Weighted Network Analysis pp 249-277 | Cite as

# Association Measures and Statistical Significance Measures

## Abstract

An association measure can be used to measure the relationships between two random variables. These variables may be numeric, categorical, or binary. Statistical test statistics can often be defined for deriving association measures. For example, several statistical test statistics (Fisher Z, Student *t*-test, Hotelling) can be used to calculate a statistical significance level (*p* value) for a correlation coefficient. Multiple comparison correction (MCC) procedures are needed to protect against false positives due to multiple comparisons. The Bonferroni- and Sidak correction are very conservative MCC procedures. The *q*-value (local false discovery rate) MCC is often advantageous since it allows one to detect more significant variables. To calculate the false discovery rate (FDR), one considers the shape of the histogram of *p* values. MCC procedures can often be interpreted as transformations that increase the *p* value to account for the fact that multiple comparisons have been carried out. For example, the Bonferroni correlation multiplies each *p* value by the number of comparisons. The *q*-value transformation is sometimes improper, i.e., it decreases significant *p* values. *p* values and *q*-values can be used to screen for significant variables. The WGCNA library contains several R functions that implement standard screening criteria for finding variables (e.g., gene expression profiles) associated with a sample trait *y*. In practice, many seemingly different gene screening methods turn out to be significant. *p* values (or *q*-values) can be used to formulate a statistical criterion for choosing the (hard) threshold τ when defining an unweighted correlation network. Many methods for defining unweighted networks on the basis of pairwise linear relationships between variables turn out to be equivalent.

## Keywords

False Discovery Rate Significance Measure Correlation Network Association Measure Multiple Comparison Correction## References

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