1.2 Types of Data and Levels of Measurement

Types of Data

Data may come from a population or from a sample. Generally, small letters like [latex]x[/latex] or [latex]y[/latex] are used to represent data values. Most data can be put into one of two categories:  qualitative or quantitative.

Qualitative data are the result of categorizing or describing attributes of a population. Qualitative data are also called categorical data. Hair colour, blood type, ethnic group, the car a person drives, and the street a person lives on are examples of qualitative data. Qualitative data are generally described by words or letters. For instance, hair colour might be black, dark brown, light brown, blonde, grey, or red. Blood type might be AB+, O-, or B+.  

Quantitative data are always numbers. Quantitative data are the result of counting or measuring attributes of a population. The amount of money, pulse rate, weight, the number of people living in your town, and the number of students who take statistics are examples of quantitative data. Quantitative data may be either discrete or continuous. Researchers often prefer to use quantitative data over qualitative data because it lends itself more easily to mathematical analysis. For example, it does not make sense to find an average hair colour or blood type.

All data that are the result of counting are called quantitative discrete data. These data take on only certain numerical values. For example, the number of phone calls received in a day could be zero, one, two, or three.  

All data that are the result of measuring are quantitative continuous data, assuming that we can measure accurately. Measuring angles in radians might result in such numbers as [latex]\frac{\pi}{6},\;\frac{\pi}{3},\frac{\pi}{2},\; \pi,\;\frac{3\pi}{4}[/latex] and so on.  For example, the number of books in a backpack is discrete data, and the weight of the backpack is continuous data.  

Levels of Measurement

In addition to being classified as quantitative or qualitative, data is classified into four 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 applied to every set of data.   Qualitative data has a level of either nominal scale or ordinal scale. Quantitative data has a level of either interval scale or ratio scale.

Data that is measured using a nominal scale is data that can be placed into categories. Colours, names, labels, favourite foods, and yes/no survey responses are examples of nominal level data. Nominal scale data are not ordered, which means the categories of the data are not ordered. For example, trying to “order” people according to their favourite food does not make any sense. Putting pizza first and sushi second is not meaningful. Smartphone companies are another example of nominal scale data. Some examples are Sony, Motorola, Nokia, Samsung, and Apple. This is just a list of different brand names, and there is no agreed upon order for the categories. Some people may prefer Apple, but that is a matter of opinion. Because nominal data consists of categories, nominal scale data cannot be used in calculations.

Data that is measured using an ordinal scale is similar to nominal scale data in that the data can be placed into categories, but there is a big difference. The categories of ordinal scale data can be ordered or ranked. An example of ordinal scale data is a list of the top five national parks in the country because the parks can be ranked from one to five. Another example of using the ordinal scale is a cruise survey, where the responses to questions about the cruise are “excellent,” “good,” “satisfactory,” and “unsatisfactory.”  These responses are ordered from the most desired response to the least desired. In ordinal scale data, the differences between two pieces of data cannot be measured or calculated. Similar to nominal scale data, ordinal scale data cannot be used in calculations.

Data that is measured using an interval scale is similar to ordinal level data because it has a definite ordering. However, the differences between interval scale data can be measured or calculated, but 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 (Celsius and Fahrenheit), 40° is equal to 100° minus 60°. The differences in temperature can be measured and make sense. But there is no starting point to the temperature scales because 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 ratios do not make sense and cannot be done. For example, 80°C is not four times as hot as 20°C (nor is 80°F four times as hot as 20°F). So there is no meaning to the ratio of 80 to 20 (or four to one) in either temperature scale. In general, ratios have no meaning in interval scale data.

Data that is measured using the ratio scale takes care of the ratio problem and gives us the most information. Ratio scale data is like interval scale data, but it has a starting point to the scale (a 0 point), and ratios can be calculated. For example, four multiple choice statistics final exam scores are 80, 68, 20 and 92 (out of a possible 100 points). The data can be put in order from lowest to highest: 20, 68, 80, 92. The differences between the data have meaning:  92 minus 68 is 24. Ratios can be calculated:  80 is four times 20. The smallest possible score is 0.

Video: “Nominal, ordinal, interval and ratio data: How to Remember the differences” by NurseKillam [11:03] is licensed under the Standard YouTube License.Transcript and closed captions available on YouTube.

Exercises

1. Classify each of the following as qualitative or quantitative. For quantitative data, classify as discrete or continuous. Identify the level of measurement for each data.
   1. Number of times per week.
   2. Size of automobile (compact, midsize, large).
   3. Age.
   4. Weight of package shipped.
   5. Temperature.
   6. Satisfaction rating (good, fair, poor).
   7. Shoe size.
   8. Attendance at home games.
   9. Country of origin.
   10. Number on team uniform.
   11. Number of tickets sold to a concert.
   12. Percent of body fat.
   13. Favourite baseball team.
   14. Time in line to buy groceries.
   15. Number of students enrolled at Evergreen Valley College.
   16. Most-watched television show.
   17. Brand of toothpaste.
   18. Distance to the closest movie theatre.
   19. Number of competing computer spreadsheet software packages.
   Click to see Answer

   1. Quantitative, discrete, ratio
   2. Qualitative, nominal.
   3. Quantitative, discrete, ratio.
   4. Quantitative, discrete, ratio.
   5. Quantitative, continuous, interval.
   6. Qualitative, ordinal.
   7. Quantitative, discrete, interval.
   8. Quantitative, discrete, ratio.
   9. Qualitative, nominal.
   10. Qualitative, nominal.
   11. Quantitative, discrete, ratio.
   12. Quantitative, continuous, ratio.
   13. Qualitative, nominal.
   14. Quantitative, continuous, ratio.
   15. Quantitative, discrete, ratio.
   16. Qualitative, ordinal.
   17. Qualitative, nominal.
   18. Quantitative, continuous, ratio.
   19. Quantitative, discrete, ratio.

    

“1.3 Sampling and Data“, “1.4 Frequency, Frequency Tables, and Levels of Measurement” and “1.6 Exercises” from Introduction to Statistics by Valerie Watts is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.