# Scaling Method

For physical objects, you can describe what they look like in terms of temperature, time, distance, and so on. There are also measuring tools such as thermometers, clocks, rulers, etc.

On the other hand, for psychological ones, these measures are not clear. For example, there is a way to measure the "brightness" of light even with the same "brightness", but if you are asked to "measure" the "brightness" of your personality, you will be in trouble.

The method of calculating such a scale is called the "scaling method". Also known as Quantification theory.

## Direct and indirect methods

The method of listening to and examining the numbers of the scale you want to measure directly, such as the SD method, is called the "direct method". For example, if it was the brightness of the personality, "If light is 7 and darkness is 1, how many will it be?" and so on.

The direct method is also a type of scaling method, but the indirect method is more complex in terms of data science, and various methods have been proposed. Hereinafter, when I write "scaling method" on this page, I mean the indirect method.

By the way,Ferimi Estimation is a method of estimating the value of a scale, whether physical or psychological. In the case of Fermi estimation, we estimate the scale we want to know by examining the mathematical structure of the scale we want to know and collecting the parts that can be estimated.

## Types of scaling methods

Design of Experiments is divided into two methods: the method required to collect data and the method of analyzing the collected data, and uses a combination of them. Scaling is a combination of methods for collecting data and analyzing collected data.

### Scaling Method

Qualitative variables cannot be handled numerically as they are. One direction is to do a Cross Tabulation and proceed to handle aggregated data.

Another direction is to do a Dummy Variablen to allow you to use the quantitative method of variables.

### How to improve the accuracy of uncertain measurements

It is difficult to obtain a highly accurate value in one psychological scale. There is also ambiguity in the scale itself. Therefore, it is not enough to make the same measurement many times and increase the number of samples.

Converting a group of binary variables into a single continuous variable is a way to address the ambiguity of the scale itself by grouping similar scales together.

## Pair evaluation

In the SD method, you tell the opposing things and ask where in between. If you ask a question like this, it is easy to answer roughly where it is.

In the SD method, opposing things are paired, but even for things that are not necessarily opposite, such as "apples and tangerines" or "plan A and plan B", if there are only two things to compare, it will be easier to answer with a sensory estimate how similar they are and which is how bigger.

### Data analysis of pairwise evaluation of opposing concepts (direct method)

Data with opposite concepts, such as "light and dark", is a direct method of scaling. Once the data of the pair evaluation is obtained, the subsequent data analysis becomes a so-called tabular data analysis. You can look it up in the graph.

### Data analysis of parallel concepts pair evaluation (indirect method)

There are usually three or more categories such as "apples and tangerines" and "plan A and B".

For parallel concepts, examine all combinations of the two. Then we get a distance matrix or a pairwise comparison matrix.

For information about distance matrices, see Multi Dimensional Scaling , For pairwise comparison matrices, AHP can be used to obtain coordinate data with a scale constructed, such as "apples 5.3, tangerines are 3.1".

By the way, as a use of pair evaluation data, in addition to the scale construction method, Network Analysis using a Graph of Network is used. ISM and DEMATEL are our friends.

## Multidimensional scaling methods in a broad and narrow sense

When there is an explanation of "Multi Dimensional Scaling" or "MDS" in the relatively new literature of data science, It is often a scaling method from distance data. It is often introduced as one of the Visualization by compressing high dimensions into two dimensions. When this meaning is in the narrow sense (narrow meaning). The story of constructing a scale for things that cannot be directly measured, such as psychology, is also a multidimensional scaling method. It is often referred to simply as "scaling" or "scaling" rather than "multidimensional scaling". This meaning is broad, and includes multidimensional scaling in the narrow sense.