Measurement: Level-4 in Inquiry
Formulation
Measurement introduces the notion of a generally applicable unit when quantifying comparisons. The unit is generally applicable insofar as all scientists are expected to use it in every instance when ordering is desired. The unit is referred to as «the standard».
| L7: ? |
| L6: ? |
| L5: ? |
| L4: Agree Measurements
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| L3: Arrange Comparisons
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| L2: Define Concepts
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| L1: Collect Data
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Popular Definitions:
Measurement is viewed as the heart of scientific work, almost definitional. This taxonomic formulation provides what is generally missing: a theoretical model where measurement is conceived as:
(a) an activity designed to accomplish a goal, together with
(b) other factors/elements essential to meet that goal.
So, although there are many definitions, they are unsatisfactory because measurement is not placed within the human system of endeavour that is absolutely essential for inquiry.
Example: A definition like "the determination of the magnitude of some inherent property of a body" sounds sensible but it takes for granted notions like 'magnitude', 'property' and 'body'.
The practical goal for a standard is reproducibility of quantification to within close limits at different times and places. Natural phenomena are preferred to minimize changes over time, but stability of a standard is not guaranteed. Standards can change as phenomena are better understood.
Example: Length
The standard for length has gone through several versions over the past two centuries. Length was initially defined using the earth's circumference, or via a pendulum length for a given period. Then it was defined via markings on a prototype bar of platinum and iridium at 0°C. Then it was defined via wavelengths of a particular light frequency. The current scientific standard refers to the distance travelled by light in a vacuum. Practical problems still exist.
Note: The particular system chosen for quantification—e.g. metres (decimal), yards, feet & inches (non-decimal)—is an issue of scaling (see below).
Function: To accord validity to quantitative comparisons through use of a socially agreed standard unit.
Example: Probability
Probability is subjectively an amount of expectation or belief. To compare probabilities, it is necessary to refer to a property of physical systems in which events occur in a consistent but not unique way. The standard unit comes into focus when that probability is converted to odds: i.e. x to 1.
Measurement can be based on simple counts where a unit is intrinsic e.g. when you measure attendance at a cinema via ticket sales, the standard unit would be the sale of one ticket. Social agreement on this would not be problematic.
Cumulation: There can now be a standardized quantity of a categorized phenomenon. Measuring-L4 is a sophisticated form of comparing-L3, the difference being a standard reference unit for the concept-L2, with which all data-L1 must be compared (rather than to each other).
Features
Uncertainty Puzzle: How much is it?
The concern here is to enable absolute and objective quantification. Using the standard unit allows for arithmetical manipulation.
Inherent Error: Random error.
On a sufficiently small scale, which is usually the scale of a study, two measurements are never identical. The cause of the variation is not necessarily known. With a sufficient number of measurements, statistical methods can establish confidence intervals and measure the likely error.
Example: Measuring potency
Drug potency is measured using a standard chosen so that the difference of log tolerance between it and the drug are little affected by systematic differences between groups of animals. However, as no two animals are biologically identical, they will not respond identically to the drug. Multiple animals must be tested.
Locus of Control: External-social-objective
Standardization requires an objective perspective with no doubts as to the definition of the unit. The universal unit must be widely accepted and that means conformity enforced by social control. The unit is typically defined by an international committee of scientists, However, the enormous power of quantification and its impact on systems and statistics often demands official control. So the recommended unit may need to be independently endorsed by institutions within each country.
Use of Numbers: Precise quantification and calculation.
The use of a standard unit permits ratio scales i.e. doubling the scale number is equivalent to a doubling of the value of some actual property. Numerous mathematical manipulations of quantities can be performed with a confident belief that they parallel actuality.
Measurements may be precise while not paralleling subjective estimations or physical reality. This is because measurement entails a loss of contact with specifics e.g. the average family may have 2.15 children, but no actual family does.
Example: Sound
Loudness (subjective) is represented by wave amplitude (objective), and pitch (subjective) is represented by wave frequency (objective). However, parallelism between objective and subjective assessments holds only over a limited range, and in a non-linear fashion.
Notions of 'measurement scales', 'levels of measurement' and 'levels of scaling' were in the social sciences. However, they may engender confusion.
Stevens' definition of measurement as "the assignment of numerals to objects and events according to rules" conflates two matters that need distinguishing.
The position taken here is that measurement and scaling are useful names for two different functions as follows:
- Measurement is about defining a standard unit for comparing data of a particular sort (i.e. the concept).
- Scaling is about assigning numbers to objects, properties, events, variable values &c (i.e. to any representation of reality).
Confusion has occurred because assigning numbers to a category (as 'values' of a 'variable') allows the precision and power of mathematical reasoning to be applied, which is something devoutly desired by social scientists.
Limitations of Mathematics
Important as mathematics is, quantitation alone is not sufficient for a precise and useful representation of reality. Flawed paradigms or confused categories render mathematics meaningless.
In economics particularly, assumptions to ensure mathematical methods are applicable have led to it becoming disconnected from the well-springs of human activity. The seeming control and predictive power of mathematics has contributed to its many flawed intrusions into economic and social life.
Relation to the Experience Domain
Measuring as an activity intrinsically involves all previous levels. However, the process required specifically at this 4th Level is conformity to the standard unit. Conforming will be dependent on an inquirers experience-RL4. While definition of the fundamental unit is a social matter, each inquirer must personally identify with that choice. The idea behind the unit has to feel right or the measurement will not be understood and trusted. Emotions seem to be important e.g. as of 2014, the USA (in company with Liberia and Burma) had not accepted the 1960 International System of Units.
The emotional quality of this level is noticed by most people when dealing with a foreign currency, or indeed any other alien standard. Discomfort fosters spontaneous rejection and often clumsy efforts to mentally convert the value to the personally preferred standard.
Example: Land Area
Land is socially and emotionally fundamental to living. Those who use acres, find hectares strange and avoid speaking of ares, deciares or decares. If you reside in Thailand, land areas are measured in rai, ngaan, and talang wah. Because land is so important each culture has developed area notions accepted as valid and institutionalized within that society regardless of the views of those in other countries.
Measurements are inherently valuable, but they are not knowledge.
- Knowledge calls for measurements to be placed in the context of other measurements, and this forces a move up to the next and highest level for actual representation: relations-L5.
Originally posted: 23-Aug-2015.