Variables & Scales of Measurements

1. Variables & Scales of Measurements Moazzam Ali Assistant Professor Department of English University of Gujrat

2. Concepts • Concepts are highly subjective as their understanding varies from person to person, and therefore, may not be measurable. In a research study it is important that the concepts used should be operationalised in measurable terms so that the extent of variation in respondents’ understanding is reduced not eliminated. • Concept is a generalized idea about a class of objects, attributes, occurrences, or processes. • Measurability is the main difference between a concept and a variable. A concept cannot be measured whereas a variable can be subjected to measurement.

3. Concept—an Abstraction of Reality • Honesty, sincerity, morale are all concepts that label to some phenomenon (reality) • They are abstractions that exist only as mental images of things we want to talk about. To do research, we have to convert concepts to things we can observe. We do this by defining concepts in terms of measurable variables. • Measurement is a process of ascertaining the extent or quantity of the concept, idea, or construct.

4. Concepts, Indicators & Variables If you are using a concept in your study, you need to consider its operataionalization, that is, how it will be measured. In most cases, to operationalise a concept you first need to go through the process of identifying indicators—a set of criteria reflected of the concept—which can then be converted into variables.

5. Variable • Anything (concept/term) that can take on differing or varying values. Variation can be in quantity, intensity, amount, or type. • Examples are: Production units, Absenteeism, Gender, Religion, Motivation, Grade, Age. • Variables represent concepts. Like concepts, variables are defined in words, but, as used in social research, variables have a special characteristic. Variables have two or more observable forms or values. • The opposite notion to a variable is a constant, which is simply a condition or quality that does not vary between cases/subjects. The number of cents in a United States dollar is a constant

6. Concepts, Indicators & VariablesExample • The concept ‘growth of a plant’ can easily be converted into indicators and then variables. To decide objectively if a plant is ‘growing’, one first needs to decide upon the indicators of ‘growth’. • Example: Effect of Light & Temperature on the Growth of Tomatoes. Variables are: • (1) growth of tomatoes measured/operationalized in terms of its indicators e.g. Numbers of leaves per plant, length of stem, number of flowers per plant & yield per plant; • (2) intensity, wavelength, frequency & color of light; • (3) type of temperature & temperature in degrees Celsius

7. Concept and Variables

8. Variables and Attributes • An attribute is a specific value on a variable. For instance, the variable sex or gender has two attributes: male and female. Attributes are what social scientists measure to describe a variable. • Attributes are the observable characteristics of variable; variables are the logical combinations of attributes. Male and female, for example, are the attributes of the variable we call gender. The numbers of persons in a household, from 1 to perhaps 20 or more, represent the attributes of the variable, household. Similarly, the variable agreement might be defined as having five attributes: 1 = strongly disagree; 2 = disagree; 3 = neutral; 4 = agree; 5 = strongly agree

9. Variables & Attributes

10. Types of Variables • Independent variable is the cause supposed to be responsible for bringing about change/s in a phenomenon or situation. Usually, the researcher cannot manipulate the independent variable • Dependent variable is the outcome of the change/s brought about by changes in an independent variable • Extraneous variables are the several others factors operating in real-life situation may affect changes attributed to independent variables. These factors, not measured in the study, may increase or decrease the magnitude or strength of the relationship between independent and dependent variables.

11. Types of Variables • Intervening variables are sometimes called the confounding variables. They link independent and dependent variable. In some situations the relationship between independent and dependent variables cannot be established without the intervention of another variable. The cause variable will have the assumed effect only in the presence of an intervening variable.

12. Independent, Dependent and Extraneous Variables in Causal Relationship

13. Scales of Measurements

14. Scales of Measurement • Measurement (or observation) is the process of determining and recording which of the possible traits of a variable an individual case/subject exhibits or possesses. • When we construct a scale of measurement we need to follow two particular rules: • First, the scale must capture sufficient variation to allow us to answer our research question(s). • Second, a scale must allow us to assign each case into one, and only one, of the points on the scale.

15. Scales of Measurement: Rule I • The scale must capture sufficient variation Age for a group of students highlights an intrinsic problem when we try to set up a scale to measure sufficient variation for a continuous variable (Age) that does not arise when we try to measure a discrete variable (Sex). • The sex of students is a discrete variable with only two possible categories (male or female) which cannot be subdivided and a scale can measure its variation sufficiently. However, the age of students, on the other hand, is a continuous variable and can be infinitely subdivided, and hence is difficult to measure in its all possible variations . • We will always have to ‘round off’ the measurement and treat a continuous variable as if it is discrete. Practically, No measurement scale can ever hope to capture the full variation expressed by a continuous variable

16. Scales of Measurement: Rule II • A scale must allow us to assign each case/subject into one, and only one, of the points on the scale. • This statement actually embodies two separate principles of measurement. • The principle of exclusiveness: No case/subject should have more than one value for the same variable. • The principle of exhaustiveness: Every case/subject can be classified into a category.

17. Levels of Measurement We generally talk about measurement scales having one of four distinct levels of measurement: • Nominal • Ordinal • Interval • Ratio

18. Nominal Scale • A nominal scale of measurement classifies cases into categories that have no quantitative ordering. It simply defines groups of the subjects. The values are given different names, hence the term nominal. • Example: Muslim, Hindu, Jewish, Christian

19. Please specify your discipline:  Arts  Humanities  Pure Sciences  Social Sciences Gender:  Male  Female Nominal Scale

20. Ordinal Scale • An ordinal scale of measurement, in addition to the function of classification, allows cases to be ordered by degree according to measurements of the variable. So, ordinal scales enable us to rank cases. However, the difference in property (low/medium & medium/high) or attribute between levels may not be the same. • Example: level of intensity –low, medium, high • Nominal and ordinal scales are sometimes collectively called categorical scales. However, an ordinal scale provides additional information.

21. Your income is: □ Below 30,000 □ 30,100 to 50,000 □ 50,100 and above Ordinal Scale

22. Interval Scale • An interval scale has units measuring intervals of equal distance between values on the scale. • Ordinal scales permit us to rank cases in terms of a variable; we can, for example, say that one case is ‘better’ or ‘stronger’ than another. But an ordinal scale does not allow us to say by how much a case is better or stronger when compared with another and the distances – intervals – between the categories are unknown. • So, we not only can say that one case has more (or less) of the variable in question than another, but we can also say how much more (or less). Thus someone who is 25 years old has 7 years more age than someone who is 18 years old; we can measure the interval between them. Moreover, the intervals between points on the scale are of equal value over its whole range.

23. Ratio Scale • A ratio scale has a value of zero indicating cases where no quantity of the variable is present. • A ratio variable, has all the properties of an interval variable, and also has a clear definition of 0.When the variable equals 0.0, there is none of that variable. • Notice that an observation of 0 years represents a case which possesses no quantity of the variable ‘Years at School’. Such a condition is known as a true zero point and is the defining characteristic of a ratio scale, as opposed to an interval scale. • However, heat measured in degrees Celsius does not have a ‘true’ zero. There is a zero point, but 0°C does not indicate a case where no heat is present – it is cold but not that cold! Instead, 0°C indicates something else: the point at which water freezes.

24. Levels of Measurement

25. Thanks