The circadian response of each gene with an upstream LRE is conditionally independent of its light response.

The independence is achieved by conditioning on the WCC-response. Genes are classified as “not circadian” or circadian, “not light-responsive” (NL) or “light-responsive” (L), or not WCC-responsive or WCC-responsive. Observed (O) and Expected (E) counts of these genes under the hypothesis of no association between the circadian and light responses conditional on the WCC-response are reported along with the chi-squared test of no association. See Fig. 11 for counts of genes by category of response. The no response category was computed as 5702−4365 (sum of counts in the remaining 7 categories). All duplicates of wc-1, wc-2, frq, and other genes were removed from the observed counts of genes (O) with upstream LREs in Fig. 11 to be classified into 8 categories below. The probability estimate of a gene being WCC-responsive is r = (2308/5702). The probability estimates of a gene being circadian or light-responsive when it is known not be WCC-responsive are pC = (1496/3394) or pL = (1001/3394), respectively. The probability estimates of a gene being circadian or light-responsive when it is known to be WCC-responsive are qC = (926/2308) or qL = (710/2308). These probability estimates can be used to compute the expected (E) counts below.
As an example 441 = pC×pL×(1−r)×5702.
*The chi-squared statistic is X2 = 7.20 with df = 2 and critical value C = 5.99 for α = 0.05.