lecture 27 (reasoning)

Question 1

positive manifold?

Answer 1

• when 2 tests measure similar things, if someone is better in one they will be better on the other
• this might be due to a common underlying variable (general intelligence example)

Question 2

relevant proprieties of numbers?

Answer 2

• Identity (nominal): a value stating if people are similar or different (the differences between numerical values do not represent amount but quality)
• Order (ordinal): rank order relative to each other is given (no information about the actual amount of difference)
• Quantity (ratio / interval): values giving the magnitude of differences between people (differences between numbers are indicative of something)

Question 3

possible meanings of 0?

Answer 3

• no existence (absolute zero)
• arbitrary quantity (arbitrary zero)
• psychological tests can produce a score of 0 even if it is not considered possible that someone does not have a certain psychological attribute -> can either mean that the attribute could not be measured or that the person does not have a measurable amount of the attribute

Question 4

fundamental measurement?

Answer 4

• type of measurement in which has no prior quantification
• it’s qualitative, it does not involve numbers

Question 5

campbell?

Answer 5

• measurements have certain rules that had to be adhered to to be classified as measurement

rules:
1. each object is represented by a single number
2. The sum of two assigned numbers represents the result of an empirical combination of objects (concatenation operation)

• Norman Campbell claimed that (fundamental) measurement always required concatenation -> this meant measurement was impossible in psychology, which lacked concatenation operations

Question 6

standard sequence?

Answer 6

• a sequence of weights where the difference between each weight is 1 unit (what is a unit is arbitrary)
• how you turn a qualitative system into a numerical representation that has the proprieties of a measurement

Question 7

how to form a standard sequence?

Answer 7

• check notebook -> we have an intuitive pre scientific understanding of how this works
• numerical symbols are assigned such that relations between numbers mirror relations
  between objects
• representational measurement theory: numerical structures are mirroring empirical structures

Question 8

transformations?

Answer 8

if you transform the numbers from the standard sequence, the numerical relations cease to represent the empirical relations

Question 9

isomorphism?

Answer 9

• representation of empirical things as accurate numerical things
• numeric relations are isomorphic to empirical relations

Question 10

Stevens?

Answer 10

• stated that measurement is indeed the assignment of numerals according to rules but the rules can be freely defined
• representational solutions: scale levels are defined based on the transformations that keep the isomorphism intact

Question 11

scalling?

Answer 11

linking numbers to behavioral observations with the goal to create a measure

Question 12

Steven’s measurement levels?

Answer 12

• nominal: numbers only represent equivalence (objects that get the same number have the same property)
• ordinal: numbers represent order (objects that are assigned higher numbers have more of the property represented)
• interval: numbers represent order, but distances between assigned numbers also have a definite meaning that is the same at all levels of the scale. zero is arbitrary -> e.g.: temperature in degrees Celsius; most psychological tests are on this level!!
• ratio: numbers represent order, distances between assigned numbers and ratio of numbers have meaning. zero is not arbitrary but indicates absence of the property

Question 13

measurement levels and admissible transformations?

Answer 13

• nominal: transformations are arbitrary as long as you’re consistent in assigning the symbols -> any transformation will leave the representation intact
• ordinal: all transformations that leave the order of the numbers intact are admissable
• interval: all transformations that preserve order and distances between numbers are admissible (all linear transformations
  Y=a+bX, were b is a positive constant)
• ratio: all transformations that preserve the ratio between numbers are admissible
• the stronger the scale level, the less you can do to the assigned numbers without breaking the mirror, since the representation of the world is so tight

Question 14

why shouldn’t you perform t tests on nominal data according to steven’s rules?

Answer 14

because the data are at the interval level of measurement, so only linear transformations are admissible

Question 15

professor Lord’s opinion?

Answer 15

• it is stil reasonable to do a t test on nominal data even tho it violates the rules (football numbers example)
• you shouldn’t be dogmatic about Steven’s rules -> you should understand that you can do things w/ your data that can lead to insight or important information, even thought they break the pre set rules

Question 16

pragmatic approach?

Answer 16

• transform your data according to transformations you think should not matter and rerun your analysis
• if conclusions don’t change, they are robust (good thing)
• if conclusion do change, investigate why and reconsider your scale levels
• not p hacking if you are open about the process