Defining the Nature of an Attribute Being Measured

Instructor: Michael Gundlach
When we want to do a statistical study, we need to first figure out the nature of the thing we're trying to measure. We need to determine what attribute we're going to measure, and how we're going to measure that attribute. Figuring this out can be surprisingly complex.

What's for Lunch?

Imagine we're trying to figure out the most popular lunch at a local high school. How would we figure this out? If the high school isn't too large, we could talk to the whole student body. If the high school is big, though, perhaps it would only be feasible to talk to some of the students. How would we determine which students to talk to? What are we going to ask them? How are we going to determine which lunch is the most popular? These are the types of questions we need to ask when trying to develop a statistical study.

Populations and Attributes

To do a statistical study, we first need to determine what population we're going to study, and what attribute we're going to measure. A population is any group of people, animals, objects, etc. that we want to learn something about. An attribute of that population is a specific characteristic that can be measured in some way. In the example above, our population was the students at the local high school, and our attribute under investigation was favorite food.

The attributes we measure come in two main types, quantitative and categorical. Quantitative attributes are attributes we measure using numbers. For example, your height is a quantitative attribute. On the other hand, a categorical attribute is something measured without using numbers. For example, your favorite food is a categorical attribute.

Types of Studies

Once we've chosen our population and attribute, we need to figure out how we're going to collect the measurement. There are three main types of statistical studies: experiments, observational studies, and surveys.

In an experiment, we use some sort of treatment on the population and observe the result. For example, suppose we're trying to determine if wearing a red hat helps people run faster. We would split our study group into two groups, a treatment group and a control group. The treatment group receives the treatment, while the control group does not. In the red hats example, we give the treatment group red hats and the control group no hats, time them while they all run a mile, and compare their times.

An observational study is a study where an attribute of members of the population is examined but not influenced in any way. For example, if you wanted to determine how many people jaywalk across the street in front of a certain business, you could hang out at the business and count the number of jaywalkers.

A survey is a study where individuals in a population are asked questions and their responses are collected and compared. The study mentioned earlier, where we would ask high school students about their favorite lunch foods, is an example of a survey.

Sample Types

Once we've determined how we're going to study our population, we need to determine what members of the population will be studied. Any study that examines every member of a population is called a census. Since doing a census is often unfeasible, we often examine a sample, or part of the population. There are many ways a sample of a population can be selected.

One of the most common ways a population is sampled is through a voluntary response sample. In this type of sample, people in a population can choose whether or not to participate. Telephone and email surveys are both examples of studies using a voluntary response sample.

Another type of sample is a convenience sample. This sampling method selects members of the population who are the most convenient to access. For example, you could conduct the lunch survey we talked about before by talking to the first ten students you encounter after walking into the lunchroom.

A systematic sample is where members of the population are picked in some systematic way to participate in the study. For example, you could conduct your lunch survey by getting a list of all the students in the high school and talking to every tenth student on the list.

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