Operations applied to various variables from the Questionnaires in the SPSS depends on Scale assigned to the variables. Assigning a particular scale of measurement depends on the numerical properties variable have, as discussed in the last article "Scales of Measurement".

Operations applied to various variables from the Questionnaires in the SPSS depends on Scale assigned to the variables. Assigning a particular scale of measurement depends on the numerical properties variable have, as discussed in the last article "Scales of Measurement".

In today's article various scales that are used in data analysis are discussed.

There are 4 scales of measurement, namely Nominal, Ordinal, Interval and Ratio, all variables fall in one of these scales.Understanding the mathematical properties and assigning proper scale to the variables is important because they determine which mathematical operations are allowed. That determines statistical operations we can use. Operations applied to various variables from the Questionnaires in the SPSS depends on Scale assigned to the variables. Assigning a particular scale of measurement depends on the numerical properties variable have, as discussed in the last article "Scales of Measurement".

In today's article various scale that are used in data analysis are discussed. There are 4 scales of measurement, namely Nominal, Ordinal, Interval and Ratio, all variables fall in one of these scales. Understanding the mathematical properties and assigning proper scale to the variables is important because they determine which mathematical operations are allowed. That determines statistical operations we can use.

The 4 scales are in the order of Nominal, Ordinal, Interval and Ratio scale with Nominal having least mathemathical properties, followed by Ordinal and Interval, whereas Ratio having most mathemathical properties.

## Nominal Scale

From the Statistical point of view it is the lowest measurement level. Nominal Scale is assigned to items that is divided into categories without having any order or structure, for instance Colors do not have any assigned order, We can have 5 colors like Red, Blue, Orange, Green and Yellow and could number them 1 to 5 or 5 - 1 or number them in a mix, here the numbers are assigned to color just for the purpose of identification, and ordering them Ascending or Descending doesnt mean that Colors have an Order. The number gives us the identity of the category assigned. The only mathematical operation we can perform with nominal data is to count. Another example from research activities is a YES/NO scale, which is nominal. It has no order and there is no distance between YES and NO.

## Ordinal Scale

Next up the list is the Ordinal Scale. Ordinal Scale is ranking of responses, for instance Ranking Cyclist at the end of the race at the position 1, 2 and 3. Not these are rank and the time distance between 1 and 2 may well not be the same as between 2 and 3, so the distance between points is not the same but there is an order present, when responses have an order but the distance between the response is not necessarily same, the items are regarded or put into the Ordinal Scale. Therefore an ordinal scale lets the researcher interpret gross order and not the relative positional distances.

Ordinal Scale variables have the property of Identity and Magnitude. The numbers represent a quality being measured (identity) and can tell us whether a case has moreof the quality measured or lessof the quality measured than another case (magnitude). The distancebetween scale points is not equal. Ranked preferences are presented as an example of ordinal scales encountered in everyday life.

## Interval Scale

A normal survey rating scale is an interval scale for instance when asked to rate satisfaction with a training on a 5 point scale, from Strongly Agree, Agree, Neutral, Disagree and Strongly Disagree, an interval scale is being used. It is an interval scale because it is assumed to have equal distance between each of the scale elements i.e. the Magnitude between Strongly Agree and Agree is assumed to be the same as Agree and Strongly Agree. This means that we can interpret differences in the distance along the scale. We contrast this to an ordinal scale where we can only talk about differences in order, not differences in the degree of order i-e the distance between responses.

### Properties of Interval Scales

Interval scales have the properties of:

- Identity
- Magnitude
- Equal distance

Variables which fulfill the above mentioned properties are put in this scale. The equal distance between scale points helps in knowing how many units greater than, or less than, one case is from another. The meaning of the distance between 25 and 35 is the same as the distance between 65 and 75.

## Ratio Scale

A Ratio Scale is at the top level of Measurement. The factor which clearly defines a ratio scale is that it has a true zero point. The simplest example of a ratio scale is the measurement of length (disregarding any philosophical points about defining how we can identify zero length) or money. Having zero length or zero money means that there is no length and no money but zero tempratue is not an absolute zero, as it certainly has its effect. Ratio scales of measurement have all of the properties of the abstract number system.

### Properties of Ratio Scale

- Identity
- Magnitude
- Equal distance
- Absolute/true zero

These properties allow to apply all possible mathematical operations that include addition, subtraction, multiplication, and division. The absolute/true zero allows us to know how many times greater one case is than another. Variables falling in this category and having all the above mentioned numerical properties fall in ratio scale.

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