Lecture 26: Measurement theory & statistics

Question 1

measurement theory met klei: wat is het doel

Answer 1

hij wil een nieuwe scale maken, dus met gelijke stappen.

Question 2

unit =

Answer 2

arbitrary

Question 3

wat heb je nodig voor die klei dingen

Answer 3

equivalence & order

Question 4

wat is het belangrijkste hieraan

Answer 4

concatenation

Question 5

concatenation =

Answer 5

putting 2 things in together -> aaneenschakeling

Question 6

wat was het verhaal van de klei

Answer 6

dat physics altijd hetzelfde is, maar mensen kan je niet zo exact voorspellen. zij zullen altijd op een andere manier reageren etc.

Question 7

statistics is een soort van….

Answer 7

filosofie! mensen hebben er verschillende meningen over en hier kunnen dus ook echt verschillen tussen komen.
er zitten allerlei motivations achter deze normen, en het zijn keuzes die mensen hebben gemaakt. mensen hebben redenen voor die keuzes. dus er is altijd een line of reasoning achter!!!

Question 8

wie had regression en correlation ontdekt

Answer 8

galton

Question 9

dus wanneer dat mensen psychologische kenmerken gingen meten

Answer 9

1869

Question 10

wat vond spearman

Answer 10

positive manifold: positieve correlatie tussen allerlei intelligentie testen (bv verbal en arithmetics)

Question 11

psychologists get too comfortable in using the word measurement.

Answer 11

physistics zijn het hier niet mee eens.

Question 12

wat was de uitleg van spearman voor positive manifold

Answer 12

general intelligence

Question 13

wat zei campbell

Answer 13

dat je niet zomaar mag zeggen measurement, en dat dat niet kan bij psychologie: suggests objectivity and precision and scientific standing.

Measurement is the result of a process of assigning numbers such that:
– Each object is represented by a single number
– The sum of two assigned numbers (..+…=…) represents the result of an empirical combination of objects (e.g., laying two rods end-to-end, or putting two masses in one arm of a pan balance)
– This is known as a concatenation operation

Question 14

dus wat is een concatenation operation

Answer 14

wat hij deed met klei: een objectieve schaal maken met stapjes en dus steeds een combinatie van objecten -> concatenation operation.

Question 15

numerical symbols are assigned in such a way that….

Answer 15

relations between numbers mirror relations between objects.

Question 16

hoe noem je deze methode met scales en numerical relations

Answer 16

representationalism

Question 17

wat gebeurt er als je alle nummers opeens ^2 zou doen

Answer 17

destroyed numerical relationships -> numerical relations no longer mirror empirical relations.

Question 18

strong scale levels ….

Answer 18

do NOT allow transformations!!!!!!!

Question 19

wat is dus een common misperception

Answer 19

mensen denken dat je meer kan met interval en ratio scales. maar je kan hier eigenlijk minder mee: want je mag ze niet zomaar transformeren!!! because they carry so much information

Question 20

dus norman campbell zei dat….

Answer 20

fundamental measurement always requires concatenation -> psychology lacks concatenation operations. je kan levels of extraversion bv niet zo makkelijk combineren, of political attitude

Question 21

interval =

Answer 21

0 point is arbitrary

Question 22

ratio =

Answer 22

0 point has meaning

Question 23

wat is een tegenargument tegen het besluit dat je in psychologie niet echt kan spreken van measurement

Answer 23

all the big measurements and statistical innovations come from psychology!

Question 24

wat zei stevens

Answer 24

er zijn verschillende types measurements;

nominal, ordinal, interval and ratio

Question 25

scale levels are therefore defined by….

Answer 25

the set of transformations that leave the mirror intact. it depends on the rule that is followed

Question 26

wat zei stevens over measurement definitie

Answer 26

= the assignment of numerals according to rule (any rule may do!)

Question 27

so one is always measuring, the only question is:

Answer 27

at what level????

Question 28

any systematic way of assigning numerals to objects, could be seen as measurement, but

Answer 28

but they are different kinds!

