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Summary Measurement Theory and Assessment II - EXAM PREP

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Course
Meten en Diagnostiek 2 (P_BMETDIA_2)

Institution
Vrije Universiteit Amsterdam (VU)

Measurement Theory and Assessment II - EXAM PREP Lecture 1. Introduction Lecture 2. Linear Regression Lecture 3. Logistic Regression Lecture 4: Test Dimensionality Lecture 5: Exploratory Factor Analysis (EFA) (Multiple factors) Lecture 6: Confirmatory...

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psychology
mta ii
measurement theory and assessment ii

Institution
Vrije Universiteit Amsterdam (VU)
Education
Psychologie
Course
Meten en Diagnostiek 2 (P_BMETDIA_2)

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‭Lecture 1. INTRODUCTION‬
‭●‬ ‭Psychometrics:‬‭assessing the attributes of psychological‬‭tests‬
‭○‬ ‭Interindividual = compare the behavior of different people‬
‭○‬ ‭Intraindividual = compare the behavior of the same person at different points in‬
‭time‬
‭●‬ ‭Criterion-referenced tests‬‭: compare each score with‬‭a‬‭predetermined‬‭cut-off point‬
‭●‬ ‭Norm-referenced tests:‬‭compare each score with a‬‭reference‬‭sample‬‭and‬‭norm‬
‭●‬ ‭Path diagram‬
‭○‬ ‭Latent variable (unobservable)‬
‭○‬ ‭Items (observable)‬
‭○‬ ‭Error (unobservable LV)‬
‭●‬ ‭Psychological theory‬
‭○‬ ‭Decides what is relevant to be measured‬
‭○‬ ‭Informs statistics: make “distributional assumptions” based on theory‬
‭●‬ ‭Statistics: analysis of individual differences‬
‭●‬ ‭Causality‬
‭○‬ ‭Relative items:‬‭item directly and causally related‬‭to the LV‬
‭(correlated)‬
‭○‬ ‭Formative items‬‭: items are not causally dependent‬‭on the‬
‭index variable - items scores determine the test score‬
‭●‬ ‭Properties of Numeral‬
‭○‬ ‭Property of identity‬‭: differentiate between categories‬‭of people (‬‭mutually‬‭exclusive‬‭&‬‭exhaustive‬‭)‬
‭○‬ ‭Property of order:‬‭indicate the‬‭rank‬‭order‬‭of people‬‭relative to each other along a‬‭single‬‭dimension‬
‭(implies transitivity)‬
‭○‬ ‭Property of quantity‬‭: adds information concerning‬‭amount‬‭to the numeral expressed in numerical counts‬
‭of units‬
‭■‬ ‭Absolute zero:‬‭absence of the attribute‬
‭■‬ ‭Relative zero:‬‭assignments of zero to an arbitrary‬‭value‬
‭●‬ ‭Measurement Levels‬
‭○‬ ‭Nominal scale‬‭: Numbers are simply ways to code‬‭categorical‬‭information‬
‭■‬ ‭Property of identity‬
‭○‬ ‭Ordinal scale:‬‭Numbers assigned have meaning in that‬‭they demonstrate a‬‭rank order‬‭of the classes‬
‭■‬ ‭Property of identity & order‬
‭○‬ ‭Interval scale‬‭: Provides a rank order of objects where‬‭differences in scale values express‬‭differences in‬
‭amount‬
‭■‬ ‭Property of identity + order + amount‬
‭■‬ ‭Zero is‬‭relative‬‭(not absolute)‬
‭○‬ ‭Ratio scale‬‭: Property of identity + order + amount‬‭+‬‭absolute zero‬

