Ariel Elman-Walker
Home Pregnancy Tests
In a home pregnancy test (HPT), there are different probabilities of whether the test reads
positive when the woman is pregnant (sensitivity - true positive), negative when the woman is
pregnant (false negative), positive when the woman is not pregnant (false positive), and negative
when the woman is not pregnant (specificity - true negative). Each of these probabilities varies
depending on the brand of test.
For 6 brands, these are the probabilities for true and false positives and negatives:
Brand of HPT
True Positive
Reads positive
when woman is
pregnant
False Negative
Reads negative
when woman is
pregnant
True Negative
Reads negative
when woman is
not pregnant
False Positive
Reads positive
when woman is
not pregnant
Predictor
0.97
0.03
0.96
0.04
Answer
0.78
0.22
0.64
0.36
Advance
0.86
0.14
0.91
0.09
Daisy 2
0.975
0.025
0.605
0.395
e.p.t. plus
0.90
0.1
0.92
0.08
First Response
0.929
0.071
1
0
The actual probability of the test being correct or incorrect given that it reads one of these result is
based off of the probability of the woman being pregnant, which is difficult to determine and varies
based on multiple factors.
If x is used to represent the probability of a woman being pregnant, and a represents the sensitivity
(true positive), and b represents specificity, then in a tree-diagram, the probability looks like this:
The formula for conditional probability is:
So the equations for these conditions are as follows:
The test reads positive and the woman is pregnant:
Probability that the woman is pregnant given that the test reads positive:
The test reads negative and the woman is pregnant:
Probability that the woman is pregnant given that the test reads negative:
The test reads negative and the woman is not pregnant:
Probability that the woman is not pregnant given that the test reads negative:
The test reads positive and the woman is not pregnant:
Probability that the woman is not pregnant given that the test reads positive:
For each brand of HPT and each probability of a woman being pregnant, the values of a, b, and x
can be substituted the probability of each event can be found. For instance, one event which is of
particular significance is if the woman is pregnant, yet the test reads negative.
The formula for this event would be
Using the graphing system Desmos, this formula can be made visual for each type of HPT.
(Note: the formula is switched around slightly, but it is still the same)
In each of the following graphs for the different pregnancy tests, the y-axis shows the probability of
the test reading negative, while the x-axis shows the probability of a woman being pregnant given
that the test reads negative. Under each graph is the probability of the event happening if the
woman’s chance of becoming pregnant was 50%.
Predictor
If x = 0.5 :
y=
0.5(1-0.97)
.
0.5(1-0.97)+(1-0.5)0.96
=
0.015
0.0927
=
0.11
0.43
.
=
0.0162
Probability: 1.6%
Answer
If x = 0.5 :
y=
0.5(1-0.78)
.
0.5(1-0.78)+(1-0.5)0.64
Probability: 25.6%
.
=
0.256
Advance
If x = 0.5 :
y=
0.5(1-0.86)
.
0.5(1-0.86)+(1-0.5)0.91
=
0.07
0.525
.
=
0.133
Probability: 13.3%
Daisy 2
If x = 0.5 :
y=
0.5(1-0.975)
.
0.5(1-0.975)+(1-0.5)0.605
Probability: 3.97%
=
0.0125
0.315
.
= 0.0397
e.p.t. plus
If x = 0.5 :
y=
0.5(1-0.90)
.
0.5(1-0.90)+(1-0.5)0.92
=
0.05
0.51
=
0.0355
0.5355
.
=
0.098
.
0.0663
Probability: 9.8%
First Response
If x = 0.5 :
y=
0.5(1-0.929)
.
0.5(1-0.929)+(1-0.5)1
=
Probability: 6.63%
In conclusion, the higher the woman’s chance of being pregnant is, the higher the chance of a false
negative, when the test reads negative when she is actually pregnant.