1. Intro to Stats and Collecting Data

Intro to Stats

1. Intro to Stats and Collecting Data

Intro to Stats

3:41 minutes

Problem 1.R.5

Textbook Question

Distinguish between sampling and nonsampling error.

Verified step by step guidance

Step 1: Define sampling error as the error that arises due to the fact that a sample, rather than the entire population, is used to make inferences. It occurs because the sample may not perfectly represent the population.

Step 2: Explain that sampling error is a natural part of the sampling process and can be reduced by increasing the sample size or using better sampling techniques.

Step 3: Define nonsampling error as all other errors that are not related to the act of sampling. These include errors such as measurement errors, data processing errors, nonresponse errors, and bias.

Step 4: Emphasize that nonsampling errors can occur even if the entire population is surveyed, and they often have a larger impact on the accuracy of results than sampling errors.

Step 5: Summarize by contrasting the two: sampling error is due to chance variation in selecting a sample, while nonsampling error is due to mistakes or biases in data collection, recording, or analysis.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Sampling Error

Sampling error refers to the variability or difference between a sample statistic and the actual population parameter caused by observing only a subset of the population. It arises naturally because samples may not perfectly represent the entire population, and it can be reduced by increasing sample size.

Nonsampling Error

Nonsampling error includes all errors not related to the act of sampling, such as data collection mistakes, measurement errors, nonresponse bias, or data processing errors. These errors can affect the accuracy of results regardless of sample size and often require careful study design and quality control to minimize.

Distinction Between Sampling and Nonsampling Errors

The key difference is that sampling error is due to chance variation in selecting a sample, while nonsampling error stems from flaws in data collection or handling. Understanding this distinction helps in identifying sources of error and improving the reliability of statistical conclusions.

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Textbook Question

[DATA] Ramp Metering [See Problem 13 in Section 11.3.] Ramp metering is a traffic engineering idea that requires cars entering a freeway to stop for a certain period of time before joining the traffic flow. The theory is that ramp metering controls the number of cars on the freeway and the number of cars accessing the freeway, resulting in a freer flow of cars, which ultimately results in higher speeds on the road. To test whether ramp metering is effective in reducing travel times, engineers in Minneapolis, Minnesota, conducted an experiment in which a section of freeway had ramp meters installed on the on-ramps. A random sample of 15 cars on the highway for a Monday at 6 P.M. with the ramp meters on and a second random sample of 15 cars on a different Monday at 6 P.M. with the meters off resulted in the following speeds (in miles per hour).

a. What is the explanatory variable in this study? What is the response variable?

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Textbook Question

Efficacy of e-Cigs Do electronic cigarettes assist in helping individuals quit smoking? Researchers found 300 current smokers to volunteer for a study in which each was randomly assigned to one of three treatment groups. Group 1 received an electronic cigarette (e-cig) in which each cartridge contained 7.2 mg of nicotine, Group 2 received an e-cig that contained 5.4 mg of nicotine, and Group 3 received an e-cig that contained no nicotine. The subjects did not know which group they were assigned. During the course of the 52-week intervention, subjects dropped out of the study. At the end of the study 65 subjects remained in Group 1, 63 in Group 2, and 55 in Group 3. After 52 weeks, it was determined via questionnaire whether the subject quit smoking entirely. Results of the study are presented in the following table.

b. Researchers wanted to know whether electronic cigarettes may be used to help individuals abstain from cigarette smoking. What is the response variable? Is it qualitative or quantitative?

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Textbook Question

c. To what population do the results of this study apply?

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Textbook Question

Putting It Together: Women, Aspirin, and Heart Attacks In a famous study by the Physicians Health Study Group from Harvard University from the late 1980s, 22,000 healthy male physicians were randomly divided into two groups; half the physicians took aspirin every other day, and the others were given a placebo. Of the physicians in the aspirin group, 104 heart attacks occurred; of the physicians in the placebo group, 189 heart attacks occurred. The results were statistically significant, which led to the advice that males should take an aspirin every other day in the interest of reducing the chance of having a heart attack. Does the same advice apply to women?

In a randomized, placebo-controlled study, 39,876 healthy women 45 years of age or older were randomly divided into two groups. The women in group 1 received 100 mg of aspirin every other day; the women in group 2 received a placebo every other day. The women were monitored for 10 years to determine if they experienced a cardiovascular event (such as heart attack or stroke). Of the 19,934 in the aspirin group, 477 experienced a heart attack. Of the 19,942 women in the placebo group, 522 experienced a heart attack. Source: Paul M. Ridker et al. “A Randomized Trial of Low-Dose Aspirin in the Primary Prevention of Cardiovascular Disease in Women.” New England Journal of Medicine 352:1293–1304.

e. How does randomization deal with the explanatory variables that were not controlled in the study?

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Textbook Question

Define each of the following. Lurking variable

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Textbook Question

Define each of the following. Confounding

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Textbook Question

"Designing an Experiment Researchers want to know ifthere is a link between hypertension (high blood pressure) andconsumption of salt. Past studies have indicated that theconsumption of fruits and vegetables offsets the negative impactof salt consumption. It is also known that there is quite a bit ofperson-to-person variability in the ability of the body to processand eliminate salt. However, no method exists for identifyingindividuals who have a higher ability to process salt. The U.S.Department of Agriculture recommends that daily intake of saltshould not exceed 2400 milligrams (mg). The researchers wantto keep the design simple, so they choose to conduct their studyusing a completely randomized design.

How many treatments would you recommend? Why?"

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Textbook Question

Divorce The following graph represents the results of a survey, in which a random sample of adult Americans was asked, “Please tell me whether you personally believe that in general divorce is morally acceptable or morally wrong.” If Gallup claimed that the results of the survey indicate that 8% of adult Americans believe that divorce is acceptable in certain situations, would you say this statement is descriptive or inferential? Why?

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