The scale of measurement numbers in statistics – mathematica education

According to Stevens (in Nazir, 2003) measurement is the determination or administration of numbers to objects or phenomena according to certain rules. Three keywords needed in measurement are numbers, determination, and rules.

The measurement scale is a very important knowledge before someone does data processing. The measurement scale was first introduced by SS Steven. Basically, each statistical tool (count) can not be used just like that, there are requirements (assumptions that must be met), for example: data scale, data distribution, data independence, and data variability.

Based on its nature, there are four scale distinctions:

1. Nominal

The nominal size is the simplest measure, where the number given to the object has the meaning as a label, and does not show any level. Objects are grouped into set-set, and all members set are given numbers. The set-set may not overlap and be left and exclusive (exclusive and exhaustive)

The nature of the nominal scale is distinguishing.

Example: Gender (Male, Female), Religion (Islam, Catholicism, Christianity, Hinduism, Buddhism).

Examples of statistical methods: Chi-square, crostab, correspondence analysis, logistics regression, latent profile analysis.

2. Ordinal

Ordinal size is the number given contains the level of level. The nominal size is used to sort objects from the lowest to the highest or vice versa. This size does not provide absolute value to the object, but only gives a sequence (ranking). If we have a set of objects numbered from 1-N, namely n = a, b, c, d, …, n, and another set, namely r = 1, 2, 3, 4, …, n, and a correspondence is made between the set R with the set n with the rules where the smallest object is given the number 1, the second largest object is given 2, and so on, the ordinal size has been used.

The nature of the ordinal scale is the difference, there is a sequence.

Example: level of education (elementary, junior high, high school, college), accreditation value (A, B, C, D, E).

Examples of Statistical Methods: Spearman Correlation, Ordinal Logistics Regression, Attribute Agreement Analysis.

3. In the interval

As with ordinal size, the size of the interval is to sort people or objects based on an attribute. In addition, it also provides information about intervals between one person or object with another person or object. The same interval or distance at the interval scale is seen as representing the same interval or distance to the measured object. So, if we measure the achievement index (IP) of five students and it is found that students A has IP 4, B, 3,5, C, 3, D, 2,5, and E, 2, then we can conclude

that the interval between students A and C (4 – 3 = 1). Intervals between two research objects can be reduced or added with the intervals of two other objects.

The nature of the interval scale is to distinguish, there is a sequence, has the same distance.

Example: Age, Psychological Test Assessment Score.

Examples of statistical methods: Pearson correlation, regression analysis, factor analysis, K-Means cluster, discriminant.

4. Scale ratio

The size of the ratio, is a measure that includes all the previous sizes coupled with one other trait, namely this size provides information about the absolute value of the measured object. The size of the ratio has a zero point, therefore the distance interval is not expressed with the difference in the average number of one group compared to the zero point. Because there is a zero point, the size of the ratio can be made multiplication or division. The number on the ratio scale indicates the actual value of the measured object.

Nature: distinguishes, there is a sequence, has an absolute zero value.

Example: sales value (sales), number of customers.

Examples of statistical methods that can be used: Pearson correlation, regression analysis, factor analysis, K-Means cluster, discriminant analysis, time series analysis.