Scales of Variable Measurement

Variable measurement is the process of assigning values or attributes to an object. There are four types of Variable Measurement Scale, namely Nominal, Ordinal, Interval, Ratio. The lowest scale is the Nominal and the highest is the Ratio Scale. A measurement scale that is higher will have the characteristics of a measurement scale below it. The four measurement scales were proposed by a psychologist, Stanley Smith Stevens, in 1946 in one of his scientific articles entitled "On the theory of scales of measurement".

The focus of research design and statistical analysis is the study of variables. When you want to study a phenomenon, the first step is to define the phenomenon under study, in this case is to determine the variables that we observe and then determine how you measure these variables. This process is known as operational definition . It is clear here that to understand a phenomenon, we must first understand the terms variables and measurement scales. If you do not clearly define how to measure the variables you want to study, you will eventually experience confusion in determining the right research design and in determining the appropriate statistical analysis procedure.

When you have determined the design of the variables to be studied, the next step is to determine how to measure them? For example, an indicator that will be used as a representative of the characteristics of crop yields is seed weight. How to measure it? The method of measuring the weight of the seeds includes determining the measurement scale of the plant seed weight variable. Measurement is the basis of scientific inquiry . Everything we do starts with measuring the object we are going to study. Measurement is the assignment of numbers or codes to an object. There are four types of measurement scales , namely nominal , ordinal , and interval, Ratio . The lowest scale is the Nominal and the highest is the Ratio Scale. A measurement scale that is higher will have the characteristics of a measurement scale below it. For example, a Ratio scale will have Nominal, Interval, and Ordinal characteristics.

Pay attention to the values / data contained in the Gender Variable. Can you tell the difference between male and female gender? Of course you can! Barb is a girl while Cris is a boy. Here we can determine between those of the same gender (=) and those of a different gender (≠). Can you sort or rank? L > P or L < P? Of course we can't rank it! Likewise with skin color, here we can only distinguish without being able to rank it!

We can only distinguish or categorize the value/code of these variables, but we cannot rank them. Such a measurement scale is called Nominal

Now consider the Letter Quality variable. Barb and Chris get the same score (=) which is A, and different (≠) with Tina who only gets a Quality Letter B. In this example, apart from that we can see who gets the same quality letter (=) and who is different ( ), we can also rank them. Values that get A are more (>) better than those who get B. Likewise for the Rank variable. Rank 1 is certainly better than rank 11.

What About Behavioral Variables? Bonnie's behavior is the same (=) with Brenda, while Barb's behavior is different (≠). Barb's behavior is better (>) than Bonnie or Brenda. The difference in behavior scores between Mike (65) and Tina (60) is 5 points. The difference is the same as the difference between Tina (60) and Ron (55) which is 5. The value of 60 = 55 + 5 and 65 = 60 + 5. The value scale used has the same interval/distance. The same interval means that the weights/values of 5 in the above example are the same. For example, for the temperature variable, the difference between the temperature of 35 °C and 36 °C = 1 °C. Likewise, the temperature difference between 100 °C and 101 °C is 1 °C. Number 1 there weighs the same, in the sense that the difference in heat is the same.

Values/attributes of Behavioral Variables and Body Temperature, apart from being able to be distinguished , sorted ( ranked ), also have the same interval /distance . Such a measurement scale is called the Interval

How is it different from a ratio scale? On the ratio scale, in addition to the value of the variables can be distinguished, sorted (ranked), have the same interval / distance, can also be compared (ratio). Pay attention to the data on the Weight variable. Mike's weight = 90 kg, and Tina's = 45 kg (Nominal trait). Mike's weight was different from Tina's; Mike is heavier than Tina (Ordinal Traits), the Weight Difference Between Mike and Tina is 45 kg, the same as the difference between Bonie (55) and Mark (100) which is 45 kg (Interval Traits). Apart from these traits, we can also say that Mike (90 kg) is twice as heavy as Tina (45 kg).

In this case we can do a comparison / ratio. Why? Because the variable has an absolute value of 0. Confused right?? Is there a quantitative variable that does not have a value of 0 or has a value of 0 but is not absolute? There it is! what is an example? The behavior scale there is only from 20-100, not having a value of 0. Notice the behavior scores for Barb (80) and Ron (40). Here we can't say Barb is twice as good as Ron! Not RATIO! So what has a value of 0 but not absolute? Well, for example Temperature (in Celsius or Fahrenheit). The number 0°C does not mean that the object has no temperature ! 100°C doesn't mean 2 times hotter than 50°C! not RATIO!

In contrast to Weight Variables. Weight has an absolute value of 0! The number 0 indicates that the object has no weight!

Ok, are you still confused? to be more confused, in the following description will be discussed again about the meaning of the four measurement scales along with examples!

Nominal Variables/Nominal Scale

Nominal variables are variables with the lowest level of measurement scale and can only be used for qualitative classification or categorization . That is, the variable can only be measured in terms of whether the characteristics of an object can be distinguished from other characteristics, but we cannot measure or even rank the categories.

