Week 3

Question 1

What does the first principal component (PC) explain in PCA?

Answer 1

Most variance

Each subsequent PC explains less variance than the previous one.

Question 2

In PCA, all principal components are _______.

Answer 2

uncorrelated

This property allows for the independent interpretation of each component.

Question 3

What is sometimes difficult to interpret in PCA?

Answer 3

Factor-item correlation (factor loadings)

These correlations indicate how strongly each item relates to the factors.

Question 4

Which labels can you put on factor 1 and factor 2 based on the provided correlations?

Answer 4

• 1: Psychological complaints
• 2: Physical complaints

The labels are based on the loadings of the items on each factor.

Question 5

What indicates a low incremental validity in predictors?

Answer 5

High correlation between X1 and X2

Predictor 2 explains a small unique amount of the criterion.

Question 6

What is the aim of Principal Component Analysis (PCA)?

Answer 6

Find factors that explain as much variance as possible

PCA seeks to create a weighted combination of item scores.

Question 7

What does high correlation between predictors indicate?

Answer 7

Low incremental validity

This means that the second predictor adds little value beyond the first.

Question 8

What does incremental validity measure?

Answer 8

The additional value of a test on top of existing information

It is important for understanding how well a new test predicts outcomes.

Question 9

In the context of predictive validity, what does range restriction lead to?

Answer 9

Underestimation of predictive validity

This occurs when only high-scoring candidates are selected.

Question 10

What is the Multiple Group Method (MGM) used for?

Answer 10

Confirming expected groupings of variables

It assesses whether the expected structure is found in the data.

Question 11

What is the variance accounted for (VAF) in PCA?

Answer 11

How well the factors represent the variation in the data

VAF is usually between .30 - .80.

Question 12

What does a scree plot help determine?

Answer 12

The number of principal components

It shows where the variance explained begins to level off.

Question 13

What is the Kaiser criterion in PCA?

Answer 13

Eigenvalue > 1

This criterion helps decide how many components to retain.

Question 14

What is the goal of rotation in PCA?

Answer 14

To achieve a clearer structure of factors

Rotation helps to maximize the variance accounted for by each factor.

Question 15

What does factor analysis aim to do?

Answer 15

Summarize many variables into fewer factors

It retains as much information as possible.

Question 16

What is the difference between exploratory and confirmatory factor analysis?

Answer 16

• Exploratory: Structure of the test
• Confirmatory: Confirm assumed structure

Exploratory seeks to discover patterns, while confirmatory tests hypotheses.

Question 17

What does item-rest factor correlation measure?

Answer 17

Correlation of an item with the factor sum score excluding that item

It helps assess the item’s contribution to the factor.

Question 18

What is the relationship between predictors and criterion in incremental validity?

Answer 18

Correlation with criterion Y should be as high as possible

Correlation with existing predictors X should be as low as possible.

Question 19

What does a high loading on both principal components indicate?

Answer 19

Items may need rotation for clearer interpretation

This situation complicates the identification of distinct factors.

Question 20

What is the central idea of factor analysis?

Answer 20

There are similar patterns of responses that cluster together

These patterns help identify underlying constructs.

Question 21

What does VAF stand for?

Answer 21

Variance accounted for

VAF is used to describe the proportion of variance in a dependent variable that is predictable from the independent variables.

Question 22

What is the aim of rotation in factor analysis?

Answer 22

Substitute PC’s by new factors with in total the same amount of VAF

This aims to achieve a clearer interpretation of the factors.

Question 23

How do we determine the number of principal components?

Answer 23

• Researcher may have an idea about the number of factors
• Procedure stops when this number of factors is reached

This is a subjective decision based on prior knowledge or exploratory analysis.

Question 24

Using the Eigenvalue criterion, how many components are concluded for ‘statistics anxiety’?

Answer 24

Four components

This is because there are 4 components with an Eigenvalue larger than 1.

Question 25

What does the **scree plot criterion** help determine?

Answer 25

Number of factors before 'bend' ## Footnote This visual method helps identify the optimal number of factors to retain.

Question 26

List the **four components** identified in the interpretation of statistics anxiety.

Answer 26

* Fear of computers * Fear of statistics * Fear of mathematics * Fear of peer evaluations ## Footnote These components reflect different aspects of anxiety related to statistics.

Question 27

What is **criterion-related validity**?

Answer 27

Validity related to the prediction of criterion behavior ## Footnote It assesses how well one measure predicts an outcome based on another measure.

Question 28

What is the typical range for **validity coefficients**?

Answer 28

* r < .10: small * r .30: moderate * r .50: large ## Footnote These rules of thumb help interpret the strength of the relationship between test scores and outcomes.

Question 29

What are some reasons for **low validity coefficients**?

Answer 29

* Low reliability of the criterion * Ignoring different meanings of the criterion * Assuming a linear relation ## Footnote These factors can lead to underestimating the predictive validity of tests.

Question 30

What is **incremental validity**?

Answer 30

Improvement of prediction on top of existing predictors ## Footnote It refers to the additional explained variance provided by a new predictor.

Question 31

Define **predictive validity**.

Answer 31

How well a test score predicts a criterion ## Footnote This involves assessing the correlation between test scores and future outcomes.

Question 32

What is the difference between **predictive validity** and **concurrent validity**?

Answer 32

* Predictive validity: predictions confirmed by future criterion data * Concurrent validity: agreement between test results and criterion data at the same time ## Footnote Both types assess the validity of a test but at different time points.

Question 33

In **PCA**, how are factors found?

Answer 33

Factors are found one by one ## Footnote The process involves finding weights that explain maximum variance for each principal component.

Question 34

What is the aim of a **student well-being survey** in factor analysis?

Answer 34

To identify dimensions like academic stress, social support, life satisfaction ## Footnote This helps in understanding the structure of well-being among students.

Question 35

What does **factor analysis** demonstrate in terms of validity?

Answer 35

Internal structure validity ## Footnote It shows whether the test measures what it is supposed to measure.

Question 36

What are the types of jealousy identified in the **jealousy scale** theory?

Answer 36

* Reactive Jealousy * Anxious Jealousy * Possessive Jealousy ## Footnote These types help in constructing items that measure different aspects of jealousy.