L2 - Factor Analysis Flashcards
Factor Analysis Understanding
What is Covariance?
The degree to which two variables vary together
If one variable gets larger, does the other one change as well? Does it change the same way? Does it stay the same?
What is this formula?
What does it mean?
The covariance between two variables ‘x’ and ‘y’
In each variable, it is the formulation for the deviation scores.
For any value of x find the distance from the mean of the distribution and do the same the corresponding score for y.
Multiply those together, do that for everybody and then divide that by the number of people. That is the covariance.
Why might the numerical value of the covariance be hard to interpret?
For it depends on the variances of both variables and there is any number of units of measurement it might have.
What does this formula represent?
How we define the correlation between two variables.
What is the Pearson’s correlation coefficient?
It is a measure of the linear correlation between two variables X and Y
In Pearson’s correlation coefficient, what does r = 0, r = 1 and r = -1 represent?
1 = perfect positive linear relationship
0 = there is no correlation
- 1 there is a perfect negative linear relationship
- The values reflect the strength of the relationship*
Can Pearson’s correlation tell us about non-linear relationships between variables?
No, for this graph there is a clear predictive ability and correlation yet Pearson’s says there is 0 correlation.
Can only tell us linear correlations.
How do you get shared (common) variance from a correlation coefficient?
You square the correlation coefficient and then convert the result of that into a percentage.
- e.g. 0.3 squared = .09*
- .09*100 = 9%*
Correlation of 0.3 means the variables share a 9% common variance.
What size of the correlation coefficient is roughly needed for a ‘large, high or strong’ meaning or interpretation?
What is the shared (common) variance?
0.7 - 0.9
50% - 80%
These are rules of thumb and not necessarily completely accurate and depends on what you are measuring.
What size of the correlation coefficient is roughly needed for a ‘moderate or modest’ meaning or interpretation?
What is the shared (common) variance?
0.4 - 0.6
16-36%
What size of the correlation coefficient is roughly needed for a ‘small, weak, low’ meaning or interpretation?
What is the shared (common) variance?
<0.3
Less than 10%
What is a latent variable?
Variables that are not directly observed by are rather inferred from other variables that are observed.
What is a manifest variable?
A variable that can be directly measured or observed.
What does exploratory factor analysis (EFA) do?
It reduces a large number of variables to a smaller number of factors (these are latent variables) and describes the correlations among the variables in terms of these factors (latent variables)
Why is exploratory factor analysis (EFA) useful?
It helps us understand the structure of a set of variables - the relationships.
Therefore it is useful to help us develop theories (like personality)
Helps us develop instruments to measure the things we are interested in (personality inventory, iq test items)
Data reduction - bringing a large number of variables to a smaller more manageable number,