For example, we can say that the sexes of the 2 people are different, one is female and the other is male. Here we can distinguish the characteristics of the two, but we cannot measure and say which is "more" or which is "less" of the qualities represented by these variables. We can only code/label the two characteristics, for example the number 0 for women and the number 1 for men. The code/number label can be exchanged. The code there only serves as a differentiator between the two objects and does not indicate order or continuity. Number 1 does not indicate higher or better than 0.

The only arithmetic operators that can be used on a nominal scale are "=" or "≠" . Other examples of nominal variables are:

• type of soil,
• varieties,
• race,
• color,
• form,
• city,
• Blood group
• Types of diseases
• Religion
• Ethnic group
• KTP/SIM/Student Card Number

Ordinal Variable/Ordinal Scale

Ordinal variables allow us to sort rank of the object we measure. In this case we can say A is "better" than B or B is "less" good than A, but we cannot say how much more A is than B. Thus, the limit of one value variation to another is not clear, so what can be compared is only whether the value is higher, the same, or lower than the other values, but we cannot say how much the difference in distance (interval) between these values. A common example of an ordinal variable is the socioeconomic status of the family. For example, we know that the upper middle class is higher in socioeconomic status than the lower middle class, but we cannot say how much more or say that the upper middle class is 18% higher.

The arithmetic operators that can be used on an ordinal scale are the signs "=", "≠", "<" and ">" . For example, the numeric code for the lower class = 0, the middle = 1, and the upper = 2. The number 0 is different from 1 or 2 (arithmetic operators: = and ), 0 is lower than 1 (arithmetic operators: < and >), Example:

• Education level or wealth
• Disease severity
• Cure rate
• Degree of malignancy of cancer

Variable Interval/Interval Scale

Interval variables not only allow us to classify , rank order , but we can also measure and compare the size of differences between values. For example, temperature, which is measured in degrees Fahrenheit or Celsius, is an interval scale. We can say that the temperature is 50 degrees higher than the temperature of 40 degrees, and so the temperature is 30 degrees higher than the temperature of 20 degrees. The difference in temperature difference between 40 and 50 degrees is the same as the temperature difference between 20 and 30 degrees, which is 10 degrees. It is clear here that on the interval scale, apart from being able to differentiate (categorize), sort the values, we can also calculate the difference/difference and the distances or intervals can also be compared. The difference between the two values on the interval scale already has a significant meaning, in contrast to the difference on the ordinal scale which has no meaning. For example,

The arithmetic operators that can be used on an ordinal scale are the signs "=", "≠", "<", ">", "+", "-" . For example temperature: 30 +10 = 40 degrees. Another Interval Scale Example:

• Intelligence level (IQ)
• Some specific measurement index

Ratio Variable/Ratio Scale

Ratio variables are very similar to interval variables; In addition to already having all the properties of interval variables, absolute zero points can also be identified , making it possible to express ratios or comparisons between the two values, say x is twice as much as y. Examples are weight, height, length, age, temperature in kelvin scale. For example, weight A = 70 kg, weight B = 35 kg, Weight C = 0 kg. Here we can compare ratios, for example we can say that A's weight is twice the weight of B. C's weight = 0 kg, meaning C has no weight. The number 0 here is clear and meaningful and the number 0 indicates the absolute value of 0. It is a bit difficult to distinguish between interval scales and ratios. The key is at number 0, is the zero value absolute (meaning) or not? For example, temperature can be an interval scale but it can also be a ratio scale, depending on the measurement scale used. If we use the Celsius or Fahrenheit scale, it includes an interval scale, whereas if Kelvin is used, the temperature includes a ratio scale. Why? Because the temperature of 0 degrees Kelvin is absolute! Not only can we say that the temperature is 200 degrees higher than the temperature of 100 degrees, but we can also say with certainty that the ratio is actually twice as high.

The arithmetic operators that can be used on a ratio scale are the signs "=", "≠", "<", ">", "+", "-", "x" and "÷" . For example, the value of A's weight is 70 kg, B's weight is 35 kg.

• Arithmetic operators "=", "≠", we can say Weight A is different from Weight B (A B);
• Arithmetic operator "<", ">": A is heavier than B (A > B),
• Arithmetic Operators "+", "-": The difference between the weight of A and B = 35 kg (A – B = 70 – 35 = 35) kg,
• The arithmetic operators "x" and "÷":A are twice as heavy as B ( A = 2xB).

Example:

• Time, length, height, weight, age
• The level of certain substances and the number of cells
• Drug dosage, etc.

The interval scale has no ratio characteristics. Most statistical data analysis procedures do not distinguish between data measured on interval and ratio scales .

Measurement scale summary:

The relationship between the measurement scale and the type of data (quantitative and qualitative)

Flowchart to determine the variable measurement scale

Info!