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(solution) Biometry questions (cheap test, SFI positive, SFI negative)

Biometry questions (cheap test, SFI positive, SFI negative) 

Testing for the presence or absence of a specific disease, medical condition, or illegal


drug is common. The results of these tests are never as simple as they appear to be on


many TV shows and movies. As patients become more and more critical consumers of


medical information from their doctors, they must be aware of the quantitative and


statistical reasoning that lurks behind the reported facts and figures. For example, if a


medical test is reported as ?95% accurate? and you get a ?positive? result, what is the


chance that you actually have that medical condition?


In this lab, you will explore the results of medical tests. The story that we use is for a


made-up disease, but the statistics involved are what medical professionals use to


evaluate such tests.


Here are some definitions that you will need:


False positive (FP): when a patient receives an incorrect positive test result for a


disease BUT the patient does not have the disease.


False negative (FN): when a patient receives an incorrect negative test result for a


disease BUT the patient does have the disease.


True positive (TP): when a patient receives a correct positive result (does have the




True negative (TN): when a patient receives a correct negative test result (does not


have the disease).


Sensitivity: the probability that a test correctly produces a positive test result when the


patient does have the disease.


Specificity: the probability that a test correctly produces a negative test result when the


patient does not have the disease. A new, faster, cheaper test (we?ll call it CHEAP) has been developed to diagnose a fairly


common disease called SpringFeverItis (we?ll call it SFI). The SFI virus causes people to


daydream, miss work and school, wear skin-bearing clothing, and spend excessive


amount of time in the sun. The manufacturers of this CHEAP test claim that it is 95%


effective in detecting when a person has the SFI virus. This new test will be compared to


the ?gold standard? test (which we will consider to be perfectly accurate), a timeconsuming and expensive test for SFI. When a patient is said to be SFI-positive, we


mean that the time-consuming and expensive test has determined a patient to be SFIpositive. 1 Assume a simple random sample of 100 people is selected to be tested. Using the timeconsuming and expensive test, it is determined that 32 of them have SFI, but the CHEAP


test only found 30 of these. Similarly, CHEAP reported a ?negative? result to only 61 of


the 68 SFI-negative people.


1. (2 points) The two-way table below has the appropriate counts from these 100


patients. Also fill in the appropriate initials for TP, TN, FN, and FP from the


definitions above. CHEAP test results


CHEAP test positive Actual SFI status


SFI positive


SFI negative


7 2 61 32 CHEAP test negative 30 68 2. (1 points) Enter this data into SPSS to get a table of the counts. (It should look very


much like the table above.) 3. (1 point) Have SPSS produce a table with the joint and marginal percentages. 4. (2 points) What is the percentage of all patients who received a CHEAP positive test


result? Is this a joint, marginal, or conditional percentage? 5. (2 points) Out of all the patients given the CHEAP test, what is the percentage of


false negatives? Is this a joint, marginal, or conditional percentage? 6. Your roommate is unsure of his SFI status and gets the CHEAP test. His parents are


devastated to hear that he has a positive test result. Knowing some statistics, you


want to present him with a good reason why they should not be so upset yet. For


patients who receive a positive CHEAP test result, what is the probability that they


actually are SFI-positive? Is this a joint, marginal, or conditional percentage? Also


write a note to your roommate explaining why your calculation should reassure him, 2 and tell him what he should do now. Use at least one of the terms defined in the


definitions box on page 1. 7. (2 points) What is the sensitivity rate? Is this a joint, marginal, or conditional


percentage? 8. (4 points) Is there an association between the CHEAP test results and actual SFI


status? (For a really poor test, the answer would be ?no.? Think about it.) State your


hypotheses, use SPSS to perform a chi-squared test, and give your test statistic and Pvalue. (Use an =0.01.) State your conclusion in terms of the problem. 9. (2 points) Is it appropriate to do a chi-squared test here? Why or why not? 3


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Jan 30, 2021





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