Levels of Measurement
The way a set of data is measured is called its level of measurement. Correct statistical procedures depend on a researcher being familiar with levels of measurement. Not every statistical operation can be used with every set of data. Data can be classified into four levels of measurement. They are (from lowest to highest level):
- Nominal scale level
- Ordinal scale level
- Interval scale level
- Ratio scale level
Nominal Scale Level
Data that is measured using a nominal scale is qualitative. Categories, colors, names, labels and favorite foods along with yes or no responses are examples of nominal level data. Nominal scale data are not ordered. Nominal scale data cannot be used in calculations.
Ordinal Scale Level
Data that is measured using an ordinal scale is similar to nominal scale data but there is a big difference. The ordinal scale data can be ordered. Like the nominal scale data, ordinal scale data cannot be used in calculations.
Interval Scale Level
Data that is measured using the interval scale is similar to ordinal level data because it has a definite ordering but there is a difference between data. The differences between interval scale data can be measured though the data does not have a starting point.
Temperature scales like Celsius (C) and Fahrenheit (F) are measured by using the interval scale. In both temperature measurements, 40° is equal to 100° minus 60°. Differences make sense. But 0 degrees does not because, in both scales, 0 is not the absolute lowest temperature. Temperatures like -10° F and -15° C exist and are colder than 0.
Interval level data can be used in calculations, but comparison cannot be done. 80° C is not four times as hot as 20° C (nor is 80° F four times as hot as 20° F). There is no meaning to the ratio of 80 to 20 (or four to one).
Ratio Scale Level
Data that is measured using the ratio scale takes care of the ratio problem and gives you the most information. Ratio scale data is like interval scale data, but it has a 0 point and ratios can be calculated. You will not have a negative value in ratio scale data.
For example, four multiple choice statistics final exam scores are 80, 68, 20 and 92 (out of a possible 100 points) (given that the exams are machine-graded.) The data can be put in order from lowest to highest: 20, 68, 80, 92. There is no negative point in the final exam scores as the lowest score is 0 point.
The differences between the data have meaning. The score 92 is more than the score 68 by 24 points. Ratios can be calculated. The smallest score is 0. So 80 is four times 20. If one student scores 80 points and another student scores 20 points, the student who scores higher is 4 times better than the student who scores lower.
“State & County QuickFacts,” U.S. Census Bureau. http://quickfacts.census.gov/qfd/download_data.html (accessed May 1, 2013).
“State & County QuickFacts: Quick, easy access to facts about people, business, and geography,” U.S. Census Bureau. http://quickfacts.census.gov/qfd/index.html (accessed May 1, 2013).
“Table 5: Direct hits by mainland United States Hurricanes (1851-2004),” National Hurricane Center, http://www.nhc.noaa.gov/gifs/table5.gif (accessed May 1, 2013).
“Levels of Measurement,” http://infinity.cos.edu/faculty/woodbury/stats/tutorial/Data_Levels.htm (accessed May 1, 2013).
Courtney Taylor, “Levels of Measurement,” about.com, http://statistics.about.com/od/HelpandTutorials/a/Levels-Of-Measurement.htm (accessed May 1, 2013).
David Lane. “Levels of Measurement,” Connexions, http://cnx.org/content/m10809/latest/ (accessed May 1, 2013).
Some calculations generate numbers that are artificially precise. It is not necessary to report a value to eight decimal places when the measures that generated that value were only accurate to the nearest tenth. Round off your final answer to one more decimal place than was present in the original data. This means that if you have data measured to the nearest tenth of a unit, report the final statistic to the nearest hundredth.
In addition to rounding your answers, you can measure your data using the following four levels of measurement.
- Nominal scale level: data that cannot be ordered nor can it be used in calculations
- Ordinal scale level: data that can be ordered; the differences cannot be measured
- Interval scale level: data with a definite ordering but no starting point; the differences can be measured, but there is no such thing as a ratio.
- Ratio scale level: data with a starting point that can be ordered; the differences have meaning and ratios can be calculated.
When organizing data, it is important to know how many times a value appears. How many statistics students study five hours or more for an exam? What percent of families on our block own two pets? Frequency, relative frequency, and cumulative relative frequency are measures that answer questions like these.