Question 29

representational solution= (4 dingen)

Answer 29

• measurement involves an act of representation
• measurement attempts to capture the structure of an attribute in symbolic form
• numeric relations are isomorphic to empirical relations
• scale levels are defined by the set of transformations that leave the isomorphism intact

Question 30

nominal =

Answer 30

numbers only represent equivalence (same number means equivalence in some sense, gaat niet over meer of minder). the objects that have the same number have the same property

Question 31

voorbeeld nominal

Answer 31

postal codes

Question 32

ordinal =

Answer 32

numbers represent order, objects that have higer numbers have more of the outcome.

Question 33

voorbeelden ordinal

Answer 33

rankings

Question 34

interval =

Answer 34

numbers represent order, but distances have meaning that is the same at all levels of the scale. zero point is arbitrary.

Question 35

voorbeeld interval

Answer 35

temperatuur in graden celcius
IQ (want 0 betekent niet dat je helemaal niet kan nadenken!)
SAT scores
years
income range
grade levels in school

Question 36

ratio=

Answer 36

numbers represent order, distances between assigned numbers have meaning, and the ratio of numbers have meaning as well.

zero point is not artbitrary, but indicates the absence of the property (dus 0 betekent ook echt niets van de outcome)

Question 37

voorbeeld ratio

Answer 37

mass in kilogram

Question 38

hoe waren deze scale levels defined

Answer 38

they are defined by the set of transformations that leave the mirror (= overeenkomst numerical and empirical relations) intact.

Question 39

michell zegt

Answer 39

there is no such thing as qualitative measurement. measurement is always quantitative measurements!! you have to show that you have these.

Question 40

dus wie zei dat qualitative measurement kon, en wie niet

Answer 40

stevens: ja
michell: nee

Question 41

welke transformations mag je maken bij nominal

Answer 41

all one to one transformations

Question 42

welke transformations mag je maken bij ordinal

Answer 42

all monotonic transformations are admissible (dus als de order maar intact blijft)

Question 43

welke transformations mag je maken bij interval

Answer 43

all transformations that preserve order and distances, dus alle lineaire transformaties.

X = a+bX

Question 44

welke transformations mag je maken bij ratio

Answer 44

all transformations that preserve the ratio between numbers, were b is a positive constant. want je moet het absolute zero punt behouden!

X=bX

Question 45

so: the … the scale level, the .. you can do to the assigned numbers without…

Answer 45

the stronger the scale level, the less you can do to the assigned numbers without breaking this mirror

Question 46

hoe zie je deze transformaties in statistiek

Answer 46

Parametric tests such as t-test and ANOVA are
sensitive to transformations that change distances between scale points
-> As a result, nonlinear transformations will change one’s conclusions

Question 47

No t-tests if …..

Answer 47

the data aren’t at the interval level of measurement

Question 48

wat was het punt van Lord artikel

Answer 48

Lord’s professor draws a sensible conclusion about football numbers, on the bases of illegal statistics!
Thus, prohibitions like “don’t run ANOVAs on nominal data” aren’t always justified…

het gaat om de interpretatie, als je het goed begrijpt kun je wel transformaties maken.

Question 49

dus het uiteindelijke punt is dat regels…

Answer 49

niet zijn vastgesteld, rules can change, and are based on assumptions and argumentation: not engraved in stone. it is not a fact but a norm!!!

there are all kinds of philosophical and methodological problems and assumptions underlying these things.

Question 50

dus bruggetje tussen stevens en lord

Answer 50

• The reasoning behind Stevens’ rules is strong and makes a lot of sense
• Also is a good argument for non-parametric statistics, because these are not sensitive to nonlinear transformations
• However, as Lord shows, clever people who know what they are doing can still obtain sensible results

Question 51

wat is een oplossing voor de verschillen tussen stevens en Lord

Answer 51

• One way is through the concept of robustness
• Transform your data according to transformations you think should not matter
• Then rerun the analyse
• If conclusions don’t change, they are robust and you’re
  in good shape
• If conclusion do change, investigate why and reconsider your scale levels

dus het gaat om replicatie! steeds hetzelfde vinden = robust

Question 52

• Methodological rules are not written in stone, but are based on assumptions and arguments
• Under the tapestry of Field and SPSS live all kinds of interesting methodological bugs
• We methodologists usually keep them in check, but it’s good to know they exist

Answer 52

oke