Measurement basics

Statistics deals with data, and the data may or may not be numbers. For example, planning the production of data through a sample or an experiment does not, by itself, produce numbers. Once we have our sample respondents or our experimental subjects, we must still measure whatever characteristics interest us. First, think broadly: Are we trying to measure the right things? Are we overlooking some outcomes that are important, even though they may be hard to measure?

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EXAMPLE 1 But what about the patients?

Clinical trials tend to measure things that are easy to measure: blood pressure, tumor size, virus concentration in the blood. They often don’t directly measure what matters most to patients—does the treatment really improve their lives? One study found that only 5% of trials published between 1980 and 1997 measured the effect of treatments on patients’ emotional well-being or their ability to function in social settings.

Once we have decided what properties we want to measure, we can think about how to do the measurements.

Measurement

We measure a property of a person or thing when we assign a value to represent the property.

We often use an instrument to make a measurement. We may have a choice of the units we use to record the measurements.

The result of measurement is a numerical variable that takes different values for people or things that differ in whatever we are measuring.

image What are your units? Not paying attention to units of measurement can get you into trouble. In 1999, the Mars Climate Orbiter burned up in the Martian atmosphere. It was supposed to be 93 miles (150 kilometers) above the planet but was, in fact, only 35 miles (57 kilometers) up. It seems that Lockheed Martin, which built the Orbiter, specified important measurements in English units (pounds, miles). The National Aeronautics and Space Administration team, who flew the spacecraft, thought the numbers were in metric system units (kilograms, kilometers). There went $125 million.

EXAMPLE 2 Length, college readiness, highway safety

To measure the length of a bed, you can use a tape measure as the instrument. You can choose either inches or centimeters as the unit of measurement. If you choose centimeters, your variable is the length of the bed in centimeters.

To measure a student’s readiness for college, you might ask the student to take the SAT Reasoning exam. The exam is the instrument. The variable is the student’s score in points, somewhere between 400 and 1600 if you combine the Evidence-Based Reading and Writing and Mathematics sections of the SAT. “Points” are the units of measurement, but these are determined by a complicated scoring system described at the SAT website (www.collegeboard.com).

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How can you measure the safety of traveling on the highway? You might decide to use the number of people who die in motor vehicle accidents in a year as a variable to measure highway safety. The government’s Fatality Analysis Reporting System collects data on all fatal traffic crashes. The unit of measurement is the number of people who died, and the Fatality Analysis Reporting System serves as our measuring instrument.

Here are some questions you should ask about the variables in any statistical study:

  1. 1. Exactly how is the variable defined?

  2. 2. Is the variable an accurate way to describe the property it claims to measure?

  3. 3. How dependable are the measurements?

We don’t often design our own measuring devices—we use the results of the SAT or the Fatality Analysis Reporting System, for example—so we won’t go deeply into that aspect of measurement. Any consumer of numbers, however, should know a bit about how they are produced.