Comparison: Level-3 in Inquiry

Formulation

Comparisons introduce the notion of value, which is taken to be synonymous with quantity in a vague undefined way. Comparing occurs in many contexts, but for it to be part of rigorous inquiry, the comparing must be carried out systematically.

So comparing-L3 must be arranged by setting up a situation with given concepts-L2 that allow for collecting data-L1. The comparer is often an assistant who fully understands the goal of the study, or sometimes a subject guided by a scientist while the study goals are hidden or disguised.

Function: To apportion value systematically to things.
Comparing is about making visible and tangible the presence of a difference within a distinction (concept). It is also referred to as ranking or ordering.

Cumulation: Quantity
There is now a quantity of a categorized phenomenon. Comparing involves use of a particular concept-L2 in the light of specific data-L1.

Features

Uncertainty Puzzle: Which is more?
With a focus on value, this puzzle becomes: which is better? There are just three possible responses: •X is more than Y, •X is equal or equivalent to Y, •X is less than Y. So that reduces the degree of uncertainty considerably.

The reduction in uncertainty has fostered development of a range of ordering techniques: e.g. paired comparisons, successive approximation, reference gambles, minimum context of difference.

Inherent Error: Systematic bias.
Repeatedly over-valuing or under-valuing when comparing. This may occur deliberately, inadvertently or unconsciously.

Use of Numbers: Ordering.
Because comparables may be ranked, the natural ordering of rational numbers can be used. This is called ordinal scaling e.g. with 10 items, there can be 10 ordered positions: 1 (lowest),2,3,4,5,6,7,8,9,10 (highest). However, items that are equivalent will share a number, so not all numbers from 1 to 10 may need to be used.

In comparing, the cipher '0' is often used to mean 'the same as' or 'equi-valent' (as on a weigh balance for example).

Locus of Control: Internal-personal-subjective.
Comparing-L3 is an application of personal judgement. While concepts-L2 (often called variables in studies)—like heaviness or hardness or beauty—may be shared, the assignment of value (i.e. comparison-L3) in any particular situation is subjective. Anyone can arrange a comparison using any quality they prefer, and then insist that their view is meaningful, regardless of the views of others.

This inherent subjectivity requires some form of control within scientific studies. This may involve •training raters, •using several judges and checking for inter-rater reliability, and •asking a rater to make the same comparison at different times and checking for intra-rater reliability. Reliability in comparing is commonly taken to mean validity, but this is not necessarily so.

Relation to the Change Domain

Comparing involves change because in the absence of some difference in state, which may have a variety of causes, no comparison is possible. Ordering and the assignment of value must be deemed acceptable by the comparer: which is the psychosocial pressure that has been postulated for Change-RL3.

More: Maroon-styled terms are from the Change Domain

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Comparisons are too personal, and calculations of quantity too limited.

• So the use of quantity must be generalized and brought under social control, which forces a move up to a the next level: measurement-L4.

Originally posted: 23-Aug-2015.