The results of the gene analyses of the CD data are summarized in Table 2, which shows the number of significant genes at a number of different p-value thresholds.

The comparison of competitive methods is somewhat more complicated, due to the fact that ALIGATOR, INRICH and MAGENTA all use discretization using a p-value cutoff.

For INRICH the results are strongly dependent on the SNP p-value cutoff used, with three significant gene sets at the 0.0001 cutoff but none at the higher ones, further emphasizing the problem of choosing the correct cutoff.

This suggests that the different methods, or methods at different p-value cutoffs, are sensitive to distinctly different kinds of gene set associations.

For the mean 12 statistic, a gene p-value is then obtained by using a known approximation of the sampling distribution [20,21].

For the top 12 statistic such an approximation is not available, and therefore an adaptive permutation procedure is used to obtain an empirical gene p-value .

The empirical p-value for a gene is then computed as the proportion of permuted top 12 statistics for that gene that are higher than its observed top 12 statistic.

The gene analysis in MAGMA is based on a multiple linear principal components regression [18] model, using an F-test to compute the gene p-value .

To perform the gene-set analysis, for each gene g the gene p-value pg computed with the gene analysis is converted to a Z—value 2g 2 (ID—1(1 — pg), where (ID—‘1L is the probit function.

By definition, a p-value is the likelihood of obtaining a test statistic equal to or more extreme than the value that is observed if the null hypothesis is true—it increases cumulatively as one progresses through a set of rank ordered test statistics.

For a dataset generated from this null model, the p-values should be uniformly distributed from 0 to 1, exclusive: the highest Kendall’s 1‘ out of N tests should have a p-value of 1 / (N + 1), the second highest test statistic has a p-value of 2/ (N + 1), and the ith highest test statistic has a p-value of i/ (N + 1) [35].

ITK_CYCLE computes the Kendall T values for all the reference time series against the signal of interest and then performs a selection step for the lowest p-value (i.e., the highest 1‘), which we refer to here as the “initial” p-value .

Choosing a Benjamini-Hochberg adjusted p-value cutoff of 0.05 (i.e., 5%), the number of genes and overlap between methods can be seen in Figs.

However, for large time series the ITK_CYCLE null distribution is approximately normal, allowing for a convenient, fast p-value estimate.

However, this requires recomputing null distributions via MC sampling because the construction procedure introduces correlations between data points, resulting in p-value underestimates if not corrected.

First we identify the set of GO terms (pathways) that are significantly enriched within the given set of seed genes using Fisher’s exact test (Bonferroni corrected p-value <0.5).

(2) and consequently a lower p-value .

Similarly, between two proteins with the same number of connections to seeds k5, the one with lower k will result in lower p-value .

Finally, we calculate the exact p-value for the remaining nodes.

We use a genome-wide significance cutoff of p-value g 5 - 10—8.

We found that only between ~ 1%-5% of the communities detected by the different methods are significantly enriched ( p-value < 0.05, Fisher’s exact test) with any set of disease proteins (Fig.

To evaluate Whether a certain protein has more connections to seed proteins than expected under this null hypothesis, we calculate the connectivity p-value , i.e.

1H shows that the connectivity p-val-ues within the sets of known disease proteins are very significantly ( p-value < 10—241, Kolmogorov-Smirnov test) shifted towards smaller values when compared to the distributions expected for randomly scattered proteins.

lowest p-value ) is added to the set of seed nodes, increasing their number from so —>51 2 50+1.

the number of seed genes 5 on which the p-value in Eqs.

We identified ~ 100 cancer-type-specific significantly mutated domain instances (SMDs) in 21 cancer types (S2 Table; P-value = 10—7, Fisher’s Exact test, False Discovery Rate (FDR) <0.05).

Enrichment for Cancer Census genes was both strong and significant (~ 12-fold enrichment; P-value 2 5X 10—34, Fisher’s Exact test), and suggests the remaining 54 genes that are not already known to be cancer drivers represent good candidates.

Of the 94 genes encoding cancer type-specific SMDs, 24 were found in the Sleeping Beauty dataset (~ 3-fold enrichment; P-Value 2 7X 10—06, Fisher’s Exact test).

These 52 genes were enriched for evidence of involvement in cancer, with 16 being Cancer Census genes (enrichment factor ~ 11.9; P-value = 6.7 X1043, Fisher’s Exact test), and 15 being candidate cancer genes according to the Sleeping Beauty screen (enrichment factor ~ 4.5; P-value = 1.9 X10'6, Fisher’s Exact test).

We chose a P-value threshold (OL = 10—7) yielding a false discovery rate (FDR) of less than 0.05.

We made a heat map representation of the hierarchical clustering of SMDs in different cancers using the “heatmap.2” R package based on the —log ( P-value ) of each cancer-type-specific domain instance.

We calculated the mutational hotspots within each domain instance encoded by a single gene based on Fisher’s Exact test with a P-Value cutoff 0.01 (FDR <0.05).

If the null hypothesis of statistical independence of these two variables cannot be rejected in a chi-squared test using a p-value of p = 0.05 the seX ratio is set to zero, SR(x,t) = O. Lead/lag indicator.

