8.3: Quantway Core 1.9 Workforce (Health Care) - Student Lesson

INTRODUCTION

In this collaboration, we will be making quantitative statements about data that can be displayed in two-way frequency tables. Two-way frequency tables are used to display data based on two categorical variables, where each cell shows how many observations fall in each category.

Consider the following example. Out of 170 students who took a Chemistry 201 test,

• 20 students passed it even though they didn’t complete the corresponding Test Review assignment provided by the instructor
• 80 students passed after completing the corresponding Test Review assignment provided by the instructor
• 60 students didn’t pass it, and they didn’t complete the corresponding Test Review assignment provided by the instructor
• 10 students didn’t pass it even though they completed the corresponding Test Review assignment provided by the instructor

The given dataset of 170 students can be displayed in the following two-way frequency table:

In your group, can you think of other examples of data that can be displayed in a two-way frequency table like the one above?

SPECIFIC OBJECTIVES

By the end of this collaboration, you should understand that

• a percent has different uses, including being used to express the likelihood (or probability) of a certain event.
• it is important to select the correct comparison value and reference value when calculating percentages.

By the end of this collaboration, you should be able to

• extract relevant information from a table.
• select the appropriate values to calculate probabilities.

SPECIFIC LANGUAGE AND LITERACY OBJECTIVES

By the end of this collaboration, you should be able to

• read and comprehend the problem situation about HIV testing.
• complete a Double-Entry Journal (DEJ) with contextual and quantitative information from the problem situation about HIV testing.
• demonstrate an understanding of mathematics by writing complete and correct responses to questions.
• demonstrate the ability to interpret, predict, analyze, and revise answers about HIV testing.
• use appropriate quantitative and health care vocabulary to discuss mathematics in this lesson.

PROBLEM SITUATION: HIV TESTING

Lilia is a screening counselor in an HIV testing clinic called the ScreenMe Clinic. The Human Immunodeficiency Virus (HIV) is a virus that damages the body’s ability to defend against sicknesses. There are effective treatments for people with HIV. But, there is no cure for HIV. This means that once you have HIV, you have it for life. HIV can, but doesn’t always lead to AIDS.³ 1.2 million people in the United States are infected with the HIV virus. 1 in 7 people with HIV are unaware of their infection.

If you think you may have been exposed, it is important to get tested for HIV. Knowing if you have HIV can help prevent spreading the virus. Unfortunately, HIV cannot be cured by medicine. But, there are medicines available to help prevent it from turning into AIDS.

As a screening counselor, Lilia gives HIV tests and counseling to clients about results. There are several HIV tests available. The ScreenMe Clinic uses the ELISA test. Often clinics use the ELISA test because it can be done using saliva or blood. It can provide quick results. This is important because sometimes people who get tested do not come back to get their results. About 30-39% of people who get tested for HIV do not return for the results. With the ELISA test, almost all clients receive their results because clinics provide the results during the testing visit.⁴

The problem is the ELISA test is not always accurate. Sometimes the test returns a positive result even though the person does not have HIV. Lilia has to share results with patients. This can be complicated and difficult. Here is an example: Imagine a person takes the ELISA test. He tests positive for HIV. Lilia has to tell him: “Your preliminary test result is positive. But, we do not know for sure if you are infected with HIV. We need to get the results from a confirmation test. In the meantime, you should take precautions to avoid passing the virus to other people.”⁵

An example of a confirmation test is the Western Blot test. The patient is tested using the Western Blot test to confirm that the ELISA result is correct. Results from the Western Blot test can take over two weeks to come back, but are accurate.

Patients in this situation get very upset. Often they suffer from extreme anxiety while waiting for the results from the Western Blot test. Lilia wants the clinic to consider a different type of screening test. She needs you to analyze ELISA test data. You must help Lilia determine if ScreenME should continue to use the test, or look for a new one. Data will include information about how often the ELISA test provides results that are not accurate.

