ABCDEFGHIJKLMNOPQRSTUVWXYZ
1
2x2 Contigency tables for medical screening test given sensitivity, specificity, prevalence, and population
2
January 2011
3
Major edit: July 2014
4
Major edit and uploaded to Google Docs: March 2016
5
6
7
8
Click on the sheet below labeled "Reference" for definitions, formulas, explanations, etc.
9
10
base rate0.01prevalence of the disease/condtion in the population
11
sensitivity0.95probability of test coming out positive given patient has the disease/condition
12
specificity0.82probability of test coming out negative given patient does not have the disease/conditionpopulation10,000
13
14
15
2X2 CONTINGENCY TABLE SHOWING RATES / PROBABILITIES
2X2 CONTINGENCY TABLE SHOWING FREQUENCIES
16
17
Person has conditionTotalsConditional ProbabilitiesPerson has conditionTotalsConditional Probabilities
18
yesnoTest results correctTest results incorrectYesNoTest results correctTest results incorrect
19
Test positive0.00950.17820.18775.06%positive predictive value94.94%false discovery rateTest positive951,7821,8775.06%positive predictive value94.94%false discovery rate
20
Test negative0.00050.81180.812399.94%negative predictive value0.06%false omission rateTest negative58,1188,12399.94%negative predictive value0.06%false omission rate
21
Totals0.010.991Totals1009,90010,000
22
sensitivity or true positive ratefalse positive rate or alpha or type 1 errorsensitivity or true positive ratefalse positive rate or alpha or type 1 error
23
95.00%18.00%95.00%18.00%
24
false negative rate or beta or type 2 errorspecificity or true negative ratefalse negative rate or beta or type 2 errorspecificity or true negative rate
25
5.00%82.00%5.00%82.00%
26
Conditional ProbabilitiesConditional Probabilities
27
28
29
30
Person has conditionTotalsConditional ProbabilitiesPerson has conditionTotalsConditional Probabilities
31
YesNoTest results correctTest results incorrectYesNoTest results correctTest results incorrect
32
Test positiveABA + BA / (A+B)P(has condition | positive)B / (A+B)P(no condition | positive)Test positivetrue positive (TP)false positive (FP)total positive resultsA / (A+B)P(has condition | positive)B / (A+B)P(no condition | positive)
33
Test negativeCDC + DD / (C+D)P(no condition | negative)C / (C+D)P(has condition | negative)Test negativefalse negative (FN)true negative (TN)total negative resultsD / (C+D)P(no condition | negative)C / (C+D)P(has condition | negative)
34
TotalsA+CB+DA+B+C+D = 1Totalspeople with conditionpeople without conditionpopulation
35
P(positive | has condition)P(positive | no condition)P(positive | has condition)P(positive | no condition)
36
A / (A+C)B / (B+D)TP / (TP + FN)FP / (FP + TN)
37
P(negative | has condition)P(negative | no condition)P(negative | has condition)P(negative | no condition)
38
C / (A+C)D / (B+D)FN / (TP + FN)TN / (FP + TN)
39
Conditional ProbabilitiesConditional Probabilities
40
41
42
Click on the sheet below labeled "Reference" for definitions, formulas, explanations, etc.
43
44
45
46
Steps in (manually) filling the contigency tables given sensitivity, specificity and base rate (prevalence):
47
1. Fill in cell A+C with the base rate
48
2. A = base rate * sensitivity
49
3. C = base rate - A
50
4. B+D = 1 - base rate
51
5. D = (B+D) * specificity
52
6. B = (B+D) - D
53
7. With cells A, B, C, D filled, the other totals and various conditional probabilities can now be easily computed for
54
8. To obtain the frequency table, multiply each cell (except conditional probability cells) by the population.
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100