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Summary Homework exercises

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Summary of 23 pages for the course FSWP2-052-A at EUR (Homework exercises)

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  • March 21, 2024
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  • 2022/2023
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2.5C Psychometrics – Theoretical Concepts
Chapter 3
i. Mean /Skewness and Median/
ii. Variance
iii. Standard Deviation
iv. Covariance (Size/Direction)
v. Correlation (Size/Direction)
vi. Composite scores
vii. Variance-Covariance Matrix
viii. Binary Items
ix. T-scores
x. Percentile ranks
xi. Normalization
xii. Normalizing VS Standardizing


Chapter 4
i. Dimensionality
ii. Eigenvalues (3 methods:/ +[]-)
iii. Orthogonal rotation/Varimax /Output explanation/
iv. Oblique/Non-orthogonal rotation
a. Factor Matrix
b. Pattern Matrix
c. Structure Matrix
d. Factor Correlation Matrix
v. Simple structure
vi. How an item gets from negative loading to positive loading after rotation?



Chapter 5
i. CTT assumption The mean of Xo is equal to the mean of Xt in the population
ii. CTT assumption  The correlation between Xe and Xt is zero
iii. CTT assumption  The correlation between Xe and every variable Y is zero
iv. CTT assumption  The correlation between Xe and Xo is not zero
v. Conceptualize reliability as
a. the ratio of true score variance to observed variance
b. the lack of error variance
c. the squared correlation between observed scores and true scores.

Chapter 6
i. Parallel forms
ii. Alternate forms reliability /Problems/
iii. Carryover effects
iv. Systematic Error
v. Unsystematic Error /Effects on reliability/
vi. Test-retest reliability/Problems with systematic/unsystematic error/
vii. Equal error variance assumption
viii. Equal true scores assumption
ix. Effect of +3 scale points on reliability

, 2.5C Psychometrics – Theoretical Concepts
x. Split-half reliability/Length/Why not used often
xi. Cronbach’s alpha/When do we use the standardized alpha/
xii. Assumption of essentially tau equivalent items
xiii. Assumption of stability
xiv. Test length/Adding items and reliability
xv. Heterogeneity X Reliability
xvi. Difference Scores



Chapter 7
i. Regression to the mean /Adjusted scores/
ii. Confidence intervals
iii. Attenuation
iv. Effect size/Cohen’s d
v. Item-total correlation
vi. Correlated-items total correlation
vii. Discrimination index



Chapter 8
Chapter 9
Chapter 10
Chapter 11

, 2.5C Psychometrics – Theoretical Concepts
Chapter 3
Mean /Skewness and Median/
Definition: A statistical measure of central tendency that repsesents the average score in the data

Calculation: By summing the all the scores and dividing this sum by the number of participants (N)

The mean follows the tail

When a distribution is skewed to the right  Mean > Median

When a distribution is skewed to the left  Mean < Median

When a distribution is normal  Mean = Median



Variance
Definition: Statistical measure of variability that tells us how spread out the scores in a dataset are.

Cannot be negative since we square the outcome, and squares cannot be negative

Calculation: i. By taking each score in the dataset, subtracting the meal of all scores from that
score

ii. Squaring the results, and then adding all the squared differences.

iii. This sum is then divided by the total number of scores



Standard Deviation
Definition: Statistical measure of variability that tells us how spread out the scores in a dataset are.

Cannot be negative for the same reason as the variance

Calculation: The square root of the variance


Covariance (Size/Direction)
Definition: Statistical measure that indicates the degree to which two variables are related to each
other.

Used to asses the relationship between two sets of scores

Can take values between -infinity and +infinity

Does not provide information about the strength or direction of the relationship between X and Y

Sign (+/-): Tells us whether the relationship between the variables is positive or negative

Positive covariance  When X increases, Y increases

Negative covariance  When X increases, Y decreases

Covariance of 0  There is no linear relationship between the two variables

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