Understanding The Measurement of Variables
Content Outline
- Introduction
- Measurement of Variables
- Scales of Measurement of Variables
- Summary
Introduction
Variables can measure simple phenomena directly (for example, hair color,
age, income, etc.) or more complex concepts that may require a more indirect measurement (for example,
socioeconomic status, academic achievement, etc.). When a study involves complex phenomena,
researchers usually identify variables that measure only one or two dimensions of a complex concept. For
example, if a study involves socioeconomic status, a researcher may pick “income” as the variable, while
another researcher may pick “social class” as an indicator. Yet, socioeconomic status can actually mean
not only these two elements, but could also refer to education status, and other similar elements.
Therefore, researchers need to be careful in identifying variables to stand in for complex phenomena
Measurement of Variables
The identification and measurement of variables involve two necessary elements we
need to remember:
- Variables have conceptual definitions that essentially explain what the variable is attempting to capture.
- Variables also have operational definitions that define how the variable will be measured in the context of the study.
Let us look at our earlier example of socioeconomic status to understand this better. When we talk of
socioeconomic status, we may be referring to a number of different aspects such as income, educational
levels, class, occupational prestige, etc. This is the conceptual definition. However, in the context of a
research study, a researcher only wants to focus on income levels of the sample. Thus, she uses “income”
to be the operational definition of socioeconomic status within the context of her study. In the same way,
since there is no direct way to measure “intelligence” which relates to both the capacity of an animal to
acquire information or knowledge as well as to apply that acquired knowledge and information to solve
problems or reach their goals. Researchers who are interested in exploring this concept in a study will
need to identify a variable for doing so. Therefore, a researcher may choose to use “IQ test score” to
operationalize the concept of “intelligence.” They may even specify what type of IQ test to use.
Researchers therefore need to be very clear about both definitions of the variable. The conceptual definition is important because a researcher needs to understand all the complexities of a certain concept or construct. The operational definition is important because if this is inaccurate, it may lead to the identification of an inappropriate/incorrect variable, which can negatively influence the study and study incomplete or inaccurate because you may not be able to find a variable that captures all aspects of a concept completely. Therefore, your goal should be to select the best possible variables to describe the concept. As suggested earlier, a good way to make sure you select the most appropriate variables is to review studies similar to yours, and check if the variables used would be appropriate or applicable to your study. If it is not possible to find appropriate variables in the literature, you may want to conduct some pretests to make sure the measures you have selected are appropriate. You could also use different measures of a concept to check how the results differ. For example, instead of using only “income levels’ to operationalize the concept of socioeconomic status, you could also use “educational levels” or “ownership of different assets” in a single study to see how these multiple measures influence your findings.
When researchers want to check on the accuracy of their operational definition, they perform tests of “validity” and “reliability.” “Validity” refers to the extent to which a measurement process truly measures the variable that it claims to measure. For example, we could ask to what extent income levels truly measure socioeconomic status. For instance, consider the hypothetical case of a land-owning family whose land and animals produce just enough during a year of poor rainfall to feed a large joint family but not enough to sell in the open market. Such a family would show a low family income but could not be compared to other families without land who have a similar family income. Our land-owning family still has assets such as land or cattle to sell off in case they face a problem which other families do not. So income level may be a poor indicator of socio-economic status and, in this situation, this particular way of operationally defining the phenomenon is not every effective.
“Reliability” refers to the extent to which repeated measurements under the same conditions produce the same or similar results. Thus, if measurement of IQ levels in several different contexts, but within the same conditions, provides us with similar results, we would conclude that IQ level is a reliable measure of intelligence. Validity and Reliability are partially related to some extent. A measurement cannot be reliable if it is not valid. For example, if the measurement of IQ level (as a measure of intelligence) shows significant variances in repeated measurements (which is the test of reliability), we would question its validity as a measure of intelligence. However, the reverse does not hold true – a measurement does not have to be valid to be reliable. For example, height cannot be considered a valid measure for intelligence because does not appear to have a direct connection with intelligence. However, repeated studies show that height is correlated with intelligence. Thus, height is a reliable measure of intelligence, even though it is not a valid measure.
Researchers therefore need to be very clear about both definitions of the variable. The conceptual definition is important because a researcher needs to understand all the complexities of a certain concept or construct. The operational definition is important because if this is inaccurate, it may lead to the identification of an inappropriate/incorrect variable, which can negatively influence the study and study incomplete or inaccurate because you may not be able to find a variable that captures all aspects of a concept completely. Therefore, your goal should be to select the best possible variables to describe the concept. As suggested earlier, a good way to make sure you select the most appropriate variables is to review studies similar to yours, and check if the variables used would be appropriate or applicable to your study. If it is not possible to find appropriate variables in the literature, you may want to conduct some pretests to make sure the measures you have selected are appropriate. You could also use different measures of a concept to check how the results differ. For example, instead of using only “income levels’ to operationalize the concept of socioeconomic status, you could also use “educational levels” or “ownership of different assets” in a single study to see how these multiple measures influence your findings.
When researchers want to check on the accuracy of their operational definition, they perform tests of “validity” and “reliability.” “Validity” refers to the extent to which a measurement process truly measures the variable that it claims to measure. For example, we could ask to what extent income levels truly measure socioeconomic status. For instance, consider the hypothetical case of a land-owning family whose land and animals produce just enough during a year of poor rainfall to feed a large joint family but not enough to sell in the open market. Such a family would show a low family income but could not be compared to other families without land who have a similar family income. Our land-owning family still has assets such as land or cattle to sell off in case they face a problem which other families do not. So income level may be a poor indicator of socio-economic status and, in this situation, this particular way of operationally defining the phenomenon is not every effective.
