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Measurement scales are used to categorize and/or quantify variables. This lesson describes the four scales of measurement that are commonly used in statistical analysis: nominal, ordinal, interval, and ratio scales.

Properties of Measurement Scales

Each scale of measurement satisfies one or more of the following properties of measurement.

1)Identity. Each value on the measurement scale has a unique meaning.

2)Magnitude. Values on the measurement scale have an ordered relationship to one another. That is, some values are larger and some are smaller.

3)Equal intervals. Scale units along the scale are equal to one another. This means, for example, that the difference between 1 and 2 would be equal to the difference between 19 and 20.

4)A minimum value of zero. The scale has a true zero point, below which no values exist.

There are four types of data or measurements scales called nominal, ordinal, interval and ratio. These measurement scale is made by Stanley Stevens.

Nominal scales:

Nominal measurement is used to label a variable without any ordered value. For example, we can ask in a questionnaire ‘What is your gender? The answer is male or female. Here gender is a nominal variable and we associate a value 1 for male and 2 for a female.’

They are numerical for name sake only. For example, the numbers 1,2,3,4 may be used to denote a person being single, married, widowed or divorced respectively. These numbers do not share any of the properties of numbers we deal with in day to life. We cannot say 4 > 1 or 2 < 3 or 1+3 = 4 etc. The order of listings in the categories is irrelevant here. Any statistical analysis carried out with the ordering or with arithmetic operations is meaningless.

Ordinal scales:

These data share some properties of numbers of arithmetic but not all properties.

For example, we can classify the cars as small, medium and big depending on the size.

In the ordinal scales, the order of the values is important but the differences between each one is unknown.

 

Interval scales

In an interval scale one can also carryout numerical differences but not the multiplication and division. In other words, an interval variable has the numerical distances between any two numbers

Ratio scales:

Ratio scales are important when it comes to measurement scales because they tell us about the order, they tell us the exact value between units, and they also have an absolute zero–which allows for a wide range of both descriptive and inferential statistics to be applied. Good examples of ratio variables include height and weight. Ratio scales provide a wealth of possibilities when it comes to statistical analysis. These variables can be meaningfully added, subtracted, multiplied, divided). Central tendency can be measured by mean, median, or mode; Measures of dispersion, such as standard deviation and coefficient of variation can also be calculated from ratio scales.

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