The p-value for each lead and lag indicator is the probability of obtaining the observed values for I lead(d,-,x) and I lag(d,-,x) from the surrogate data.

In the enlarged sample only one out of the 123 comorbidities using the inpatient sample has a p-value greater than 0.05 (M23), all other remain significant (p<0.05).

Lead/lag behavior is identified for male and female DM1 and DMZ patients if the null hypothesis that the observed indicator values for I lead(di,x) and I lag(d,-,x) can be obtained from randomized surrogate data can be rejected with a p-value of p< 0.01.

For the age groups with the smallest p-value the relative risks RR, patient ages, and the corresponding p-values are shown for DM1 and DM2, respectively.

Comorbidity data for DMl patients, the relative risks RRI, the confidence intervals for RRI, if applicable the p-Value for the co-occurrence analysis, and the sex ratio for each diagnosis and age group.

Comorbidity data for DM2 patients, the relative risks RRZ, the confidence intervals for RRZ, if applicable the p-Value for the co-occurrence analysis, and the sex ratio for each diagnosis and age group.

Given a set of triplets (e.g., the triplets in Which RFl is MYC) and a particular logic gate g, we calculate a hyper-geometric enrichment p-Value to describe the enrichment of triplets consistent With the gate g as opposed to other gates as follows: The p-Value is equal kg is the number of triplets consistent With the gate g in the set, K is the total number of triplets consistent With the gate g, and N is the total number of triplets.

Out of these, 162 are consistent with the AND gate (with enrichment by hypergeometric test p-value <1.3*10'3), and 159 are consistent with “T 2 RH” (with enrichment by hypergeometric test p-value <7.5*10'5) making them the dominant logic gates for yeast FFL.

From these triplets, 446 match “T = RFZ” When RF2 is MYC (hy-pergeometric test p-value < 2.5*10'124), and 201 match “T = ~RF1+RF2” When RF1 is a miRNA and RF2 is MYC (hypergeometric test p-value < 4.1*10'25).

For example, in analyzing 871 AND-gate-consistent triplets, we found that deleting either of their TFs gave rise to substantial down-regulation of their target genes, i.e., the logarithm expression fold changes were significantly less than zero (t-test p-value = 0.068).

The two most enriched logic gates are “T = RF1” (133 triplets, hypergeometric test p-value < 4.3*10' 27) and “T = RF1+RF2 (OR)” (211 triplets, hypergeometric test p-value < 1.1*10'21)

The power of a statistical test generally depends on three factors: first, the sample size; second, statistical significance as measured by the threshold p-value used to assess significance; and third, the effect size, which quantifies departures from the null hypothesis.

For the LOGS metacommunity, and when the local dynamics are strictly neutral (7/ = 0 for model HL or c = 0 for model PC), the models are equivalent to the SNM, and the power is equal to the threshold p-value for statistical significance (0.05 in our study).

To calculate the p-value of our test, we compare the value of a test statistic for the test data set with values of the test statistic for data sets generated by the null model.

The p-value for the test is the fraction of neutral data sets Whose maximum likelihood is lower than the maximum likelihood for the test data set, i.e.

The neutral model is rejected if the p-value is less than the chosen threshold for statistical significance, which we take to be 0.05.

with lowest p-value ) are identified for a range of 31 to 86 ORFs per GO term, with a mean value of 62.3 ORFs per GO term.

All enrichment Widgets list a term, a count and an associated p-Value .

The p-Value is the probability that result occurs by chance, thus a lower p-Value indicates greater enrichment Without corrections.

The p-Value is calculated using the Hypergeometric distribution.

To calculate a p-Value , a Monte Carlo sampling algorithm was implemented.

The p-Value was defined as the rank of the real PEACS score in the null distribution diVided by 10,000.

The empirical p-value was then determined by ranking the PEACS score for the given perturbation relative to the PEACS scores generated by this Monte Carlo procedure.

Displayed are the PEACS scores, uncorrected p-Value, Bonferroni corrected p-Value , and significance (* = raw p<0.01; T = Bonfer-roni-corrected p<0.05) for genes with at least 3 knockdown conditions with 2-fold or higher knockdown.

Kendall's tau-b for each such pair is calculated with an accompanying Z-score from which a p-value can be calculated.

PR-PR pairs ranked by Fisher exact test p-Value calculated from 2013 HIVDB sequences.

From these quantities, a Z-score and p-Value can be computed assuming a normal distribution using Z = (PfPs)/SE.

A p-Value is computed for each mutation at all 599 positions for Which the mutation is detectable in at least 5 patients Who failed therapy.

The coefficients give the relative importance of each feature to the predictor; associated p-values indicate the confidence in those coefficient values (a large p-value indicates an unreliable estimate of the feature contribution).

Antibody feature:function and feature:feature correlations were computed over the set of 80 vaccinated subjects and assessed using Pearson correlation coefficient and p-value .

For each function and each group, the feature with the largest-magnitude feature:function correlation coefficient was identified; each such feature also had the best feature:function p-value within its group, < = 0.001.