4 SCALES OF MEASUREMENT IN QUANTITATIVE RESEARCH

 The scales of measurement refer to the relationship among the values that are assigned to the attributes for a variable. Scales of Measurement are so important that, first, in the sense that knowing the level of measurement helps you decide how to interpret the data from that variable. When one knows that a measure is nominal, then this indicates that the numerical values could be just short codes for the longer names.

Second, knowing the level of measurement helps the researcher decide what statistical analysis is appropriate on the values that were assigned. If a measure is nominal, then it means there is no need to average the data values or do a t-test on the data.

 There are typically four levels of measurement also known as scales of measurement: Nominal, Ordinal, Interval and Ratio that are defined or described in terms of variables.

Nominal Scale

A nominal scale is one of the scales of measurement, which  deals with variables that are non-numeric or where the numbers have no value. In other words, we can put them in any order and it would not matter. In nominal measurement the numerical values just "name" the attribute uniquely. No ordering of the cases is implied. For example, jersey numbers in basketball are measures at the nominal level.

A player with number 30 is not more of anything than a player with number 15, and is certainly not twice whatever number 15 is. Jersey numbers have no value as far as telling us anything about the ability of the players; it is just a way to identify them. Other examples of variables measured on a nominal scale include gender, race and the number on pool balls.

Consider an example of the students’ math test score as in relation to the type of breakfast they take; while scores on a math test are reported as numbers, eating breakfast is not numeric. A person eats a healthy breakfast, an unhealthy breakfast or no breakfast at all. These are not numbers but categories.

For the statistical analysis, sometimes a researcher will give non-numeric variables numeric values. For example, we might say that students who eat a healthy breakfast are -1, the students who eat an unhealthy breakfast are 0 and the students who do not eat breakfast are +1. These numbers are just a way to mark who is in which group but do not really have value.

Ordinal Scale

The ordinal scale not only classifies but also introduces an order into the data. These might be rating scales where, for example, ‘strongly agree’ is stronger than ‘agree’, or ‘a very great deal’ is stronger than ‘very little’. It is possible to place items in an order, weakest to strongest, smallest to biggest, lowest to highest, least to most and so on, but there is still an absence of a metric – a measure using calibrated or equal intervals.

Therefore one cannot assume that the distance between each point of the scale is equal, i.e. the distance between ‘very little’ and ‘a little’ may not be the same as the distance between ‘a lot’ and ‘a very great deal’ on a rating scale. One could not say, for example, that, in a 5-point rating scale (1 = strongly disagree; 2 = disagree; 3 = neither agree nor disagree; 4 = agree; 5 = strongly agree) point 4 is in twice as much agreement as point 2, or that point 1 is in five times more disagreement than point 5.

However, one could place them in an order: ‘not at all’, ‘very little’, ‘a little’, ‘quite a lot’, ‘a very great deal’, or ‘strongly disagree’, ‘disagree’, ‘neither agree nor disagree’, ‘agree’, ‘strongly agree’, i.e. it is possible to rank the data according to rules of ‘lesser than’ of ‘greater than’, in relation to whatever the value is included on the rating scale.

An ordinal scale of measurement looks at variables where the order matters but the differences do not matter. When you think of 'ordinal,' think of the word 'order.' In the case of letter grades, we do not really know how much better an A is than a D. We know that A is better than B, which is better than C, and so on. But is A four times better than D? Is it two times better? In this case, the order is important but not the differences.

In ordinal measurement the attributes can be rank-ordered. Here, distances between attributes do not have any meaning. For example, on a survey you might code Educational Attainment as 0 = less than High School.; 1 = some High School.; 2 = high school certificate; 3 = some college; 4 = college degree; 5 = post college. In this measure, higher numbers mean more education. But is distance from 0 to 1 same as 3 to 4? Of course not. The interval between values is not interpretable in an ordinal measure.

Ordinal data include items such as rating scales and Likert scales, and are frequently used in asking for opinions and attitudes.

Interval Scale

The interval scale introduces a metric or a regular and equal interval between each data point as well as keeping the features of the previous two scales, classification and order. This lets us know ‘precisely how far apart the individuals, the objects or the events that form the focus of our inquiry are’. As there is an exact and same interval between each data point, interval level data are sometimes called equal-interval scales (e.g. the distance between 3 degrees Celsius and 4 degrees Celsius is the same as the distance between 98 degrees Celsius and 99 degrees Celsius).

[ Examples Interval Scales of measurement

However, in interval data, there is no true zero. Let us give two examples. In Fahrenheit degrees the freezing point of water is 32 degrees, not zero, so we cannot say, for example, that 100 degrees Fahrenheit is twice as hot as 50 degrees Fahrenheit, because the measurement of Fahrenheit did not start at zero. In fact twice as hot as 50 degrees Fahrenheit is 68 degrees Fahrenheit

Let us give another example. Many IQ tests commence their scoring at point 70, i.e. the lowest score possible is 70. We cannot say that a person with an IQ of 150 has twice the measured intelligence as a person with an IQ of 75 because the starting point is 70; a person with an IQ of 150 has twice the measured intelligence as a person with an IQ of 110, as one has to subtract the initial starting point of . In practice, the interval scale is rarely used, and the statistics that one can use with this scale are, to all extents and purposes, the same as for the fourth scale: the ratio scale.

Ratio scale

Scales of measurement - Ratio Scale

Finally, in ratio measurement there is always an absolute zero that is meaningful. This means that you can construct a meaningful fraction (or ratio) with a ratio variable. Weight is a ratio variable. In applied social research most "count" variables are ratio, for example, the number of clients in past six months. This is because you can have zero clients and because it is meaningful to say that "...we had twice as many clients in the past six months as we did in the previous six months."

The ratio scale embraces the main features of the previous three scales of measurement, i.e. classification, order and an equal interval metric. However, it adds a fourth, powerful feature which is a true zero or absolute zero. This enables the researcher to determine proportions easily: ‘twice as many as’, ‘half as many as’, ‘three times the amount of, and so on. Because there is an absolute zero, all of the arithmetical processes of addition, subtraction, multiplication and division are possible.

Measures of distance, money in the bank, population, time spent on homework, years teaching, income, Kelvin temperature, marks on a test and so on are all ratio measures as they are capable of having a ‘true’ zero quantity. If I have one thousand dollars in the bank then it is twice as much as if I had five hundred dollars in the bank; if I score 90 per cent in an examination then it is twice as many as if I had scored 45 per cent.

The opportunity to use ratios and all four arithmetical processes renders this the most powerful level of data among scales of measurement. Interval and ratio data are continuous variables that can take on any value within a particular, given range.