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Follow these directions to answer the Focus Question.

Read

Examine and study definitions and explanations for statistical terms used in data collection and data interpretation.

Research

Explore the designated web sites to find more explanations of the statistical terms, to review examples of surveys and case studies, and to examine why some methods of data collection cause biased results.

Respond

Define statistical terms, match sampling techniques with scenarios, and identify methods of data collection that may bias survey results.

You will need to print a copy of the Respond sheet to complete this lesson. After selecting Respond, click Print (upper right corner).

Statistics

Statistics is a branch of mathematics that deals with the collection, organization, analysis, and interpretation of information that is usually presented numerically.

  1. Collection: Numerical information called data is gathered from some or all of the individuals or objects that apply to the study.
  2. Organization: The numerical information is then organized into a chart, table, tally, graph, or other form that is appropriate to the needs of the study.
  3. Analysis: Numerical operations and/or organization methods are often used to determine growth/decline, majority/minority, scales, expense, safety, measures of center (mean, median, mode), or other tendencies.
  4. Interpretation: The charts or numerical operations are indicators that determine conclusions or predictions. Examples of interpretation include using the results of the SAT test to determine who will be successful in college studies or determining where the needs of the U.S. population will exist in the coming decade by conducting a census every ten years.

Population

Population is the entire group of individuals or objects under investigation for a particular study. The population could be a small group, or it could consist of thousands of individuals. For example, your teacher might need to collect data for your class of students. The entire population would be the number of students in your math class. The number of individuals in the population would be small compared to, for example, a study that has a population consisting of all the people in the world who have diabetes.

Sample

A sample is a subset of the population. The collection of data from every person who has diabetes would be impractical, overwhelming, and expensive. Therefore, researchers would try to find a group of people with diabetes who represent the entire population. That group would be called a sample of the population.

Random Sample

Ideally, every object or member of the population has an equal opportunity to be selected for the sample. In addition, the chance that the object or individual is chosen for the sample group is independent from previous choices. Thus, members of the sample are selected randomly.

Bias

Bias can result from differences between the population and the sample group and from the way in which the data is collected and analyzed. Researchers try to keep those differences to a minimum to diminish error in the analysis and interpretation of the data. Some factors that can cause biased results are listed below:

  • Information bias—The samples are not randomly chosen.
  • Measurement bias—The tools for measurement are invalid or not calibrated. For instance, a survey of questions might be worded in a manner that encourages specific answers or results.

Note: blue links direct you to external web sites. These sites and their content are not controlled by SAS.

Note: blue links direct you to external web sites. These sites and their content are not controlled by SAS.

Site 1: Statistics Glossary
  • Select the Basic Definitions.
  • Read and record the definitions of the terms listed in questions 1 and 2 of the Respond sheet.
  • Use the terms to categorize the scenarios described in questions 3-7.
Site 2: 20 Questions a Journalist Should Ask About Poll Results
  • Read the article and skim the questions and answers.
  • Use this material to answers questions about bias on the Respond sheet (questions 8-11).

Definitions of Statistical Terms

  1. Write three or four sentences to distinguish between the terms population and sample as they relate to statistical research.
  1. Return to the Main Contents page and click Sampling. For the first four terms listed below, write a brief description, drawing from the examples given for each, to help you distinguish among the different methods of sampling. Then, include a description for bias as it relates to sampling.
  1. Simple random sampling
  1. Stratified sampling
  1. Cluster sampling
  1. Quota sampling
  1. Bias

Sampling Techniques

Determine which of the sampling methods, listed in question 2, is being used in each situation.

  1. Election pollsters call people throughout the nation to determine the issues people believe are important in the coming election.
  1. For a class assignment, a student asks everyone on his school bus to complete a survey.
  1. A surveyor stands on the street corner to ask 200 adults (100 men and 100 women) what their favorite fast food chain is.
  1. An insurance company examines numerous claims (damages in dollar amounts) made from car accidents that only involve teenage drivers in order to justify higher premiums for the insurance.
  1. County commissioners divide a county into eight sectors in order to interview residents, randomly, about public services available in their neighborhoods.

Interpreting Poll Results

  1. State the major difference between scientific and unscientific polls.
  1. List three examples of "unscientific pseudo-polls."
  1. "When the interview is conducted" has an impact on the responses in a poll. Name three other "methods" that can bias the results.
  1. Explain why polls by mail, Internet, or telephone do not always provide the best means to gather data.

Homework

  1. Find a news article that reports on the results of a poll. Highlight the section of the article that indicates the sample population that was surveyed and staple the article to this Respond sheet. Write three or four sentences that reflect your insights as to whether the poll is scientific or unscientific, based on the sampling techniques used by the statisticians.
  1. Now, answer the original Focus Question: How are sampling techniques during data collection important to the analysis and interpretation of results?