STATS 9 HOMOGENEITY Flashcards
Fundamentally, what is test validity?
The extent to which the test measures the attribute it is supposed to measure
Define test homogeneity?
A test measuring just ONE attribute
What is a (common) Factor?
a common cause making all items in a homogeneous test correlate
What are factor models?
Single factor model - in a homogeneous test, all items score are made up of common factor (true score) and unique factor (error score)
Do unobserved factors have a natural scale?
NO, the scale of F is arbitrary, we always set it as a standardised variable
What is Communality and Uniqueness?
Because the common factor and the unique parts are mutually uncorrelated, item variance can be partitioned into variance due to the common factor and unique variance
What are the objectives of factor analysis?
To see if a test is homogeneous by “fitting” a common factor model to data, finding a set of factor loadings (coefficients) that would reproduce item scores as close as possible to the observed item scores
What is the basic logic of the scree test? How can we determine the number of factors from the scree plot?
Scree tests for homogeneity by seeing if one factor accounts for all shared item variance. Any remaining variance is presumably only unique item variance, so there should be no shared variance left. 1st factor should be high, the rest should be rubble. The number of plots on the scree plot will be equal to the number of factors in the analysis.
What is validity? How do we know is a scale is valid?
Confirmation that the scale is homogeneous paired with a convincing conceptual (not statistical) analysis!
Why can’t the coefficient alpha be used to establish scale homogeneity?
Cronbach’s Alpha is NOT a measure of test homogeneity! Alpha is an estimate of RELIABILITY that ASSUMES tests are homogeneous!!
Should the common factor and unique parts be correlated?
No! The common and unique parts of a factor must be uncorrelated! OTHERWISE IT WOULD NOT BE HOMOGENEOUS
What does a score of 0 represent in a factor scale?
Exactly average!
What is standardised factor loading?
Standardised factor loading is the correlation between the factor and the item
How can we interpret a scree test?
The first Eigenvalue should be much larger than the second, etc. We can interpret this as meaning the first factor is the only important factor
Why do we want small residuals when doing factor analysis?
Means our factor models explain the variance! / Our predictions are accurate