,‭Lecture 2. LINEAR REGRESSION‬
‭●‬ ‭Linear regression = conditional‬‭MEAN.‬
‭o‬ ‭Conditional mean:‬‭mean score on a variable given the‬‭score on another variable.‬
‭●‬ ‭If we have Y= b0 + b1 * x → no te olvides que es la formula predicted value!! (y=ȳ).‬
‭o‬ ‭b0 : intercept/‬‭constant‬‭: predicted value of‬‭y‬‭when‬‭x‬‭= 0.‬
‭o‬ b
‭ 1 : slope :‬‭regression coefficient‬‭: relationship‬‭between‬‭x‬‭and‬‭y‭:‬ change in‬‭y‭,‬‬
‭as‬‭x‬‭increases by 1.‬
‭o‬ ‭No error.‬
‭o‬ ‭Predicted formula and not observed one.‬
‭o‬ ‭We look at the red line instead of a gray line.‬
‭●‬ ‭Conditional mean‬‭(of y)‬ ‭= Predicted mean‬‭(of y).‬
‭●‬ ‭Notation y I x‬
‭o‬ ‭y given x.‬
‭o‬ ‭Conditional mean‬
‭●‬ ‭Assumptions‬‭distribution of y‬‭linear regression (3):‬
‭1.‬ ‭It needs to be linear regression.‬
‭2.‬ ‭y‬‭is normally distributed for all values of‬‭x‬
‭o‬ F‭ or each value of x, y needs to be normally distributed, and the mean of normal distribution‬
‭equals the predicted score of y‬
‭o‬ ‭Therefore, the‬‭predicted score of y=conditional mean.‬
‭3.‬ ‭Variation‬‭(SD)‬ ‭in scores on‬‭y‬‭is the same for all‬‭values of‬‭x‬‭.‬
‭●‬ ‭No assumptions for‬‭distribution of x.‬
‭●‬ ‭b1‬‭: represent also the difference between the scores‬‭by the two variables. Ex: differences score men and woman.‬
‭●‬ ‭Is the relationship relevant?‬‭→‬‭we need to study‬‭→‬‭R2‬‭=‬‭variance‬‭of y‬‭explained‬‭by x = measure effect‬‭size.‬
‭o‬ ‭var (y) explained variance by x=‬‭b‭1‬ ‭2‬ ‬‭* var (x)‬
‭o‬ ‭var (y) not explained variance by x‬‭=‬‭standard error‬‭of the estimate =‬‭var (e)‬
‭o‬ ‭Total variance (y)‬‭=‬ ‭b‬‭1‬‭2‬‭* var (x)‬‭+‬‭var (e)‬
‭o‬ ‭R2‬‭=‬‭b‬‭1‬‭2‬‭* var (x)‬‭/ (‬‭b‭1‬ ‬‭2‬‭* var (x)‬‭+‬‭var (e)‬‭)‬
‭●‬ ‭Psychological variables → standardize score → multiple ways to do this:‬
‭1.‬ ‭Z-score‬
‭o‬ ‭Z score - does NOT require assumption of normality (M and s)‬
‭o‬ ‭Normalize Z score (based on empirical percentile score) - requires assumption of normality.‬
‭2.‬ ‭Other distributions (t-score)‬
‭3.‬ ‭Percentile score‬
‭o‬ ‭Empirical‬
‭●‬ ‭Does not required normal distribution‬
‭●‬ F‭ rom empirical to‬‭normalize‬‭z score also possible‬‭→ assuming normal distribution from‬
‭population‬
‭●‬ ‭Based on data‬
‭●‬ ‭Theoretical‬‭(table)‬
‭ ‬ F‭ rom z-score to percentile score‬
●
‭●‬ ‭Normally distributed‬
‭●‬ ‭Interpreting scores‬
‭○‬ ‭Variance‬‭: how much the scores in a distribution deviate‬‭from the mean‬
‭○‬ ‭Standard deviation:‬‭square root variance‬

, ‭ ‬ S‭ kewed distribution:‬‭positive → right tail/ negative → left tail‬
○
‭○‬ ‭Kurtosis‬‭: positive → taller / negative → shorter‬
‭○‬ ‭Covariance‬:‭ degree of association between the‬‭variability‬‭in‬‭two‬
‭distributions‬‭(positive/ negative)‬
‭■‬ ‭Provides information about‬‭direction‬
‭○‬ ‭Correlation‬‭: Degree of association between two variables‬
‭(strong/ weak)‬
‭○‬ ‭Correlation coefficient‬‭: number of correlation - from‬‭-1‬
‭to +1‬
‭○‬ ‭Reflects‬‭magnitude‬‭: close to -1 or +1 means that the‬
‭association is very strong‬

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