How many Cronbach’s alpha assumptions?
4
Cronbach’s alpha assumption 1
-items are essentially tau-equivalent (each item is an equally strong indicator of the true score scores, but they may differ by a constant. Items can have different means)
Cronbach’s Alpha Assumption 2
Each item’s error term is uncorrelated with every other item’s error term.
Cronbach’s Alpha Assumption 3
-The error scores are uncorrelated with the true scores. (Assumption associated with all forms of reliability).
Cronbach’s alpha assumption 4
-the items used to generate a composite score measure only 1 attribute or construct.
Standard coefficient alpha
You apply it to scores that have been converted from a raw score to a standardised score. E.g to z-scores.
Types of reliability assumption models
Parallel
Tau-Equivalent
Essentially Tau-Equivalent
Congeneric
Parallel
- Equal true score variance
- Equal means
- Equal variance.
Tau-Equivalent
- Equal true score variance
- equal means
- unequal error variances
Essentially Tau-Equivalent
- Equal true score variance
- Unequal means
- Unequal error variances
Congeneric
- Unequal true score variance (but all greater than zero)
- Unequal means
- Unequal error variances
Factors affecting reliability
- Added items to a test must be parallel to other items to increase cronbach’s alpha.
- but they really need only be essentially tau-equivalent items and possibly even congeneric in some cases.
- main thing to consider is “will adding this item reduce the mean inter-item correlation”
Sample Homogeneity
-Homogenous samples will yield lower reliability estimates than a heterogeneous sample.
Standard error of measurement (SEM)
Amount of error “around” a point estimate (observed score) in standard deviation form.
Confidence interval
- A confidence interval can be estimated around a point-estimate (observed score)
- A confidence interval reflects a range of values that is often interpreted as a range in which the true score is likely to fall.
Standard error of estimate
Typically, people calculate the 95% confidence interval around a point estimate (observed score).
2 types of correlations
Observed score correlation and true score correlation
Observed Score Correlation
- the correlation you get based on the data you have
- will be compromised to the degree to which there is measurement error in your data.
- In practice this means that the maximum correlation between two sets of scores is less than 1.0
True Score Correlation
- a hypothetical correlation you can estimate if you know the reliabilities associated with the scores.
- Not compromised by measurement error.
