Interpreting and Using Statistics in Psychological Research. Andrew N. Christopher

(2008) research, how was the variable of “status of the other participant” operationally defined?A: It was operationalized with the answers to the six questions that appear in Table 2.1.

      4 What is the difference between the reliability and the validity of a measurement?A: Reliability refers to consistency of the measurement, whereas validity refers to the appropriateness of the measurement.

      5 Explain why a measurement can be reliable but not valid.A: We can consistently measure a variable (e.g., an adult person’s height) that is irrelevant to a given situation (e.g., parenting ability). An adult’s height won’t change much, if at all, so it is reliable. But I doubt physical height has anything to do with one’s effectiveness as a parent, so it is not valid.

      6 Explain why a measurement cannot be valid if it is not also reliable.A: If a measurement is not providing consistent (reliable) scores, then we have no way of knowing what it is measuring (if it is valid). For instance, if we have a measure that is supposed to assess academic ability, but people don’t score reliably on it, then we cannot conclude it measures academic ability or anything else.

      Scales of Measurement: How We Measure Variables

      Even before you started this course, you probably knew you would be dealing with numbers. In this section, we will discuss different ways that we quantify variables. The previous section already gave you some insight into the process. Here, we will make explicit the types of data we can collect when we operationally define a variable.

      When we talk about scales of measurement, we are simply talking about assigning numbers to events or objects using rules. The rules you use to assign numbers determines the kinds of statistical tools you can use to understand the data. In this section, we distinguish four types of measurement scales according to the rules by which numbers are assigned to objects or events. In the Learning Check following this section, we will identify the scales of measurement that Terrell and her colleagues (2008) used to measure the variables in their research.

      Photo 2.1 One reason why scales of measurement are critical!

      Source: ©Theresa McCracken/CartoonStock

      Nominal Data

      A nominal scale is a measurement that divides people, objects, or events into categories according to their similarities or differences. It identifies which category an entity falls into. A nominal scale is the simplest kind of measurement scale because people, objects, or events of the same category are assigned the same number, and those of a different category get different numbers. For example, if we did a nationwide survey of college students, you might ask them what college or university they attend, whether they attend that school full time or part time, their political affiliation, and their class standing. These would be examples of nominal data. A student generally attends only one college or university and can be only a first-year, sophomore, junior, or senior.

      Nominal scale: categorical data.

      We can assign numbers to the different categories (which are often called “levels”) of a nominal variable. For example, for the variable of enrollment status (full time or part time), we can label students attending full time as “0” and those attending part time as “1.” Realize, though, that these numbers carry no meaning and are arbitrary. Obviously, students attending college full time are not somehow “less than” students attending part time. To take another example, I wore the number 44 on my jersey when I played football in high school. That does not mean I was twice as good a player as the person who wore number 22 on my team. In reality, jersey numbers identified positions that people played on their teams.

      Photo 2.2 Is the player on the right better than the player on the left?

      Source: ©iStockphoto.com/cstewart

      With nominal data, we can form what are called frequency distributions; calculate certain statistics, such as the mode; and perform what is called a chi-squared test to help us make sense of this type of data. Chapters 3, 4, and 15 will help us use nominal data.

      Ordinal Data

      An ordinal scale is a measurement that identifies people, objects, or events in categories, and the categories are ranked in order of their magnitude (e.g., from best to worst). For instance, here are five different vegetables: broccoli, asparagus, green beans, carrots, and red peppers.

      You ask me to put them in the order of my preference, with “5” for my most preferred and “1” for my least preferred. Here is my order of preference:

       5 = red peppers

       4 = asparagus

       3 = carrots

       2 = green beans

       1 = broccoli

      Each vegetable is identified by a number, which conveys magnitude, that is, how many vegetables are preferred to a specified other vegetable (e.g., relative to green beans, I like carrots, asparagus, and red peppers more, but I don’t like broccoli as much).

      Photo 2.3 Putting these vegetables in “order” gives you “ordinal” data.

      Source: ©iStockphoto.com/subjug; ©iStockphoto.com/GooDween123; ©iStockphoto.com/Floortje; ©iStockphoto.com/dionisvero; ©iStockphoto.com/suslik83

      Ordinal scale: ranked-ordered data.

      The rule for assigning numbers on an ordinal scale is that the position (rank order) of numbers on the scale must represent the rank order of the psychological attributes of the objects or events. Here, those psychological attributes are my liking of each vegetable. Notice that the scale does not tell us how much more I prefer red peppers to asparagus. It gives only the order of preference, not the difference in degree of preference. This is a major limitation of ordinal data. My preference for carrots over green beans may be fairly small, but my preference for green beans over broccoli may be quite large.

      With ordinal data, we can calculate certain statistics, such as the mode or median, and perform what is called the Spearman rank-order correlation and the Mann–Whitney U test to help us make sense of this type of data. We will learn how to use such tools in Chapters 3, 4, and 15.

      Interval and Ratio (Scale) Data

      An interval scale is a measurement in which the differences between numbers are meaningful. It includes the same information as do nominal and ordinal scales; however, with interval data, the differences between the numbers are of equal size. For example, you have probably at some point been asked to complete a customer satisfaction survey, such as those in Figure 2.3. For these items, we can easily assign numeric values to each response. We can give a 1 to a mark of “Highly Satisfied,” a 2 for “Satisfied,” and so on, with a 5 for “Highly Dissatisfied.”

      Interval scale: distance (interval) between each number is of the same magnitude.