You will analyze the likelihood or chance of getting accurate or inaccurate results. You will study “probability.” The probability of an event is the likelihood that the event occurs. Probabilities are often represented by percentages. For example, if a fair coin is flipped, there is a 50% chance it will land heads. This is because there are only two equally likely outcomes: heads or tails. “Heads” is one of those outcomes: 1 out of 2 = 1/2 = 0.5 = 50%.

(1) We know from the problem situation that 1 in 7 people infected with HIV in the U.S. do not know they have it. What is the probability that a person who is infected with HIV is unaware they have the virus?

(2) Lilia finds data on test results of a million people who were screened for HIV with ELISA, including the actual HIV status of those who were screened. Some of what she finds is presented in the table below. Fill in the empty cells in the table.

Table 1

Use the numbers in Table 1 to answer the questions below. You will use the numbers in the table to decide on the probability that this test gives correct and incorrect results. Report probabilities in percentages (%). Be careful about which numbers you use for the numerator and denominator in your calculations.

(3) If a person has HIV, what is the probability that their ELISA test will come back positive? Round to the nearest percent.

(4) If a person does not have HIV, what is the probability that their ELISA test will come back negative? Round to the nearest percent.

(5) Based on the above answers, would you say that ELISA is an accurate screening test?

(6) (a) Given that the ELISA test is not always accurate, it is possible that the test can fail to identify HIV in someone who carries HIV. This is called a false negative. Suppose that a person carries HIV. What is the probability that this person’s test will receive a negative test result? Round your answer to the nearest one-hundredth of a percent.

(b) If a person tests negative using ELISA, should they feel confident that they don’t have HIV?

(7) (a) Is there also the possibility of a false positive? Explain your answer.

(b) What is the probability that a person who does not carry HIV will receive a positive test result?

(8) After seeing the answer for Question 7(b), reconsider Question 6. Do you think ELISA is an accurate test? Write Lilia a short note explaining why you think ScreenMe should continue to use the ELISA test or replace it. Be sure to use your calculations. Write your note using complete sentences.

(9) At ScreenMe, if someone does get a positive result for HIV using the ELISA screening test, they are given the Western Blot Test. This test is 100 percent accurate in identifying HIV. However, the Western Blot test costs $200, whereas the ELISA test costs $75 and is more readily available to healthcare workers.

Do you think the ELISA screening test is a cost-effective way to identify HIV-positive status? Why or why not? Write your answer in two or three complete sentences.

FURTHER APPLICATIONS

Some athletes use performance-enhancing drugs (PEDs) to improve their performance in sports. Schools, sports leagues, and other sports organizations usually do not allow the use of PEDs. These groups can administer or give athletes a blood or urine test to determine whether the athletes are using drugs.

Imagine a situation in which 500 athletes have undergone a test to determine if they use PEDs. A positive (+) test result indicates or shows that the athlete is using a PED. A negative (–) test result indicates the athlete is not using these drugs. However, this test is not 100% accurate. This means that some errors may have occurred in the test results. The table below shows how often the test correctly determined if athletes used PEDs.

(10) The table is missing one row total and one column total. Discuss with your group what the missing numbers should be. Complete (a) and (b) in the table.

(11) You might want to know: “If an athlete is using PEDs, what is the probability that this test gives a positive result?” Use the completed table to work through the following questions.

(a) How many athletes are using PEDs?

(b) How many of the athletes using PEDs received a positive test result?

(c) If an athlete is using PEDs, what is the probability that this test gives a positive result?

(12) The table shows that one athlete who was using PEDs received a negative test result. This means the test incorrectly identified this single athlete. What percentage of athletes who are using PEDs incorrectly test negative?

(13) You might want to know: “If an athlete is not using PEDs, what is the probability that this test gives a negative result?” Work through (a) – (c) below to answer this question.

(a) How many athletes are not using PEDs?

(b) How many of the athletes not using PEDs received a negative test result?

(c) If an athlete is not using PEDs, what is the probability that this test gives a negative result? Discuss in your group. Round to the nearest whole percent.

(14) Think about a situation in which a school principal receives a positive result on a PED test for a student athlete. Answer these questions:

(a) What is the chance the result is a false positive?

