Density functions for a non-diseased group (a standard normal distribution) and a diseased group when the data is generated from two normal distributions as in Table 1.

<p>Density functions for a non-diseased group (a standard normal distribution) and a diseased group when the data is generated from two normal distributions as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0127272#pone.0127272.t001" target="_blank">Table 1</a>.</p

Actual family-wise error rates of the proposed exact approach and the existing asymptotic approach based on the adjusted residual at the nominal level of 0.05.

<p>Actual family-wise error rates of the proposed exact approach and the existing asymptotic approach based on the adjusted residual at the nominal level of 0.05.</p

Data from the malignant melanoma example for testing independence between tumor type and tumor site.

<p>Data from the malignant melanoma example for testing independence between tumor type and tumor site.</p

P-value calculation for each cell of data from the malignant melanoma example.

<p>The calculated p-value for each cell is compared to the multiple comparison correction method by Simes [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0188709#pone.0188709.ref018" target="_blank">18</a>]. The cells with significant p-values are bold.</p

Reorganized data for testing the independence from the <i>ij</i>-th cell.

<p>Reorganized data for testing the independence from the <i>ij</i>-th cell.</p

Awareness of zebra mussels of boaters from Lake Mead National Recreation Area, Nevada, USA.

<p>Awareness of zebra mussels of boaters from Lake Mead National Recreation Area, Nevada, USA.</p

Type I rate error plots for the asymptotic, C, M, C+M, and E+M approach with N = 30.

<p>Type I rate error plots for the asymptotic, C, M, C+M, and E+M approach with N = 30.</p

P-value calculation for each cell of data from the survey for the awareness of zebra mussels.

<p>The calculated p-value for each cell is compared to the multiple comparison correction method by Simes [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0188709#pone.0188709.ref018" target="_blank">18</a>]. The cells with significant p-values are bold.</p

For a 5 × 5 contingency table, frequency (Freq) and proportion (Prop) of simulated data having at least one cell is significant based on either <i>T</i>_<i>AdjR</i> or exact p-value, from a total of 2 million simulations.

<p>Γ_<i>Asy</i> and Γ_<i>Exact</i> are the number of cells with significant p-values by using the asymptotic approach and the exact approach, respectively.</p

Power comparison between the four exact testing procedures for N = 20, 30, 50, 80, and 100 from row 1 to row 5, respectively.

<p>Power comparison between the four exact testing procedures for N = 20, 30, 50, 80, and 100 from row 1 to row 5, respectively.</p