Editing Bayes' theorem (section)

====Sensitivity or specificity====
The importance of [[Specificity (tests)|specificity]] can be seen by showing that even if sensitivity is raised to 100% and specificity remains at 80%, the probability that someone who tests positive is a cannabis user rises only from 19% to 21%, but if the sensitivity is held at 90% and the specificity is increased to 95%, the probability rises to 49%.

{| class="wikitable" style="display:inline-table;"
! {{diagonal split header|Actual|Test}}
! style="width:5ex;"|Positive
! style="width:5ex;"|Negative
! rowspan="5" style="padding:0;"|
! Total
|-
! User
| style="text-align:right" | '''45'''
| style="text-align:right" | 5
| style="text-align:right" | 50
|-
! Non-user
| style="text-align:right" | 190
| style="text-align:right" | 760
| style="text-align:right" | 950
|-
| colspan="5" style="padding:0;"|
|-
! Total
| style="text-align:right" | '''235'''
| style="text-align:right" | 765
| style="text-align:right" | 1000
|-
| colspan="5" style="padding:0 0 1ex 0;border:none;background:transparent;"| 90% sensitive, 80% specific, PPV=45/235 &asymp; 19%
|}
{| class="wikitable" style="display:inline-table;"
! {{diagonal split header|Actual|Test}}
! style="width:5ex;"|Positive
! style="width:5ex;"|Negative
! rowspan="5" style="padding:0;"|
! Total
|-
! User
| style="text-align:right" | '''50'''
| style="text-align:right" | 0
| style="text-align:right" | 50
|-
! Non-user
| style="text-align:right" | 190
| style="text-align:right" | 760
| style="text-align:right" | 950
|-
| colspan="5" style="padding:0;"|
|-
! Total
| style="text-align:right" | '''240'''
| style="text-align:right" | 760
| style="text-align:right" | 1000
|-
| colspan="5" style="padding:0 0 1ex 0;border:none;background:transparent;"| 100% sensitive, 80% specific, PPV=50/240 &asymp; 21%
|}
{| class="wikitable" style="display:inline-table;"
! {{diagonal split header|Actual|Test}}
! style="width:5ex;"|Positive
! style="width:5ex;"|Negative
! rowspan="5" style="padding:0;"|
! Total
|-
! User
| style="text-align:right" | '''45'''
| style="text-align:right" | 5
| style="text-align:right" | 50
|-
! Non-user
| style="text-align:right" | 47
| style="text-align:right" | 903
| style="text-align:right" | 950
|-
| colspan="5" style="padding:0;"|
|-
! Total
| style="text-align:right" | '''92'''
| style="text-align:right" | 908
| style="text-align:right" | 1000
|-
| colspan="5" style="padding:0 0 1ex 0;border:none;background:transparent;"| 90% sensitive, 95% specific, PPV=45/92 &asymp; 49%
|}