(b) How should the principal think about this percentage? What should the principal do with this information?

STRESS REAPPRAISAL

(to be completed before the Module 1 exam, as instructed)

As you might expect, taking a math test can be a very stressful experience. Before taking the Module 1 exam, we are going to complete a short reading exercise designed to help you perform well.

In the following pages, you will be presented with scientific research. Because scientific research articles can be long, complex, and difficult to understand we had students like you summarize the research articles discussed below.

The research presented in the following materials was conducted with people with anxiety disorders to help them cope with feelings of overwhelming anxiety. More specifically, materials provide you with information about how stress can help improve performance.

While you read each summary, please try to think about how stress can help you. Then, after each one, you will be asked to write a short summary using your own words describing how the information presented can help maximize your performance on the Module 1 exam. The information you write here will be included in messages to future Quantway and Statway students designed to provide students with the confidence to thrive in testing situations.

The following summary is of Jamieson and Mendes’ 2010 study that appeared in the Journal of Experimental Psychology:

In stressful situations, people experience changes in their body. They might experience these changes as “unsettled feelings” or “butterflies in their stomach,” and conclude that they are nervous. However, the bodily changes that happen during stress can be good, not just bad. For instance, scientists have found that feelings of “butterflies” or nervousness indicate that the body is gathering resources to meet the demands of the situation. In other words, the body needs energy to perform and stress helps deliver this energy to where it is needed.

Stress can be “good” or “bad,” and the type of stress we experience depends on our perceptions and beliefs. To demonstrate how the body and mind work together, imagine you are a skier staring down a steep, icy slope with no other way off the mountain than going down this dangerous trail. Regardless of whether you like skiing, this situation would cause stress. Expert skiers may experience the stress as “excitement” if they believe they can handle the difficult trail, whereas novices are more likely to experience the stress as “fear” if the difficulty of the trail exceeds their skill level. Thus, the skier’s response (excitement vs. fear) depends on how they perceive the situation and their body’s responses.

The negative consequences of stress are the direct result of people’s beliefs that feeling anxious will make them perform poorly. However, our research from people with anxiety disorders indicates that stress does not hurt performance, but can actually help because our brain releases chemicals that help us think quickly. So, during the Module 1 exam, try and view stress as a coping tool.

In your own words please briefly describe how this information can help you perform well on the Module 1 exam:

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The following summary is of Nock et al.’s (2011) study that appeared in the Journal of Clinical Psychology:

Stress is a normal physical reaction that helps you face the challenges in your life. It is not harmful. In fact, if we did not have stress reactions we could not survive. If stress is helpful, then why do most people see it as a negative experience?

Research from patients coping with anxiety disorders indicates that negative reactions to stressful situations like taking an exam in class or going on a job interview are the result of how we think about stress (also known as “cognitive appraisals”). When the “fight or flight” system activates, our brain searches for potential sources of harm. However, in modern society there is often no physical threat. When no explanation can be found, the search turns inwards and the brain invents explanations such as, “There must be something wrong with me.” Nothing could be further from the truth.

During stressful situations remember that your body’s responses are good. Increased heart rate, sweating, and heavy breathing all help deliver oxygen where it is needed. Remember, if you find yourself experiencing stress during tests, focus on the benefits of your body’s responses.

In your own words please briefly describe how this information can help you perform well on the Module 1 exam:

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The following is an illustrative diagram that shows the biological changes that happen when we experience stress. Please take a minute to note where the changes occur and how these help us do well.

In your own words please briefly describe how this information can help you perform well on the Module 1 exam:

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Great job! You have finished the reading exercise.

Remember during the Module 1 exam, we ask that you try to remind yourself that your body’s responses to the stressful testing situation will help you to perform well.

Good luck!

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³ http://www.cdc.gov/hiv/basics/index.html

⁴ http://www.cdc.gov/hiv/testing/lab/clia/rtcounseling.html

⁵ http://www.cdc.gov/hiv/testing/lab/clia/rtcounseling.html