STEVENS, 1946: ON THE THEORY OF SCALES OF MEASUREMENT Flashcards
When does Stevens claim measurement exists?
According to Stevens (1946), measurement exists in different forms and different scales of measurement that fall into certain definite classes. These classes are determined by empirical operations invoked during measuring and by the formal (mathematical) properties of the scales. Furthermore, the statistical manipulations that can be applied to empirical data depend on the type of scale with which is it ordered.
How does stevens therefore define measurement?
Measurement is the assignment of numerals to objects or events according to rules
What does Stevens derive from his little definition?
Since assignment can occur under different rules, this leads to different kinds of scales and kinds of measurements that can be used. The type of scale depends on the character of the empirical operations performed. These operations are limited ordinarily by the nature of what is being scaled and by the choice of procedures.
List the four kinds of scales
Nominal
Ordinal
Interval
Ratio
List the basic empirical operations that can be performed on each scale
Nominal: Determination of equality
Ordinal: Determination of greater or less
Interval: Determination of equality of equality of intervals or differences
Ratio: determination of equality of ratios
The second column listing the operations needed to create each type of scale is cumulative.
What permissable statistics are allowed within each scale?
Nominal: number of cases, mode, median
Ordinal: median, percentile
Interval: Mean, standard deviation, rank-order correlation, product-moment correlation
Ratio: coefficient of variation
What are meant by intensive and extensive scales?
The decision to not use the scale names usually seen in measurement papers is based on the ambiguity of terms such as “intensive” and “extensive.” However, ordinal and interval scaled have been called intensive, and interval and ratio scales have been labelled as extensive.
What is the nominal scale?
The nominal scale is a scale of measurement used to assign events or objects into discrete categories. It is the most unrestricted assingment of numerals. The rule in this case is to not assign the same numerical to different classes or different numerals to the same class.
What is the ordinal scale?
The ordinal scale report the ranking and ordering of the data without actually establishing the degree of variation between them. It has an isotonic or order-preserving group structure.
Why should means and standard deviations not be used with ordinal scales?
Means and standard decisions should not be used with ordinal scales, since these statistics imply a knowledge of something more then the relative rank-order of data. However, sometime fruitful results can be found when this is violated. The means the standard deviations on ordinal scale are in error to the extent that the successive intervals on the scale are unequal in size.
How can you determine the mid-point of a class interval on an ordinal scale?
It is also not proper to determine the mid-point of a class interval by linear interpolation because the linearity of an ordinal scale is precisely the property which is open to question.
What is the interval scale?
The interval scale is a quantitative measurement scale where variables have an order, the difference between two variables is equal, and zero is arbitrary. It can used to measure variable that exist along a common scale in equal intervals
What are ratio scales?
Ratio scales are a quantitative measurement scale and contains most of the characteristics of the other three variable measurement scales. It is the most informative scale as it tells about the order and the number of the object between the values of the scale. This scale can transform its numerical values by multiplying each value by a constant (e.g. inches to feet). Ratio scales possess a zero point
Comment on where psychology stands with these scales
Most of the scales used widely and effectively in psychology are ordinal scales.
Most psychological measurement tried to create interval scales and it sometimes succeeds. The problem usually stems from trying to create operations for equalising the units of the scale (due to several options). Occasionally there is a concern for the location of a “true” zero but it is not often a problem since attributes usually exist in a positive degree.
Ratio scales of psychological magnitudes are rare but not entirely unknown. (Stop the cap stevens smh)
How are different types of ratio scales distinguished in physics?
In physics fundamental and derived ratio scales are distinguished. Fundamental ratio scales are represented by length, weight, and electrical resistance. Derived ratio scales are represented by density, force, and elasticity. The latter are derived in that they are mathematical functions of certain fundamental magnitudes. These scales are more common in physics than fundamental magnitudes. Fundamental scales are important instances of ratio scales.
