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Surveys and Sampling

Activity: The Affect of Sample Size on Sampling Error

Students will intuitively understand that increasing the sample size will produce a sample that better represents the population. This activity will help them to quantify this relationship, and prepare them to learn about the role sample size takes in determining the reliability of results in later chapters.


  1. Give a penny to each student in the class.
  2. Have each student flip the penny ten times and record the number of heads. After they are finished they can write the number on the board.
  3. Discuss the variation in the sampling errors. What was the largest error? How many students got the expected value of five heads? If the expected value was not known, how could the sampling error be determined?
  4. Combine all of the results into one total and calculate the proportion of heads for the class. How close is this to the expected value of 0.5?

Discussion and Research:

This would be a good opportunity to discuss the difference between classical and empirical probability, and how they are related in the Law of Large Numbers. In this case, the classical probability states that 50 \% of the flips of a fair coin will land heads, and the empirical data is the actual numbers of heads produced when the coin is flipped. The Law of Large Numbers states that the more times the coin is flipped the closer the empirical probability will come to the classical probability. An interesting extension is to apply this logic to gambling. What is the classical probability of winning any game in a casino? What does this say about your chances of winning?

Project: Survey a Representative Sample of the School

By putting to use what they have learned in a safe, familiar environment, students can solidify and gain insight into their new knowledge. This will be a fun project that allows students to learn about their classmates and themselves.

Objective: Use the techniques leaned from this section to collect a sample that represents your school and conduct an unbiased survey.


  1. Choose a sampling method described in this section that will produce a representative sample of your school. The sample size, n, should be approximately five percent of the population.
  2. Administer a survey to all the members of your sample.
  3. Record the data you collected in a spreadsheet. Calculate appropriate summery statistics for the data.
  4. Make a graph that provides a good visual representation of the data.

Analysis: Address the following topics in writing.

  • Describe the sampling method you used and why you chose it? What was challenging about taking the sample? How did you get the sampling frame? Why do you think this sample represents your school?
  • Describe the survey you administered. How did you avoid the different types of bias described in this section?
  • Describe the shape, center, and spread of the data set you collected. What conclusions can be made from the work that you did?

Experimental Design

Project: Conduct an Experiment

Designing and conducting an experiment will give the students practical knowledge in the field. The goal is for them to make their experiment as close as possible to a randomized clinical trial. It is essential that the treatments are randomly assigned. Repetition may not be possible.

Objective: Use the techniques leaned from this section to conduct an experiment where a treatment is randomly assigned to participants so that a cause and effect relationship can be determined.


1. Chose a cause and effect relationship that you can practically and ethically test with an experiment.

2. Randomly assign the treatment(s) to different groups of participants.

Note: Participants do not need to be randomly selected to be in the experiment, they just need to be randomly divided into treatment groups.

3. Apply the treatments. Use a placebo to make the experiment blind. Make it double blind if possible. Use blocking when needed.

4. Record the results in a spread sheet. Calculate appropriate summary statistics.

5. Make a graph that provides a good visual representation of the data.

Analysis: Address the following topics in writing.

  • Describe the possible effects of any confounding or lurking variables. How did you minimize, or eliminate these effects.
  • Did you get the results you expected? Were the differences between the treatment groups large enough to be significant?

Experimental Design

Research and Discuss: Experimental Ethics

Many fields depend on experimental data. Pharmaceutical companies use experiments when developing new drugs, as so do cosmetic companies when creating new beauty products. Psychologists are famous for conducting behavioral experiments. The subjects of these experiments are often animals, including people. There is a wide variety in the opinions on what is, or is not, ethical treatment of the subjects of these experiments, and when the knowledge gained by the experiment justifies the discomfort, trauma, or death of the participant.

Research Topics:

4. Find examples of experiments done on people that are considered unethical by the current standards of our society. Include examples from the fields of psychology and medicine, and example from different time periods in history. How did humanity benefit from these experiments?

5. Find examples of experiments done on animal, other than humans, that may be considered unethical. How did humanity benefit from these experiments?

6. Different organizations have developed guidelines for what constitutes an ethical experiment. Find examples from a variety of groups including psychologists, medical doctors, pharmaceutical companies, animal rights groups, governments, and any other relevant group.

Discussion Topics:

3. Compare and contrast the different philosophies on ethical experiments. How have these opinions evolved over time?

4. When is the cost to the individual subjects of the experiments justified by the benefit of the results to society?


Assign individuals or groups of students to different research topics. Have them present what they found in class to stimulate discussion.

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