# QP_SigPvalue: Computes the p-value for a statistically significant score. In QuaternaryProd: Computes the Quaternary Dot Product Scoring Statistic for Signed and Unsigned Causal Graphs

## Description

This function computes the right sided p-value for the Quaternary Dot Product Scoring Statistic for statistically significant scores.

## Usage

 `1` ```QP_SigPvalue(score, q_p, q_m, q_z, q_r, n_p, n_m, n_z, epsilon = 1e-16, sig_level = 0.05) ```

## Arguments

 `score` The score for which the p-value will be computed. `q_p` Expected number of positive predictions. `q_m` Expected number of negative predictions. `q_z` Expected number of nil predictions. `q_r` Expected number of regulated predictions. `n_p` Number of positive predictions from experiments. `n_m` Number of negative predictions from experiments. `n_z` Number of nil predictions from experiments. `epsilon` Threshold for probabilities of matrices. Default value is 1e-16. `sig_level` Significance level of test hypothesis. Default value is 0.05.

## Details

Setting epsilon to zero will compute the probability mass function without ignoring any matrices with probabilities smaller than epsilon*D_max (D_max is the numerator associated with the matrix of highest probability for the given constraints). The default value of 1e-16 is experimentally validated to be a very reasonable threshold. Setting the threshold to higher values which are smaller than 1 will lead to understimating the probabilities of each score since more tables will be ignored. If the score is not statistically significant, then a value of -1 will be returned.

## Value

This function returns a numerical value, where the numerical value is the p-value of a score if the score is statistically significant otherwise it returns -1.

## Author(s)

Carl Tony Fakhry, Ping Chen and Kourosh Zarringhalam

## References

Carl Tony Fakhry, Parul Choudhary, Alex Gutteridge, Ben Sidders, Ping Chen, Daniel Ziemek, and Kourosh Zarringhalam. Interpreting transcriptional changes using causal graphs: new methods and their practical utility on public networks. BMC Bioinformatics, 17:318, 2016. ISSN 1471-2105. doi: 10.1186/s12859-016-1181-8.

Franceschini, A (2013). STRING v9.1: protein-protein interaction networks, with increased coverage and integration. In:'Nucleic Acids Res. 2013 Jan;41(Database issue):D808-15. doi: 10.1093/nar/gks1094. Epub 2012 Nov 29'.

`QP_Pvalue`
 ```1 2 3``` ```# Computing The p-value of score 50 # for the given table margins. pval <- QP_SigPvalue(50,50,50,50,0,50,50,50) ```