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

      Figure 2.3 Example Items From a Grocery Store Customer Satisfaction Survey

      When we ask people to respond to questions such as these, which use a response range, this is an interval scale. The rule for assigning numbers on an interval scale is that equal differences between the numbers on the scale must represent equal psychological differences between the events or objects.

      Returning to our example of vegetable preferences, we could have collected such data using an interval scale. Here is how. You could have asked me how much I liked each one of the five vegetables, perhaps using an interval scale such as this one:

      If I gave red peppers a 7, asparagus a 4, and carrots a 3, it would mean my liking of red peppers is quite a bit stronger than my liking of asparagus even though asparagus is my second favorite vegetable. My liking of carrots is closer to my liking of asparagus more than my liking of asparagus is to my liking of red peppers. The interval scale gives us more details than does an ordinal scale.

      It is important to note that the interval scale does not contain a meaningful zero point. That is, a score of zero, when using an interval scale, does not indicate the absence of a variable being measured. Temperature is an example of an interval scale. A temperature of 0 degrees Fahrenheit does not mean that there is no temperature outside. Without a meaningful zero point, we cannot form ratios using interval data. So when it is 80 degrees Fahrenheit outside, we cannot say it is twice as warm as when it is 40 degrees Fahrenheit outside.

      Just as with nominal and ordinal data, there are different statistical tools we can calculate and statistical tests we can perform on interval data. We can calculate all measures of central tendency and all measures of variability (Chapter 4). We can also use t tests (Chapters 7 and 8), analyses of variance (ANOVAs; Chapters 9–11), and correlational analyses (Chapters 12 and 13). As you can see, there are a lot more statistical tools available for interval data than there are for nominal and ordinal data.

      Unlike an interval scale, a ratio scale has a meaningful zero point, as well as all of the characteristics of nominal, ordinal, and interval scales. The rule for assigning numbers on a ratio scale is that the ratios between the numbers on the scale must represent the psychological ratios between the events or objects. Examples of ratio data include many physical measures, such as time or weight. With a ratio scale and its meaningful zero point, it is possible to form ratios to make comparisons. For instance, the two minutes it takes someone to solve a statistics problem is half the time it took the person needing four minutes to solve the problem. So, we can conclude that the second person took twice as long. Someone who weighs 150 pounds is twice as heavy as someone who weighs 75 pounds.

      Ratio scale: interval data that has a meaningful zero point.

      The same sort of statistical tools can be used with ratio data as are used on interval data. That is why you might encounter a type of data called scale data. In practice, th e distinction between interval and ratio data is not nearly as important as the differences they have with nominal and ordinal data. The reason we care about scales of measurement is that some statistical techniques can only be used on interval or ratio scales. If all of your data are measured at a nominal level, then you are limited in what you can do with your data. This will be clear as we talk about how to present data in various parts of the book. Table 2.3 contains a summary of our scales of measurement.

      Scale data: refers to interval and ratio data without making a distinction between them.

Table 2.3

      Discrete Versus Continuous Variables

      In addition to classifying variables by their scale of measurement, there is another way that researchers classify variables. This second classification system is not as closely tied to statistical analyses as are the scales of measurement, but as you will observe these terms used in research, I want you to be aware of them.

      A discrete variable typically takes a whole-number value. For example, the number of children in a family is a discrete variable because only whole numbers are possible. A change in the value of a discrete value occurs one whole number at a time. If a family with three children has another child, it now has four children. No single value can occur between three and four in this example. Table 2.4 contains some examples of discrete variables in Terrell et al.’s (2008) research. We see that the variables of sex, class standing, and ethnicity are discrete variables. For each one, a respondent takes on one value or category. Most of the time, discrete variables will be measured on a nominal or an ordinal scale.

      A continuous variable is one whose measurement can take on fractional values. For example, time is a continuous variable. The passage of time may be broken into an infinite number of units. When running a 40-yard dash, one person may run it in five seconds and another person may run it in six seconds. A third person could run that distance between those two times, for instance, in 5.4 seconds. The term “continuous” means that numbers continue between the whole numbers. In Terrell et al.’s (2008) research, GPA, height, and weight are continuous variables. In addition, the three personality measures are also continuous variables. At first glance, this may seem confusing. Let’s examine the tendency to act aggressively by examining some sample items that appear at the bottom of Table 2.4. Respondents used a 1–5 response range to indicate how much each statement describes them. If we average the responses across all items on this survey, then indeed, we can obtain fractional values, which is why this is a continuous variable. Most of the time, continuous variables will be quantified by using a scale (interval or ratio) measurement.

      Table 2.4 Examples of Discrete and Continuous Variables in Terrell et al.’s (2008) Research

      Discrete variable: variable that can have only a whole number value.

      Continuous variable: variable that can have a fractional value.

      Learning Check

      Refer back to Table 2.4, which contains some of the materials from Terrell and colleagues’ (2008) research study described at the start of this chapter. Use it to answer the following questions:

      1 What, if any, are the nominal variables in this study?A: sex, class standing, ethnicity

      2 What, if any, are the ordinal variables in this study?A: none

      3 What, if any, are the scale variables in this study?A: tendency to act aggressively, grade-point average, height, weight

      4 Why is it that data collected using an interval or ratio measurement can be considered simply “scale” data?A: Both interval and ratio measurement scales can use the same statistical tools, so such a differentiation is not as important as it is for nominal and ordinal data.

      5 For each variable, identify the scale of measurement (nominal, ordinal, interval, or ratio) and whether it is discrete or continuous:A:

      The Basics of SPSS

      In any sort of statistics class, numerical information is going to be important and, really, the centerpiece