“Reliability” refers to the extent to which repeated measurements under the same conditions produce the same or similar results. Thus, if measurement of IQ levels in several different contexts, but within the same conditions, provides us with similar results, we would conclude that IQ level is a reliable measure of intelligence. Validity and Reliability are partially related to some extent. A measurement cannot be reliable if it is not valid. For example, if the measurement of IQ level (as a measure of intelligence) shows significant variances in repeated measurements (which is the test of reliability), we would question its validity as a measure of intelligence. However, the reverse does not hold true – a measurement does not have to be valid to be reliable. For example, height cannot be considered a valid measure for intelligence because does not appear to have a direct connection with intelligence. However, repeated studies show that height is correlated with intelligence. Thus, height is a reliable measure of intelligence, even though it is not a valid measure.
Scales of Measurement of Variables
Now that we have understood the issues involved with measuring variables, we can proceed to understand
the different levels of variable measurement. Researchers must be clear about these levels of
measurement because this determines the kind of statistical analysis that can be conducted. This in turn
can influence the conclusions of the study especially when we attempt to describe the relationships
between variables in the study.Variables are measured at four levels.
- Nominal variables
Nominal variables are the most basic level of measurement. These are variables that have two or more mutually exclusive and exhaustive categories. They are called ‘nominal’ because they can only be classified and counted (measured) on the basis of the names/labels of their categories. However, these categories cannot be ordered. An example of this type of variable would be the states of India. Thus, Himachal Pradesh, Uttaranchal, Maharashtra are all states of India, but they do not have an intrinsic ranking order. You would have to apply some rule in order to rank them (for example, ranking by alphabetical order or in terms of land area or in terms of infant mortality or in terms of number of seats in parliament) – there are no inherent ranks to the states. Similarly, “gender” is also a nominal variable – male/female/ third gender are the three categories within this variable, but they cannot be ranked – they can only be compared. - Ordinal variables
Ordinal variables are also variables that have two or more categories, but they are different from nominal variables because they can be ranked, and ranks are used to determine the differences between the categories. However, while we can rank them, they do not carry a numerical value. They can only measure how one value is greater or lesser than another value. An example may be asking someone how often he or she watch movies on television – their response options are Very often, Frequently, Sometimes or Never. From his or her responses, we will know that someone who responds “frequently” watches movie more often than someone who responds “sometimes.” However, none of these responses has a numerical value, so we cannot assess what is the numerical distance between “frequently” and “sometimes.” Another example would be if we were to ask someone if they approve of the Right to Education Act. They may respond “Very much in agreement with it,” or “Completely disagree with it.” These response options form the different categories of the variable “Opinion on Right to Education Act” which is an ordinal variable. - Interval variables
Interval variables are variables that have a numerical value, and are measured on a continuum. They have an equal interval between items/values. They also have a numerical value. The most common example of this type of variable is the temperature when measured in Celsius or Fahrenheit. We know that temperature is measured on a continuum on thermometer. Therefore, we know that the difference between 10 to 20 degrees Celsius is the same interval value (10 degrees) as 30 to 40 degrees Celsius. Test scores on an IQ test is another example of an interval variable. - Ratio variables
Ratio variables are also measured on a continuum and have a numerical value. The difference between ratio variables and interval variables is that in ratio variables, there is an “absolute zero”. Zero on the measurement scale indicates that there is no value of that variable or that the property being measured is completely absent at the zero level. Thus, we cannot say temperature in Celsius or Fahrenheit are Ratio variables, because 0 (zero) degrees on both these scales does NOT mean there is no temperature. In fact, zero degrees Celsius actually indicates the freezing point on the Celsius scale. However, for those of you familiar with the Kelvin scale of measuring temperature, zero Kelvin does actually indicate there is no temperature, and therefore the Kelvin scale can be regarded as a Ratio variable. Other examples of ratio variables include height, weight, currency, mass, etc. The term “ratio”, (which means a comparison of two quantities) implies that you can use the ratio of measurements.
Nominal and Ordinal variables are often referred to as Categorical variables or Qualitative variables since
they contain two or more categories. Interval and Ratio variables are known as Continuous or
Quantitative variables because they numerical values. A research study often includes different
combinations of these variables. For example, if your study looks at school dropout-ism, you may collect
nominal variables (names of the districts where the study is being conducted; gender of school dropouts),
interval variables (grades of children who dropped out – A= 90-100 marks, B=80-89 marks, etc) and ratio
variables (percentage of children who dropped out in each class).
In conclusion, variables are important because they help to measure concepts in a study. Because quantitative studies focus on measuring and explaining variables, choosing the right variables is important. The first step is to identify the correct variables to measure a property. Equally important is the conceptual definition, which explains how a variable will be defined and measured within the context of a particular study. Variables are measured on different scales, where at one end they can only be categorized or ranked, and at the other end they can be analyzed statistically.
In conclusion, variables are important because they help to measure concepts in a study. Because quantitative studies focus on measuring and explaining variables, choosing the right variables is important. The first step is to identify the correct variables to measure a property. Equally important is the conceptual definition, which explains how a variable will be defined and measured within the context of a particular study. Variables are measured on different scales, where at one end they can only be categorized or ranked, and at the other end they can be analyzed statistically.
Summary
- To check on the accuracy of their variables, researchers test the reliability and validity of their variables.
- Scales of measurement of variables are nominal, ordinal, interval and ratio
Reference
- Bhardwaj, R. S. (1999). Business Statistics. New Delhi: Excel Books. IGNOU Study Material (2005). EEC-13: Elementary Statistical Methods and Survey Techniques, Block 6.
- Kothari, C.R. (1985). Research Methodology: Methods and Techniques. New Delhi: Wiley Eastern.
- Young, P. V. (1988). Scientific Social Surveys and Research, Prentice Hall of India: New Delhi.
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