Two Way Table

[Admin]

#9733

Two-Way Tables

•    A positive result means that the test has indicated you have the disease.
•    A negative result means that the test indicated that you do not have the disease.
•    A false positive result means that you have been told you have the disease when you do not.
•    A false negative result means you have been told you do not have the disease when you actually do have it.
•    An accurate positive result means that you have been told you have the disease when you actually do have it.
•    An accurate negative result means that you have been told you do not have the disease when you really don’t have it.

It is VERY important that you read the table carefully, understanding what each cell means. A slight change in the setup can change the interpretation dramatically.

[Admin]

#14866

The two-table below shows the results of a new lie detector which is used by NSW police in conjunction with random breathe testing.

	Detector Results
	Told the Truth	Lied	Total
Accurate Result Inaccurate Result	154 96 21 12		250 33
Total	175	108	283

What percentage of people who did tell the truth were told they lied?

The people who told the truth would be those that were told they told the truth and had an accurate result = 154
Those who were told they lied and had an inaccurate result = 12
total who told the truth = 166

The percentage that were told they lied would be = $$\frac{12}{166}\times 100$$
= 7.2%

[Admin]

#14869

A test for tuberculosis was conducted on 100 people. The results are shown in the table.
a. Describe what a false positive result is.
b. How many people had a false positive result?
c. What percentage of these people had accurate result?
d. What percentage of the people who had a negative test result actually had the disease?

a. A false positive is when the test result incorrectly indicates you have the disease, when you don’t

b. A false positive would be the not accurate people without the disease: 6

c. accurate result = 92 out of 100
⁹²/₁₀₀ × 100
= 92%

d. The people who had a negative test result include the people with the disease who had a not accurate (2) and the people without the disease who had an accurate (88).
Out of these 90 people, only 2 actually had the disease: ²/₉₀ × 100 = 2.2%

[Admin]

#18886

A new test has been developed for determining whether or not people are carriers of the Gaussian virus. A two way table was used to record the results.

	Test Results
	Positive	Negative	Total
Carrier Not Carrier	74 14 16 96		88 112
Total	90	110

a. How many people were tested?

b. A person selected from the group is not a carrier of the virus. What is the probability that the test results would show this?

c. For how many of the people tested were their test results accurate?

a. total = 88 + 112
= 200

b. there are 112 people that are not carriers, out of those 96 have a negative result – ie showing they are not a carrier
P = $$\frac{96}{112}$$

= $$\frac67$$

c.  an accurate result would mean:
carrier receiving a positive result = 74
non carrier receiving a negative result = 96
accurate = 74 + 96
= 170

[Admin]

#18887

	Test Results
	Accurate	Not Accurate	Total
With Disease	130	70	200
Without Disease	250	50	300
Total	380	120	500

130 = Accurate positive: The number of people who were accurately told they do have the disease. ie, told they have it and do have it
70 = False negative: The number of people who were falsely told they do not have the disease. ie, told they do not have it and do have it
200 = The total number of people with the disease

250 = Accurate negative: The number of people who were accurately told that they do not have the disease. ie, told they do no have it and do not have it
50 = False positive: The number of people who were falsely told they have the disease. ie, told they have it and do not have it
300 = The total number of people without the disease

380 = Total number of accurate results
120 = Total number of false/inaccurate results
500 = Total number

Here is another table, set up slightly differently.

	Test Results
	Test Positive	Test Negative	Total
With Disease	130	70	200
Without Disease	250	50	300
Total	380	120	500

130 = Positive result + disease. So this would be an accurate positive. ie, told they have it and do have it
70 = Negative + disease. So this would be a false negative. ie, told they do not have it and do have it
200 = The total number of people with the disease

250 = Positive + no disease. So this would be a false positive. ie, told they have it and do not have it
50 = Negative + no disease. So this would be an accurate negative. ie, told they do no have it and do not have it
300 = The total number of people without the disease

380 = Total number of positive results
120 = Total number of negative results

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