Question

What measurement scale is this an example of: Weight?

Answer 1

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

Properties of Measurement Scales :

    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.
                        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.

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1)Nominal scale:

           In this scale, categories are nominated names hence “nominal”.
           There is no inherent order between categories.
           Also, one cannot say that a particular category is superioror better than another.

Examples:

    Gender (Male/ Female):- One cannot say that Males are better than Females, or vice-versa.

    Blood Groups (A/B/O/AB):One cannot say that group A is superior to group O, for instance.

    Religion (Hindu/ Muslim/ Christian): Here the categories cannot be arranged in a logical order.
Each category can only be considered as equal to the other

2)Ordinal scale:

          The various categories can be logically arranged in a meaningful order.
           However, the difference between the categories is not “meaningful”.

Examples:

    Ranks (1st/ 2nd/ 3rd, etc.): The ranks can be arranged in either ascending or
                                  descending order without difficulty.
    
    Ranks (Good/ Better/ Best)or (No pain/ Mild pain/ Moderate pain/ Severe pain).

3)Interval scale:

         The interval scale of measurement has the properties of identity, magnitude, and equal intervals. . The absence of an “absolute zero”.

Example:

The Celsius scale: The difference between 40 C and 50 C is the same as
         that between 20 C and 30 C (meaningful difference = equidistant).
     Besides, 50 C is hotter than 40 C (order).
         However, 20C is not half as hot as 40C and vice versa (doubling is not meaningful).

Meaningful difference: Celsius scale, the difference between each unit is the same
                                anywhere on scale- difference between 49 C and 50 C is the same as
                                the difference between any two consecutive values on the scale ( 1 unit).
                                [Thus, (2-1)= (23-22)= (40-39)=(99-98)= 1].

4)Ratio scale:

          The values can be ordered, have a meaningful difference,
          and doubling is also meaningful. There is an “absolute zero”.

Examples:

   The Kelvin scale: 100 K is twice as hot as 50 K;
                      the difference between values is meaningful and can be ordered.

   Weight: 100 kg is twice as heavy as 50 kg;
              the difference between 45 kg and 55 kg is the same as that between 105 kg and 100 kg;
              values can be arranged in an order (ascending/ descending).

   Height: 100 cm is taller than 50 cm;
          this difference is the same as that between 150 cm and 100 cm,
            or 200 cm and 150 cm; 100 cm is twice as tall as 50 cm;
            the values can be arranged in a particular manner (ascending/ descending).

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So here we can say that weight is an Ratio Scale .