Page 240 - DMTH404_STATISTICS

Statistics

Notes 16.3 Summary

 The reliability is the correlation between two parallel tests and is equal to the squared
correlation of the test with the construct.

V t
r = = percent of test variance which is construct variance. rxt = rxx  the validity
xx V x
of a test is bounded by the square root of the reliability.
How do we tell if one of the two “parallel” tests is not as good as the other? That is, what
if the two tests are not parallel?

 Although alpha is relatively insensitive to the relative contributions of group and general
factor, beta is very sensitive. Alpha, however, can be found from item and test statistics,
beta needs to be estimated by finding the worst split half. Such an estimate is
computationally much more difficult.
 All of these conventional approaches are concerned with generalizing about individual
differences (in response to an item, time, form, rater, or situation) between people. Thus,
the emphasis is upon consistency of rank orders. Classical reliability is a function of large
between subject variability and small within subject variability. It is unable to estimate
the within subject precision.

An alternative method (Latent Response Theory or Item Response Theory) is to determine
the precision of the estimate of a particular person’s position on a latent variable.

16.4 Keywords

Reliability: The reliability is the correlation between two parallel tests and is equal to the
squared correlation of the test with the construct.
Congeneric tests allow all parameters to vary but require at least four tests to estimate parameters.

k k
I 
Domain variance: Domain variance =  V  Clj =  (variances) +  (covariances)
I 1 j  l

Components of variance: Components of variance associated with a test score include general
test variance, group variance, specific item variance, and error variance.
Coefficient alpha is the average of all possible splits, and over estimates the general and
underestimates the total common variance. It is a lower bound estimate of reliable variance.

16.5 Self Assessment

1. The .................... is the correlation between two parallel tests and is equal to the squared
correlation of the test with the construct.
2. .................... tests allow all parameters to vary but require at least four tests to estimate
parameters.
3. .................... associated with a test score include general test variance, group variance,
specific item variance, and error variance.
4. .................... is the average of all possible splits, and over estimates the general and
underestimates the total common variance. It is a lower bound estimate of reliable variance.

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