Measurement Scales
Suppose we are to collect data by measuring some characteristic or trait of an object or person. The question now arises, how precise must this data be? If we are measuring height, is it ok to measure height to the nearest foot, or should height be measured more precisely? Fortunately, statistics provides several measurement scales, each differing in precision. One of the most difficult task is to figure out which scale is appropriate for the charasteristic being measured. Listed below are the measurement scales from lowest precision to highest precision.
- The Nominal Scale .................. The lowest precision
- The Ordinal Scale
- The Interval Scale
- The Ratio Scale ...................... The highest precision
.
The Nominal Scale
Use a nominal scale when the goal is to classify or catagorize objects based on some trait or characteristic. Classifying people on the basis of eye color is an example of using a nominal scale. The order of classification is of no consequence.
The Ordinal Scale
The ordinal scale differes from the nominal scale in that order matters. Use an ordinal scale when the goal is to rank or order objects. For example, baseball players may be ranked based on talent. One word of caution, we cannot say that player ranked number one has 8 more talent units than player ranked number 2, or that player ranked number 1 is has twice as much talent as player ranked number 2. Between any two ranks there are no scales or marks. Only space exist between ranks. This means that subtraction, division and multiplication are usually not meaningful when applied to an ordinal scale..
The Interval Scale
The interval scale has the same properties of the ordinal scale with the additional property that differences between ranks or levels are equal. Use an interval scale when it is desirable for differences between levels or ranks in the characteristic being measured to be the same or equal. For example, when assigining a letter grade of A, B and C on some mathematical skill, it is desirable that the skill level difference between an A and B be the same as the skill level difference a B and C . Consider the Fahrenheight temperature scale. A temperature of 100 degrees F is 10 F degrees hotter than a temperature of of 90 degrees F, and a temperature of 30 degrees F is 10 F degrees hotter than a temperature of 20 degrees F. Even so, we cannot say that a temperatute of 100 degrees F is twice as hot as a temperature of 50 degrees F. The problem with multiplication on the Fahrenheight temperature scale is that a temp of 0 degrees F does not mean the absence of heat.
The Ratio Scale
The ratio scale has all the components of the interval scale with the added property that the zero point truly means the absence of the characteristic being measured. Therefore, when we select a ratio scale we can talk not only in terms of differences of the characteristic being measured but on ratios of the characteristic being measured. For example, a person who weighs 100 pounds is twice as heavy as a person who weighs 50 pounds because a zero on the weight scale means no weight present.
The scale selected for measuring a variable determines the statistical procedures or methods that can be applies in analysis of the variable. For example, computing the average score is not meaningful on a nominal scale,