protein expression and SV data across 328 cell lines 38 , 54 , 55 , we observed a highly significant overlap ( p < 1E−100 chi-square test) of events involving CRISPR knockout effect in genes with events involving SV-associated protein over-expression (Fig. 8b ), involving 2682 genes, 178 with combined breakpoint and protein over-expression involving at least 5% of cell lines examined (Supplementary Dataset 10 ).

The result was highly significant (p<1×10 -100 ), with the largest overrepresentation coming from the case where both changed.

Likelihood ratio tests indicated a highly significant genetic effect (LRT = 197.9, df = 1, P < 10 -100 ), suggesting that approximately 70% of the phenotypic variation is attributable to genetic factors.

The ANOVA statistical difference between the expression levels of the HLA loci was highly significant ( P < 1.0 × 10 −100 ).

There was highly significant overlap (at empirical p < 10 −100 , see Methods for permutation procedure) between the DERs and histone marks associated with active chromatin, including H3K36me3 (OR=13.32), H3K4me1 (OR= 3.00), H3K4me3 (OR=5.66), and H3K9ac (OR=4.82).