copyright © 2014 pearson education. all rights reserved. 2.1-1 2.1 data types and levels of...
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Copyright © 2014 Pearson Education. All rights reserved. 2.1-1
2.1 Data Types and Levels of Measurement
LEARNING GOAL
Be able to identify data as qualitative or quantitative, to identify quantitative data as discrete or continuous, and to assign data a level of measurement (nominal, ordinal, interval, or ratio).
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What we will learn in the following sections….
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Data Types
Data Types
Qualitative (or categorical) data consist of values that can be placed into nonnumerical categories.
Quantitative data consist of values representing counts or measurements.
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EXAMPLE 1 Data Types
Classify each of the following sets of data as qualitative or quantitative.
a. Brand names of shoes in a consumer survey
b. Scores on a multiple-choice exam
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Discrete versus Continuous Data
Discrete versus Continuous Data
Continuous data can take on any value in a given interval.
Discrete data can take on only particular, distinct values and not other values in between.
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EXAMPLE 2 Discrete or Continuous?
For each data set, indicate whether they data are discrete or continuous.
a. Measurements of the time it takes to walk a mile
b. The number of calendar years (such as 2007, 2008, 2009)
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Levels of Measurement
The simplest level of measurement applies to variables that can be described solely by names, labels, or categories. We say that such data are at a nominal level of measurement.
When we describe data with a ranking or ordering scheme, such as star ratings of movies or restaurants, we are using an ordinal level of measurement.
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TIME OUT TO THINK
Consider a survey that asks “What’s your favorite flavor of ice cream?” We've said that ice cream flavors represent data at the nominal level of measurement. But suppose that, for convenience the researchers enter the survey data into a computer by assigning numbers the different flavors. For example, they assign 1 = vanilla, 2 = chocolate, 3 = cookies and cream, and so on. Does this change the ice cream flavor from nominal to ordinal? Why or why not?
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Levels of Measurement
The ordinal level of measurement provides a ranking system, but it does not allow us to determine precise differences between measurements.
If intervals are meaningful but ratios are not, we say that the data are at the interval level of measurement.
When both intervals and ratios are meaningful, we say that data are at the ratio level of measurement.
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Figure 2.1 summarizes the possible data types and levels of measurement.
Figure 2.1 Data types and levels of measurement.
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Levels of Measurement
The nominal level of measurement is characterized by data that consist of names, labels, or categories only. The data are qualitative and cannot be ranked or ordered.
The ordinal level of measurement applies to qualitative data that can be arranged in some order (such as low to high). It generally does not make sense to do computations with data at the ordinal level of measurement.
The interval level of measurement applies to quantitative data in which intervals are meaningful, but ratios are not. Data at this level have an arbitrary zero point.
The ratio level of measurement applies to quantitative data in which both intervals and ratios are meaningful. Data at this level have a true zero point.
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EXAMPLE 3 Levels of MeasurementIdentify the level of measurement (nominal, ordinal, interval, ratio) for each of the following sets of data.
a. Numbers on uniform that identify players on a basketball team
b. Student rankings of cafeteria food as excellent, good, fair, or poor
c. Calendar years of historic events, such as 1776, 1945, or 2001
d. Temperatures on the Celsius scale
e. Runners’ times in the Boston Marathon
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