The truth table in the upper-right shows the four logical possibilities for the propositions

and

being true or false together. Frequencies or counts are specified implicitly by parameter choices for each of the four logical possibilities in the columns, with a total population count initially set at 100. There are a total of 20 cases in the first two columns, where the proposition

is true (

), the remaining 80 cases being associated with

being false (

). This gives a base rate for

of 20 out of 100, or 20%, shown as a vertical line on the

axis at 0.2 in the figure. Continuing to focus on the first two columns of the table, the sensitivity of the diagnostic test,

, is set initially at 16 out of 20 or 80%. Shifting focus to the last two columns of the table, where

, the specificity of the test,

, is set initially at 56 out of 80, or 70%. From Bayes's theorem, curves showing the two inverse posterior probabilities for

being true, one based on a positive diagnostic,

, the other based on a negative diagnostic,

, are plotted in the graph for all possible base rates. Both of these curves shift as the sensitivity and specificity parameters are changed, albeit quite asymmetrically. Changes in sensitivity have a dramatic impact on the inferences to be made from negative diagnostic signals, that is, on the dashed lower curve,

, while changes in specificity have a dramatic impact on the inferences to be made from positive diagnostic signals, that is, on the solid upper curve,

. The actual inverse probabilities for the initial selection of parameters are indicated by the labeled squares on the relevant curves—a 40% chance of

with a positive diagnostic

, and a 7% chance of

with a negative diagnostic,

. The upper set of sliders can be varied to illustrate the impact of changes in the underlying parameters, while the lower set of sliders can be used to create a benchmark set of results for comparison proposes—the benchmark being illustrated in the background as curves and points of lighter shading.