Understanding Biases in Sampling Methods
Statistical studies rely on samples to draw conclusions about populations, but the method of sampling can introduce biases. This text discusses convenience sampling, voluntary response sampling, random sampling, and the implications of biased sampling methods on study results. It highlights how biased sampling can lead to inaccurate conclusions and provides examples to illustrate these concepts.
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Collecting Data Lesson 3.2 Sampling: Good and Bad Statistics and Probability with Applications, 3rdEdition Starnes & Tabor Bedford Freeman Worth Publishers
Sampling: Good and Bad Learning Targets After this lesson, you should be able to: Describe how convenience sampling can lead to bias. Describe how voluntary response sampling can lead to bias. Explain how random sampling can help to avoid bias. Statistics and Probability with Applications, 3rdEdition 2 2
Sampling: Good and Bad Many statistical studies use information from a sample to make a conclusion about an entire population. To ensure that these conclusions are accurate, we must be mindful of how the sample is selected. Convenience Sample Choosing individuals from the population who are easy to reach results in a convenience sample. Caution! Convenience sampling often produces unrepresentative data. Statistics and Probability with Applications, 3rdEdition 3 3
Sampling: Good and Bad A bad study design will consistently miss the truth about the population in the same direction if it was repeated many times. Bias The design of a statistical study shows bias if it would consistently underestimate or consistently overestimate the value you want to know when the study is repeated many times. Statistics and Probability with Applications, 3rd Edition 4 4
Weighing options? Weighing options? Convenience samples Convenience samples PROBLEM: A school nurse wants to know if students at his school are overweight, on average. After school one day, he walks to the gymnasium across the hall from his office and selects the first 20 students he sees. He weighs these 20 students and uses the sample mean weight as an estimate for the mean weight of all students at the school. Explain why this sampling method is biased. Is the mean weight of the students in the sample likely greater than or less than the mean weight of all students in the school? It is likely that the students in the gymnasium after school are more active and physically fit than the rest of the students in the school. Perhaps these students compete on an athletic team or in intramural sports. This means that the sample mean weight is likely to be less than the mean weight of all students in the school. Statistics and Probability with Applications, 3rd Edition 5 5
Sampling: Good and Bad Ann Landers once asked the readers of her long-running advice column, If you had it to do over again, would you have children? She received nearly 10,000 responses, almost 70% saying NO! Can it be true that 70% of parents regret having children? Not at all. People who feel strongly about an issue, particularly people with strong negative feelings, are more likely to take the trouble to respond. Voluntary Response Sample A voluntary response sample consists of people who choose to be in the sample by responding to a general invitation. Voluntary response samples are sometimes called self-selected samples. Statistics and Probability with Applications, 3rd Edition 6 6
Should we weigh Should we weigh another option? Voluntary response samples Voluntary response samples PROBLEM: The school nurse from the previous example decides to obtain a sample of 20 students in a different way. He submits a morning announcement stating Health data needed: if you are willing to be weighed, please come down to the health room this week. Explain why this sampling method is biased. Is the mean weight of the 20 students in this sample likely to be greater than or less than the mean weight for the entire student body? another option? It is likely that only students with low body weights will volunteer the testing. Students who are overweight are unlikely to volunteer to be weighed. As a result, the mean weight for the members of the sample is likely to be less than the mean weight for the entire student body. Statistics and Probability with Applications, 3rd Edition 7 7
Sampling: Good and Bad In convenience sampling, the researcher chooses easy-to-reach members of the population. In voluntary response sampling, people decide whether to join the sample. Both sampling methods suffer from bias due to personal choice. The best way to avoid this problem is to let chance choose the sample. Random Sampling Random sampling involves using a chance process to determine which members of a population are included in the sample. Statistics and Probability with Applications, 3rd Edition 8 8
Weighing the last option? Weighing the last option? Random samples Random samples PROBLEM: Explain how the school nurse can avoid the bias identified in the previous example. Instead of recruiting volunteers to be weighed, the nurse obtains a list of all students and randomly selects 20 to be weighed. Because no personal choice is involved, this sample should be more representative of the entire student body. Statistics and Probability with Applications, 3rd Edition 9 9
LESSON APP 3.2 Still on the phone? In June 2008 Parademagazine posed the following question: Should drivers be banned from using all cell phones? Readers were encouraged to vote online at www.parade.com. The July 13, 2008, issue of Paradereported the results: 2407 (85%) said Yes and 410 (15%) said No. 1. What type of sample did the Parade survey obtain? 2. Explain why this sampling method is biased. Is 85% likely to be greater than or less than the percentage of all adults who believe that cell- phone use while driving should be banned? Why? 3. Explain how Parade magazine could avoid the bias described in Question 2. Statistics and Probability with Applications, 3rd Edition 10 10
LESSON APP 3.2 Still on the phone? 1. What type of sample did the Parade survey obtain? 2. Explain why this sampling method is biased. Is 85% likely to be greater than or less than the percentage of all adults who believe that cell- phone use while driving should be banned? Why? 3. Explain how Parade magazine could avoid the bias described in Question 2. Statistics and Probability with Applications, 3rd Edition 11 11
Sampling: Good and Bad Learning Targets After this lesson, you should be able to: Describe how convenience sampling can lead to bias. Describe how voluntary response sampling can lead to bias. Explain how random sampling can help to avoid bias. Statistics and Probability with Applications, 3rd Edition 12 12
