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# Assignment: measurement variables

Assignment: measurement variables

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### ASSIGNMENT ON VARIABLES AND THEIR MEASUREMENT

To facilitate reading the remainder of the chapter, a brief review of variables and some of their different aspects is presented. A **variable **is any characteristic or attribute that can differ across people or things; it can take on different values. Some variables are inherent traits, such as gender or height. Others may vary due to experimenter manipulation, such as treatment groups of drug versus placebo, or due to self-selection, such as attending a two- or a four-year college. In quantitative research, variables are measured in some way and those numerical values are then used in statistical analyses. The nature of variables is important because, to some extent, it dictates the way research questions are asked and which analysis is used.

One basic distinction is that variables can be either categorical or quantitative. **Categorical variables **are those that differ across two or more distinct categories. The researcher assigns arbitrary numbers to the categories, but the numbers have no interpretable numerical meaning. For example, for categories of the variable “employment status,” we could assign the value “1” to employed full-time, “2” to employed part-time, and “3” to not employed. Additional examples of categorical variables that are individual traits are gender, ethnicity, and learning style; some that are self-selected are marital status, political party affiliation, and field of study.

**Quantitative variables **can be measured across a scale, their numeric values have meaning, and they can be subjected to arithmetic operations. The following are all examples of quantitative variables: age, height, weight, grade point average (GPA), job satisfaction, and motivation. There is an important distinction between the first three and the last three variables in this list. For such variables as age, height, and weight, zero is a meaningful value that indicates the absence of the characteristic being measured, as in something that is brand new or has no weight. The numbers have interpretable meaning. We know what five years or five feet means because there is no arbitrariness about these values or how to interpret them.

In contrast, zero is an arbitrary value for variables such as GPA, satisfaction, or motivation. A zero motivation score does not mean one has no motivation, but merely that one attained the lowest possible score for the particular instrument being used. GPA in most schools in the United States is given on a continuum from 0.0 to 4.0 but, for example, at the Massachusetts Institute of Technology (MIT), it goes from 0.0 to 5.0 (see GPA calculation and unit conversion in MIT Web page at http://web.mit.edu/registrar/gpacalc.html). The International Baccalaureate grades range from 1 to 7, based on a rubric developed from the standardized curriculum.

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For another example, consider measurements for temperature. The freezing point of water is represented as zero on a Celsius thermometer, but as 32 on a Fahrenheit thermometer. In neither case does a zero represent the absence of temperature. In each case, we understand what the numbers mean because specific interpretations have been assigned to them.

Interpretation of different grading schemes or thermometers is possible because of commonly understood unit descriptors. This is not so for such variables as job satisfaction or motivation, where scores are arbitrary and depend on the measurement instrument being used and how it has been designed. Typically, such scores are the sum or the average of responses to a set of items. The items may be statements, constructed so that all are related to the variable to be measured, and responses are often, but not always, on a Likert scale from 1 (strongly agree) to 5 (strongly disagree). The terms **scale **and **index **are often used to describe such sets of related items that, together, produce a score about some characteristic or phenomenon. For example, the Multidimensional Job Satisfaction Scale (Shouksmith, Pajo, & Jepsen, 1990) contains eleven different subscales, each a multi-item scale measure of a different dimension of job satisfaction. Another instrument, the Job Satisfaction Survey (Spector, 1985), consists of nine four-item subscales to assess employee attitudes about the job. As you can see from this example, different researchers developed different measures of the same construct, job satisfaction.

Assignment: measurement variables

Exact interpretation of a scale score’s value, or measure, for variables such as motivation or satisfaction is not important. What is important is to know that the higher the score, the more one has of the characteristic being measured and vice versa. One could, for example, examine whether males or females had higher levels of job satisfaction or if people with higher levels of job satisfaction also tended to have higher levels of motivation. To be confident of results, it is also important to know that the measures being used are reliable and have been validated.

**Reliability **relates to the consistency or dependability of a measure. Basically, if it is reliable, you can be confident that all the items that make up the measure are consistent with each other and that, if you were to use the measure again with the same individuals, they would be rated similarly to the first time. **Validity **relates to whether it is measuring what we intend it to measure, and represents the overarching quality of the measure. The purpose of using the measure is an important consideration in evaluating validity because it could be valid for one use but not for another. These concepts are complex and beyond the scope of this chapter (see Trochim, 2005 for a very understandable description of validity and reliability of measures). As a consumer of research, you should at least be aware of them and look for how research authors deal with these concepts. Do they describe their measures in detail and provide some indication of reliability and validity?

### Defining Variables

Although some variables are inherently categorical or quantitative, others may be defined in either way. Imagine, for example, that you are interested in measuring the education level of a group of individuals. You could do this categorically, by defining

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education as “highest degree earned” and using five values representing none, high school, college, masters, or doctorate as different levels of education. Or, you could do this quantitatively by defining education as “number of years of schooling,” where the resulting values would be meaningfully interpreted. This distinction is important if one is interested in studying the relationship between educational level and salary, a quantitative variable, because it relates to how the data might be analyzed and how research questions would be phrased. Using the categorical definition, you could compare the median salary value across the five categories of “highest degree earned.” The **median **represents the midpoint when all the salaries are listed from lowest to highest. One could then determine if there were any appreciable differences in salary across the five groups and whether more education (represented by having a higher degree) corresponded to higher salary.

Using the quantitative definition, you could graph the two variables in a **scatter plot **or compute a **correlation coefficient **(a measure of strength and direction of relationship for two variables) for the number of years of schooling and salary. The first would provide a visual representation of their relationship and the second a numerical one. Figure 4.1 shows how resulting data might be depicted in the two cases described. The table shows the number of people in each group and their median salary. The scatter plot shows all the data points. The correlation for this data set is 0.66. Correlation

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values range from −1 to +1, with zero indicating no relationship and 1 indicating either a negative or a positive perfect relationship depending on the sign. We could say these data showed a moderate positive relationship. Fewer years of schooling tend to correspond to lower salaries and more schooling to higher salaries.