Definition of measurement
According to Nunnally 1970, Measurement consists of rules for assigning number to objects in such a way as to represent quantities of attributes.
Rules-indicate that the procedures for assigning numbers must be explicitly formulated.
Objects-in psychology are usually people or lower animals or material objects (some instances).
Quantification- concerns how much of an attribute is present in an object numbers are used to communicate the amount.
Attribute- indicates that measurement always concerns some particular feature of objects.
Four general level of measurement:
The process of assigning a value or score to the observed phenomenon constitutes the process of measurement. The rules defining the assignment of an appropriate value determine the level of measurement. The traditional classification of level of measurement was developed by S.S. Stevens 1946.
The four levels are-
Nominal level of measurement
The measurement scale in which numbers are assigned to the categories or variable values for identification only is called a nominal scale.
Properties;
• Nominal is weakest level of measurement.
• It doesn’t posses the attributes of magnitude, equal intervals or an absolute zero point.
• The data of nominal scale have no quantities properties.
• Of the basic postulates, the first three pertaining to equality apply.
• The statistical operations for this scale are counting (frequency), % mode, and coefficient of contingency.
For example;
There are two classes for the variable gender—males and females. There are no quantitative properties for this variable or these classes and therefore, gender is a nominal variable.
Others example
Player’s jersey number, marital status, hair color etc.
Ordinal level of measurement
The measurement scale in which numbers are assigned to the categories or variable values for identification as well as ranking is called an ordinal scale.
Properties;
• It is the 2nd weakest level of measurement.
• It captures the properties of nominal scale.
• It reflects only magnitude and does not posses the attributes of equal intervals or an absolute zero point.
• The logical basis for rank order is to be found in postulates 4 and 5.
• The statistical operations for this scale are counting, ranking, mode, medians, percentiles, coefficient of contingency and rank order correlation.
For example;
An ordinal scale is obtained when a group of boys is ordered from tallest to shortest.
Other examples;
Social class, economics status, pain etc.
Interval level of measurement
The measurement scale in which numbers are assigned to the variable values in such a way that the level of measurement is broken down on a scale of equal units and the zero value on the scale is not absolutely zero is called an interval scale.
Properties;
• It is the 2nd strongest level of nominal and ordinal scales.
• It captures the properties of nominal and ordinal scale.
• It posses the attributes of magnitude and equal intervals but not an absolute zero point.
• Most of the postulates mentioned previously can apply.
• The statistical operations for this scale are counting, ranking, addition, subtraction, mean, standard deviation, Pearson product-moment correlation etc.
For example;
Concerning observed quantities we can say that objects having assigned number of 5 and 10 are as far apart on the scale as two other objects having assigned number of 15 and 20.
Other example;
Intelligence, Temperature, learning score etc.
Ration level of measurement
The measurement scale in which number are assigned to the variable values in such a way that the level of measurement is broken sown on a scale of equal units and the zero value on the scale us absolutely zero is called ratio scale.
Properties;
• It is strongest and best level of measurement.
• It captures the properties of nominal, ordinal and intervals scales.
• It posses the attributes of magnitude, equal intervals and an absolute zero point.
• All the postulates mentioned previously are applicable.
• The statistical operations for this scale counting, ranking, addition, subtraction, multiplication, division, and all statistical applications.
For example, Age, Height, weight, duration, number of items etc.
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