1 MTA

= the science concerned with the attributes of psychological tests ( not neccerly a paper and pencil test )

= the assignment of numerals of psychological characteristics of individuals according to rules

characteristics : psychological variable or construct

assignment according to test procedure ( e.g. self report)

latent traits

lot of aspects are not observable by the eye ( subjective )

we can only measure the objective ones

but how do we link them to the concepts we want to study?

1) psychological theory

2) causality

3) statistics

4) explicit representation of the latent observed variables relation ( aka path diagram )

1. latent variable
2. items
3. errors

first element

the circular shape refers to unobservable traits (latent)

psychopathology : depression , anxiety, eating disorder

personality : extroversion, neuroticism

cognition : spatial IQ, verbal IQ , memory

development : Piaget's stages, Bowlby attachment types

second element

rectangular shape refers to traits that we can observe or responses we can

can be either performance observations , self report or ratings

"I drink alcohol daily " ( yes = 1 / no = 0 )

"I like to go to parties " ( yes=1 / no= 0 )

third elements

also referred to as residuals

observable variable related to the latent trait but never perfectly = error

also unobservable ( hence the circle shape)

forth element

representation of the direction of the (causal) relationship

need to decide the operational definition of the latent variable in terms of observable variables

this helps determine which observables are needed and relevant

analysis of individual differences in item response

mean

variance

standard deviation

variance

standard deviation

mean

probability

**the sum of all values divided by the total number of values**
it's the most commonly used measure of central tendency and is often referred to as the "average."

***variance*** is the expectation of the squared deviation of a random variable from its population mean or sample mean

1. linear regression : the dependent variable is continuously distributed
2. logistic regression : dependent variable ( item) is binary or dichotomous (e.g. 0 or 1)

Pearson product moment correlation coefficient

express linear relationship between variables

correlation matrix ( of the items )

correlation : expresses the linear relationship between two variables

(1 ←→ 1)

make distributional assumptions based on theory

distribution of latent variable is based on theory concerning latent variable

theory prescribes the distribution of latent variables ( depression, working memory , Pieget's development)

1. identity
2. order
3. quantity

"either or "

categories, denoted by the numerals are mutually exclusive and exhaustive : each individual at a given time can be assigned only a single unique value

if we would assign numeral values to individuals to represent status

N = normal and , MD = manic depression

numerals with property of order indicate ranking of people relative to each other along single dimension

e.g. in the case of depression

Normal ( N or 0 )

Dysthymic (D or 1)

Major depression ( MD or 2 )

important for factor analysis as well

we need the concept to be unidimensional

labels are arbitrary

rank order a single dimension implies **transitivity** : 2 > 1 and 1 > 0 implies 2 > 0

information about amount and distance between numerals

property of identity : gigantism vs normal ( diagnosis )

property of order tall vs normal vs short (visual inspection)

property of quantity : lengths expressed in cm (cm)

property of quantity requires a definition of units of measurement ( e.g. cm)

rank order with property of quantity implies **transitivity**

divisible :measurement units define the scale

absolute zero

relative zero

means the absence of the attribute

e.g. distance in meters

the train travelled 0 meters (absolute)

means the assignment of zero to arbitrary values

e.g. temperature in C or F

0 Celsius degrees does not mean the absence of temperature

1. nominal
2. ordinal
3. interval
4. ratio

numbers are simply the ways to code categorical information

identity

gay / straight / bi / other ( 0, 1, 2, 3, )

do not represent assessment or "more or less"

it is exhaustive and mutually exclusive ( cannot be in two categories at a a time )

distribution is determined by probabilities of discrete classes

numbers assigned have meaning in that they demonstrate a rank order of the classes

identity and order

transitive ( 1<2<3<4 = 1<4)

distribution is determined by probability of discrete values

income : less than \$20.000, between \$20.000 and \$29.999 and more than %30.000

provides rank order where differences in scale values express difference in amount

identity , order and amount ( zero is relative)

celcius degrees

identity , order , amount and absolute zero

Celcius vs Farenheit , lengths in cm vs inches

this does not really occur in psychology ( we do not consider the absence to be 100%

existent )

difference changes if we go form scale to scale due to relative 0 but the ratio does not change

often have the case of scaling issue

we assume that latent variable is at interval level

normal distribution but items are ordinal

this is a miss match

treat as interval

factor analysis

item response theory