In psychological tests, grades are assigned to traits to show the difference between the traits of the different test subjects. Measuring is the assignment of a figure to objects or to characteristics of individual behavior according to a certain scale. Scaling is the way numbers are assigned to psychological traits.

What are the fundamental problems with numbers? 

In psychological measurements, figures are used to show the level of a psychological characteristic. The figures can apply to different properties in different ways.

Identity

The most important thing when measuring the characteristic is looking at the differences and similarities between people. With the differences one can divide the test subjects or objects into categories. The categories must satisfy a number of points. First, all test subjects within a category must be the same on the attribute that this category represents. Second, the categories must be reciprocally exclusive. This means that each test subject can only be classified in one category. Third, no persons may fall outside the categories. Numbers are only used here as a label for the categories. They have no mathematical value: quantitative significance can therefore not be considered.

Rank order

The ranking of the figures contains information about the relative size of a property that people possess. So whether you possess a trait to a greater or lesser extent compared to the other people in the category. Here too, the figures are only a label. They give a meaning to the ranking within the category, but have no mathematical meaning.

Quantity

Indicating the quantity provides the most information. With regard to quantity, the figures are given per person and it is therefore possible to look at the precise difference between two people. At this level, the figures also have a mathematical meaning, with these figures calculations can be made. When psychological measurements are made, it is often assumed that the scores contain the characteristic of quantity. But this is rarely a good assumption, as we will discuss later.

The number zero

There are two potential meanings of zero. Zero can mean that the object or person does not exist (absolute zero). This is for example at the reaction time. Zero can also be an arbitrary amount of a property (arbitrary zero). In this case one can think of a clock or thermometer. It is important to see whether the zero in a psychological test is relative or absolute. It is possible that the test indicates zero while the person has that characteristic. Then you can take it as a relative zero while it was initially intended as an absolute zero. Identity, ranking, quantity and the meaning of zero are important issues in understanding scores on psychological tests.  

How can the measured variable be determined?

If the property of quantity is used, the measurements must be clearly defined. An example is length. If you want to know the length of something, you can measure it with a ruler. The ruler is divided into centimeters, so you can now measure the length per centimeter. In psychology, the measured quantity is often less clear / self-evident. There are three ways in which measurement variables can be arbitrary. 

1. height, weight, etc., of a random unit are chosen. This is a decision that will be secured later on.
2. The units are not tied to one type of object. Units can be applied to many types and many different objects.
3. Units can serve different types of measurements. An example is a piece of rope with which you can measure length, but you can also use the piece of rope to measure the weight of something.

If the units are in physical form, standard measurements are based on the three points mentioned above. And are therefore arbitrary on all three points. The measurements in the psychological world are generally only arbitrary at the first point. So you can choose what the unit means and what size is used. But with these measurements, the units are usually tied to a specific object or dimension. An important exception is that standard measurements are sometimes used to measure psychological characteristics. Such as cognitive processes that are measured by a person's reaction speed.

What role do adding and counting play in psychometrics? 

Both in the physical and in the psychological world, counting is important in the measurements that we perform.

Adding

An important assumption is that the measurement size of the unit does not change when counting the units. Every piece of unity is the same. With the addition of a unit, one is added every time. This is constant. Even if the conditions of the measurement change, the size of the unit remains the same ( conjoint measurement ). With a questionnaire there are questions that are easy and questions that are difficult. As a result, with most questionnaires one point cannot be awarded for each question. More points can be awarded for questions that are more difficult. But how many points do you assign to a question? This gives a paradox: We want to translate a psychological characteristic into a list of figures to look at the quantity, but this is not exactly because we do not know how much precise unity there can be with a psychological characteristic.

Counting

A point of controversy about the relationship between counting and measuring arises when we start to count things instead of properties. Counting is only equal to measuring when the quantity of a characteristic or property of an object is reflected.

Which measuring scales are there? 

Measuring is the addition of figures to observations of behavior in order to clearly see the differences between psychological traits. There are four measurement levels, or four scales: nominal, ordinal, interval and ratio.

The nominal scale

The nominal scale is the most fundamental level of measurements. At the nominal scale, the test subjects are divided into groups and those who are equal to each other are classified together. So there are differences between the groups. You can assign numbers to the groups but those numbers only give meaning to the group. Therefore, it cannot be taken into account. In daily life figures are also assigned to individuals, but this does not belong to the nominal scale. It is important to make clear what the numbers belong to. Or to individuals or to a group (nominal measurement level).

The ordinal scale

On the ordinal scale one can look at qualitative differences between the observations of behavior. Here numbers are assigned to individuals within a group and to these numbers one can see the ranking of the individuals. These figures only indicate whether you possess a trait to a greater or lesser extent compared to the other people in the group. This does not say anything about the extent of that person's property.

The interval scale

The interval scale goes one step further than the ordinal scale. In this case, if you assign numbers to the groups, the numbers also represent a certain amount. These figures represent quantitative differences between people on the trait being measured. Furthermore, the interval scale has an arbitrary zero. If there is a zero in the list, it does not mean that the unit is absent. With the interval scale you can add and subtract quantities, but you cannot multiply them. Many psychological tests are used and interpreted as if they are based on an interval scale, but in fact the majority of all psychological tests are not based on an interval scale.

The ratio scale

Ratio scales have an absolute zero. So if there is a zero in the list, it means that the unit is absent. It is also possible to multiply at the ratio scale, which is not possible at the interval scale. According to most test experts, there are no psychological tests that contain the ratio scale. When measuring the reaction time one would think that the ratio scale is used, but this is not the case because there is no single person who can respond in zero milliseconds.

Additional point with measuring scales

In theory, it is possible that a score zero at an interval scale means a quantity of a property, but it does not mean that the property is completely absent.

For tests with dichotomous variables, the binary codes (0 and 1) can be used. Depending on the characteristic being measured, it can be interpreted as a nominal scale or as an interval scale.

What implications does scaling have?

Scaling can have important implications on statistical analyzes. Some known, basic statistical procedures can only be performed with measurements that have an interval or ratio scale and not with measurements that have a nominal or ordinal scale. Consider descriptive statistics, such as the average or the correlation. When 'hair color' is the variable to be investigated, with the following categories: 1 = blond (14 people), 2 = black (4 people), 3 = brown (2 people). Then we can calculate the "average hair color" as follows: (1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 2 + 2 + 2 + 2 + 3 + 3) / 20 = 28/20 = 1.4. Although it is mathematically possible to calculate the average hair color, it is not meaningful to do this. This is just one of the many possible examples to show that scaling therefore influences the static analyzes and interpretation of outcomes. Some researchers even go so far as claiming that parametric statistics are only valid when they relate to interval or ratio data. Regardless of whether this statement is true or not, most behavioral scientists use the assumption that tests and measurements have an interval measurement level (with the exception of very short or single-item tests, which often have problems setting up an appropriate analytical strategy).

In psychological tests, grades are assigned to traits to show the difference between the traits of the different test subjects. Measuring is the assignment of a figure to objects or to characteristics of individual behavior according to a certain scale. Scaling is the way numbers are assigned to psychological traits.