Theme 1 [Psychometric Theory]: Chapter: 3,4,5,6 & 7
Chapter 3: Basic Measurement and Statistical Concepts
Levels of measurement (not in exam)
There are numerous systems where we can assign numbers. These systems may generate data that
have different properties
Properties of measurement scales
There are 3 properties that help us to distinguish between different scales. Magnitude, equal intervals
and absolute zero.
Magnitude: is the property of ‘moreness’. Involves an attribute that is more than, less than, or equal
to another attribute.
Equal Intervals: if the difference between all points on that scale is uniform.
Absolute Zero: obtained when there’s absolutely nothing present of the attribute being measured.
With many human attributes, it is extremely difficult to define an absolute zero. There may be a level
of ability that the particular scale doesn’t measure.
Categories of measurement levels
Some aspects of human behaviour can be measure more precisely than others. This is determined by
the nature of the attribute (characteristic) being measured. Measurement serves different functions;
thus, numbers are used in different ways. Two broad groups of measurement data: Categorical data
and Continuous data.
Categorical data is in the form of discrete or distinct categories. Divided into nominal and ordinal
measurement levels
- Nominal: numbers are assigned to an attribute to describe/name it. For example, the 11
official languages of South Africa are coded from 1 – 11 in a data set.
- Ordinal: numbers are assigned to objects that reflect some sequential ordering or amounts to
an attribute. For example, people are ranked in the order in which they finished the race
Continuous data represents data that have been measured on a continuum that can be broken down
into smaller units. Divided into interval or ratio measurement levels.
- Interval: equal numerical differences can be interpreted as corresponding to equal differences
in the characteristic being measured. For example, a temperature scale (Celsius): a 1-degree
difference between two temperature readings remain constant irrespective of where on the
temperature scale the difference is observed. IQ tests scores considered to be an interval
scale.
- Ratio: most refined level of measurement. Equal differences can be interpreted as reflecting
equal differences in the characteristic being measured, but there’s also a true (absolute) zero
that indicates complete absence of what is being measured. Inclusion of zero allows for the
meaningful interpretation of numerical ratios. For example, length is measured on a ratio
scale.
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Chapter 3: Basic Measurement and Statistical Concepts
Levels of measurement (not in exam)
There are numerous systems where we can assign numbers. These systems may generate data that
have different properties
Properties of measurement scales
There are 3 properties that help us to distinguish between different scales. Magnitude, equal intervals
and absolute zero.
Magnitude: is the property of ‘moreness’. Involves an attribute that is more than, less than, or equal
to another attribute.
Equal Intervals: if the difference between all points on that scale is uniform.
Absolute Zero: obtained when there’s absolutely nothing present of the attribute being measured.
With many human attributes, it is extremely difficult to define an absolute zero. There may be a level
of ability that the particular scale doesn’t measure.
Categories of measurement levels
Some aspects of human behaviour can be measure more precisely than others. This is determined by
the nature of the attribute (characteristic) being measured. Measurement serves different functions;
thus, numbers are used in different ways. Two broad groups of measurement data: Categorical data
and Continuous data.
Categorical data is in the form of discrete or distinct categories. Divided into nominal and ordinal
measurement levels
- Nominal: numbers are assigned to an attribute to describe/name it. For example, the 11
official languages of South Africa are coded from 1 – 11 in a data set.
- Ordinal: numbers are assigned to objects that reflect some sequential ordering or amounts to
an attribute. For example, people are ranked in the order in which they finished the race
Continuous data represents data that have been measured on a continuum that can be broken down
into smaller units. Divided into interval or ratio measurement levels.
- Interval: equal numerical differences can be interpreted as corresponding to equal differences
in the characteristic being measured. For example, a temperature scale (Celsius): a 1-degree
difference between two temperature readings remain constant irrespective of where on the
temperature scale the difference is observed. IQ tests scores considered to be an interval
scale.
- Ratio: most refined level of measurement. Equal differences can be interpreted as reflecting
equal differences in the characteristic being measured, but there’s also a true (absolute) zero
that indicates complete absence of what is being measured. Inclusion of zero allows for the
meaningful interpretation of numerical ratios. For example, length is measured on a ratio
scale.
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