1.2 Data Basics
Types of Data
Data may come from a population or from a sample. Lowercase letters like x or y are generally used to represent data values. Most data falls into the following categories:
Qualitative or categorical data come in many forms. Hair color, blood type, ethnic group, the car a person drives, and the street a person lives on are examples of qualitative data. Categorical data can generally be described with words or letters. For instance, hair color might be black, dark brown, light brown, blonde, gray, or red. Blood type might be AB+, O-, or B+.
Quantitative data, also known as numerical data, always takes the form of numbers. Quantitative data is typically the result of counting or measuring attributes of a population (e.g., amount of money, pulse rate, weight, number of people living in your town, or the number of students taking statistics). Quantitative data may be either discrete or continuous.
All data that results from counting is called quantitative discrete data. This data takes on only certain numerical values. If you count the number of phone calls you receive each day of the week, you might get values such as zero, one, two, or three.
Data that is composed not just of counted numbers but of all possible values on an interval (the real numbers) is called quantitative continuous data. Continuous data is often the result of measurements like lengths, weights, or durations. The length of a phone call in minutes would be quantitative continuous data.
If we let X equal the number of points earned by one math student at the end of a term, then X is a numerical variable. If we let Y be a person’s party affiliation, then it would fall into categories such as Republican, Democrat, and Independent. Y is a categorical variable. We could do some math with values of X (for example, calculating the average points earned in class), but it makes no sense to do math with values of Y, as you can’t calculate an average party affiliation.
Example
At the supermarket, you purchase three cans of soup (19 ounces tomato bisque, 14.1 ounces lentil, and 19 ounces Italian wedding), two packages of nuts (walnuts and peanuts), four different kinds of vegetables (broccoli, cauliflower, spinach, and carrots), and two desserts (16 ounces pistachio ice cream and 32 ounces chocolate chip cookies).
Name datasets that are quantitative discrete, quantitative continuous, and qualitative.
Possible solutions
- The three cans of soup, two packages of nuts, four kinds of vegetables, and two desserts are quantitative discrete data because you count them.
- The weights of the soups (19 ounces, 14.1 ounces, and 19 ounces) are quantitative continuous data because you measure weights as precisely as possible.
- Types of soups, nuts, vegetables, and desserts are qualitative data because they are categorical.
Try to identify additional data sets in this example.
Your Turn!
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Levels of Measurement
The way a set of data is measured is called its level of measurement. The accuracy of statistical procedures depends 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 (from lowest to highest):
Data that is measured using a nominal scale is categorical data where the categories have no natural order. Colors, names, labels and favorite foods, as well as yes or no responses, are examples of nominal level data. For example, it’s not possible to rank people according to their favorite food; putting pizza first and sushi second does not create meaningful data. Smartphone companies are another example of nominal scale data. The data are the companies that make smartphones, but there is no agreed-upon order of these brands, even though people may have personal preferences. Nominal scale data cannot be used in calculations.
Data that is measured using an ordinal scale is similar to nominal scale data, but there is a big difference. Ordinal scale data can be ordered. An example of ordinal scale data is a list of the top five national parks in the United States. The top five parks can be ranked from one to five, but we cannot measure differences between the data. 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. But the differences between two pieces of data cannot be quantified. Like the nominal scale data, ordinal scale data cannot be used in calculations.
Data that is measured using the interval scale is similar to ordinal level data because it has a definite order. However, there is a meaningful difference between values of the data from an arbitrary starting point. Temperature scales like Celsius (C) and Fahrenheit (F) are measured using the interval scale. In both temperature measurements, differences make sense, but 40° is equal to 100° minus 60°. But 0ºF and 0ºC do not align because 0 is not the absolute lowest temperature in both scales. Temperatures like -10°F and -15°C exist and are colder than 0. Interval level data can be used in calculations, but one type of comparison cannot be made. 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).
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. For example, four multiple choice statistics final exam scores are 80, 68, 20, and 92 (out of a possible 100 points). The exams are machine graded. The data can be put in order from lowest to highest: 20, 68, 80, 92. 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. The score of 80 is four times better than the score of 20.
NOTE: You may collect data as numbers and report it categorically. For example, the quiz scores for each student are recorded throughout the term. At the end of the term, the quiz scores are reported as A, B, C, D, or F.
Your Turn!
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Variation in Data
Variation is present in any set of data. For example, 16-ounce cans of beverage may contain more or less than 16 ounces of liquid. In one study, eight 16-ounce cans were measured and produced the following amount of beverage (in ounces): 15.8, 16.1, 15.2, 14.8, 15.8, 15.9, 16.0, 15.5
Measurements of the amount of beverage in a 16-ounce can may vary because different people took the measurements or because the exact amount (16 ounces of liquid) was not put into the cans. Manufacturers regularly run tests to determine if the amount of beverage in a 16-ounce can falls within the desired range. As you take data, be aware that yours may vary somewhat from the data someone else is taking for the same purpose. This is completely natural. However, if two or more of you are taking the same data and get very different results, it is time for you and the others to re-evaluate your data-taking methods and your accuracy.
Data Analysis
- Identify the research objective.
- What questions are to be answered?
- What group should be studied?
- Have attempts been made to answer it before?
- Collect the information needed.
- Is data already available?
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Can you access the entire population?
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How can you collect a good sample?
- Organize and summarize the information.
- What visual descriptive techniques are appropriate?
- What numerical descriptive techniques are appropriate?
- What aspects of the data stick out?
- Draw conclusions from the information.
- What inferential techniques are appropriate?
- What conclusions can be drawn?
We will answer all of these questions and more throughout the course.
Additional Resources
If you are using an offline version of this text, access the resources for this section via the QR code, or by visiting https://doi.org/10.7294/26207456.
Figure References
Figure 1.2: Mateusz Delegacz (2017). London Jaguar 2. Unsplash license. https://unsplash.com/photos/1Ah8CAwk3vM
Figure Descriptions
Figure 1.2: A red Jaguar car sits on the street in front of a building.
Actual values (numbers or words) that are collected from the variables of interest
The whole group of individuals who can be studied to answer a research question
A subset of the population studied
Data that describes qualities or puts individuals into categories; also known as categorical data
Numerical data with a mathematical context
A random variable that takes on a countable amount of values
Data produced by a variable that takes on an uncountable, infinite number of values
Categorical data where the the categories have no natural, intuitive, or obvious order
Categorical data where the the categories have a natural or intuitive order
Quantitative data where the difference or gap between values is meaningful
Quantitative data where the difference or gap between values is meaningful AND has a true 0 value
The level of variability or dispersion of a dataset; also commonly known as variation/variability
Process of collecting, organizing, and analyzing data