Shiny app for getting some intuition on a Fisher's exact test. Intended for demonstrating the effects of changing marginal totals and individual cells of a 2x2 FET table.
See a working example at https://daler.shinyapps.io/lcdb_fet, or clone and upload your own to shinyapps.io.
Input controls can be used to build a table. Tables, pval, odds ratio, and figures are updated automatically.
Tables are shown both as total counts as well as in versions that show row percentages and column percentages to help with interpretation.
The mosaic plot shows the relative size of cells in table. When a table is not different from the null hypothesis, the gaps in the mosaic plot will form a cross-shape. The more divergent from a cross-shape, the higher the odds ratio.
The black line shows the expected distribution of the top-left cell of the table ("upregulated AND peak"), given the marginal values of the table (total genes assayed, total genes with a peak, total upregulated genes). Try modifying those values and watch the position of the null distribution shift.
The blue vertical line shows the current value of "upregulated AND peak". When the blue line is close to the middle of the black distribution, it is close to the expected value and therefore we get a non-significant p-value and odds ratios close to 1.