“highly significant”

The overall model was highly significant (likelihood ratio test = 256.5, p < 2.2 × 10−16).

The model describing recovery rate ( rr ) was highly significant ( X 2 = 27,605,272, df = 23, P< 2.2e -16 ), with each term of the model being significant ( S2 Table ).

We first assessed the variation in gene expression among the three biological replicate samples for each sex and tissue; the correlation values were highly significant between them all (Spearman's rank correlation coefficients of at least 0.95, p-value<2.2×10 −16 ; Figure S1 ).

As expected, we observed a highly significant difference between RefSeq mRNAs (NM) and RefSeq non-coding RNAs (NR) for both the CPC and the RNA-code score (CPC t = 56.4326 [2.239631;2.400904], p-value<2.2×10 −16 , RNAcode t = 39.6171 [34.44711;38.03595], p-value<2.2×10 16 ).

Results Descriptive statistics Samples differed in average symptom endorsement: Patients in Data Set 4 had the most severe symptomatology, followed by Data Set 1, Data Set 2, and Data Set 3 (see Table 1 ). Except for the comparison of Data Set 1 with Data Set 2, t (840.15) = 1.62, p = .11, Bayes factor = 0.26, 3 all other differences between the severity scores were highly significant ( t values between 8.51 and 29.29, degrees of freedom between 518.03 and 1417.3, all p values < 2.2 × 10 −16 , all Bayes factors > 4.7 × 10 13 ).

In fact, the least significant (i.e., highest) p -value observed in any factorial ANOVA corresponded to a main effect term (intrinsic disorder in Plants: p = 4.13 × 10 −6 ), while all other terms across all analyses were highly significant ( p < 2.2 × 10 −16 ).

These differences are highly significant (X 2 test p-value < 2.2e-16).

Wilcoxon rank sum test with continuity correction revealed highly significant changes for old versus young cortex and hippocampus circRNA TPM values ( P < 2.2 E-16) ( Fig. 2d ).

Further constraining the thresholds led to highly significant misfits for both positive and negative factors (positive factors, Δ χ 2 397.1, Δ DF 116, p < 2.2E-16; negative factors, Δ χ 2 444.5, Δ DF 52, p < 2.2E-16).

A MANOVA analysis revealed highly significant differences among genera with respect to biotemperature, precipitation, and evapotranspiration values associated with their records ( p = 2.2 × 10 −16 ; DF = 9; F = 20.617; Pillai’s Trace = 0.9114).

Based on the comparison of intact to degraded cartilage, the log-fold-changes in RNA expression and the differences in mean promoter region methylation values demonstrated a small but highly significant correlation (Pearson’s r = −0.08, p < 2.2 × 10 −16 , Fig. 2b , Supplementary Table S7 ).

This difference was highly significant ( P < 2.2 × 10 −16 ).

We observed a very weak but highly significant correlation in synonymous heterozygosity between species (Pearson’s r = 0.14, p<2.2e-16), consistent with some degree of conservation for genic parameters of mutation rates and/or selection at Drosophila synonymous sites [ 58 , 70 – 74 ].

This difference of 44,043 bp is highly significant (χ2 = 30823.1, df = 3, p-value < 2.2e-16) and corresponds to a 61 % increase of the S. latifolia chromosome size as compared to S. vulgaris .

Conservation and compensation of phosphosite loss by site-position turnover Surprisingly, despite the low level of site-conservation between paralogous proteins, there is a highly significant correlation in the number of phosphorylation sites between paralogs (ρ=0.35, P -value<2.2 × 10 −16 ; Figure 1B ).

This revealed a highly significant agreement of the number of events between paired replicates (Supplementary Fig. 2b , Pearson's correlation 0.997, n = 30, two-sided, p value < 2.2e−16), indicating that uvCLAP events capture the amount of pulled down RNA exceptionally well.

The correlation coefficients were highly significant in each case (PrEC: r = 0.80, p < 2.2e−16; LNCaP: r = 0.91, p < 2.2e−16; NPF: r = 0.84, p < 2.2e−16; CAF: r = 0.95, p < 2.2e−16), but not completely concordant with WGBS data (Additional file 5 : Figure S4A).

The overlap between EgrNAC26-OX and EgrNAC61-OX datasets was highly significant ( P < 2.2 × 10 −16 ), only one transcript was alternately up- or down-regulated across time points, and DEGs common to EgrNAC26-OX and EgrNAC61-OX datasets were all up- or down-regulated concordantly, demonstrating robust and consistent activation of a subset of shared genes.

The richness of species and genera were higher in the historic samples than in the recent samples, but proportions of endemic genera and species were lower in the historic samples ( table 2 ). Highly significant declines were documented both in the numbers of species ( p = 2.20 × 10 −16 ) and genera ( p = 1.13 × 10 −10 ) between the 1940s and the present ( table 1 ).

Out of 387 proteins associated with gestational age in human amniotic fluid, 225 (58%) were also associated with gestational age in rhesus and the correlation of effect sizes between the two species in the 225 overlapping false discovery rate (FDR) significant proteins was highly significant (R = 0.75; p < 2.2e–16; Fig. 4 ).

As expected, we observe an excess of sites with high values of -ln(PIP n ) in real data, whereas the number of sites that show a medium value of -ln(PIP n ) is higher for the simulated data; results are highly significant (Kolmogorov-Smirnov test, p < 2.2e -16 for both datasets).

As shown in Figure 4E and Figure S4B , genes that retain H3K27me3 in mutant iPSC showed indeed a highly significant stronger enrichment for this mark in control iPSC cells, both in terms of maximum height and average read density (p-value<2.2e-16, two tailed t-Test).

Highly significant differences in V1V2 length are seen between stage 3 and stages 1,2 and 4 (p<2.2×10 −16 , M-W rank sum test), reflecting V1V2 lengthening in chronic illness, followed by contraction in late disease.

The investigation into the relationship between the effect sizes of ASVs and their respective taxonomic groups revealed highly significant results (Kruskal–Wallis test, P − value < 2.2 × 10 − 16 ) for both N conditions on all three days, suggesting a disproportionate enrichment of large effect ASVs within certain taxonomic groups.

When comparing the log 2 FCs obtained for all genes and contrasts between qRT-PCR and array we found a highly significant correlation (pearson correlation of r = 0.96, p = 2.2e -16 and an R 2 = 0.92).