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.

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).

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.