# Collecting data and types of statistical studies

• Distinguish between observational studies, surveys and experiments.

• Explain why random selection is important in the design of observational studies and surveys.

• Explain why random assignment is important in the design of statistical experiments.

Data are usually collected in order to answer some question. Depending on the nature of the question, data collection usually involves either observing characteristics of a sample from some population or carrying out a statistical experiment. This section introduces three types of statistical studies: observational studies, surveys, and experiments.

Observational studies and surveys are designed to answer questions about a population, and usually involve generalizing from a sample to a larger population of interest. This means that it is important that the sample be selected in a way that is likely to produce data representative of the population. Remind students of their prior work with random sampling in grade 7, and if necessary, review methods for selecting a random sample and discuss why random selection is important in the design of observational studies and surveys.

Statistical experiments are usually designed to answer questions of the form “What happens if…?” or “What is the effect of …?” Provide examples of questions that could be answered by using data from a statistical experiment (such as “What is the effect of listening to music while studying on exam performance?” or “What happens to the moisture content of tortilla chips if the frying time is increased from 15 seconds to 20 seconds?”)

Provide examples of statistical experiments that compare two or more experimental conditions. In a statistical experiment, it is important to start with comparable experimental groups. Discuss how random assignment of subjects to experimental groups is one way to ensure this.

Emphasize the difference between random selection and random assignment, and focus on the purpose of random selection and of random assignment in study design.

Provide examples of each type of study and allow students to practice distinguishing between the different types of studies. You might also ask students to bring in study descriptions from the newspaper or other media sources and have them explain to the class what type of study is being described and whether it involves random selection or random assignment.

## Tasks

WHAT: This task asks students to consider different methods for selecting a sample from a small population. By looking at characteristics of the resulting samples, the importance of random selection is demonstrated.

WHY: Students often think that they can make “random selections” by just using their own judgment to make the selections. This task demonstrates the importance of using a random mechanism to do the selection if the goal is to obtain a sample that is likely to be representative of the population.

WHAT: In this task, students are given a description of a study, and asked to identify the type of study and explain why random assignment is important in its design.

WHY: This task asks students to articulate the importance of random assignment in statistical experiments.

WHAT: In this task, students are given a study question. They are asked to identify the type of study best suited to the question (assuming data collection constraints), to design survey questions, and to describe an appropriate method of sampling.

WHY: This task asks students to articulate the importance of random selection in surveys.

## External Resources

#### Description

WHAT: The introduction describes the different types of statistical studies and introduces students to the investigative process. The investigation has students critique the design of two different studies that consider handwashing behavior and think about the advantages and disadvantages of the different approaches to collecting data.

WHY: This investigation explores issues related to good study design and has students consider what type of statistical study would be appropriate for answering different kinds of questions (S-IC.B.3).

#### Description

WHAT: From the teacher’s guide: “Apple’s iTunes software has a ‘shuffle’ feature that lets you listen to your songs in random order, but that hasn’t stopped the Internet from buzzing with complaints that iTunes is anything but random—certain artists or genres tend to get grouped together, some songs never seem to get played, etc. But what, exactly, would a random playlist look like? In this lesson, students use probability to explore the idea of randomness, as well as the patterns that can emerge from random processes like shuffles. In other words, do random things actually feel random? And is true randomness a desirable characteristic in a playlist?” Although the guide specifies that students should “be able to count outcomes using combinations, permutations and the Fundamental Counting Principle,” students need not know or use this terminology.

WHY: Other activities in this section address why randomization is important. The reason to include this lesson is to help students understand what “random” means (S-IC.A.2).

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