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
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
