Measurement theory

Question 1

Measurement (campbell)

Answer 1

The result of a process of assigning numbers that;
- each object is represented by a single number
- The sum of two assigned numbers represents an emperical combination
- This is known as a concatenation operation

Question 2

Relations between numbers

Answer 2

What we use to make emperical predictions. We can for example transform numbers by squaring them. This can destroy the emperical balance, not all transformations are possible.

Question 3

Measurement levels (Stevens)

Answer 3

The assignment of numerals according to a rule. Rule is a level, can be anything, but measurements should always be made in the same level.

Question 4

Representational solution

Answer 4

Measurement involves representation. This relation should be isomorphic (should also happen in real life). The level at which you measure is described by the possible transformations: which are those that keep the isopmorphism in tact.

Question 5

Measurement scales

Answer 5

Nominal; only equivalence, same property.

Ordinal: Numbers represent order. Higher have more property

Interval: Also in order, but the difference between orders is set. Zero-point arbitrary, like degrees.

Ratio: Set order and distance has meaning, but here 0 means absence, like weight

Question 6

Transformations at measurement scales

Answer 6

Nominal; all one-to-one transformations

Ordinal; All transformations that leave the order intact (monotonic)

Interval: if order and distance between remains the same NO squares (linear)

Ratio: all that preserve the ratio. Only a positive constant.

Question 7

Main rule

Answer 7

The stronger the scale, the less you can do without breaking the mirror