Page 236 - DMTH404_STATISTICS

Statistics

Notes Vt = V1 =!V2  c = c = c 
1 2 12

Vt – v
c1 = i = average covariance
k*(k-1)
V – v

2
C12= k c12 ==> C12= k * t i
2
k*(k-1)
V – v

2
k * t i
k*(k-1) V – v k

rx1x2 =  t i *

V V k 1
t t
This allows us to find coefficient alpha without finding the average interitem correlation.
The effect of test length of internal consistency reliability.
Number of items Average r Average r
0.2 0.1
1 0.20 0.10
2 0.33 0.18
4 0.50 0.31
8 0.67 0.47
16 0.80 0.64
32 0.89 0.78
64 0.94 0.88
128 0.97 0.93

Estimates of reliability reflect both the length of the test as well as the average inter-item
correlation. To report the internal consistency of a domain (rather than a specific test with a
specific length, it is possible to report the “alpha1” for the test.

alpha
Average interitem r = alpha1 =
alpha + k*(1-alpha)
This allows us to find the average internal consistency of a scale independent of test length.


V – v k
because  = t i * is easy to estimate from the basic test statistics and is an estimate of

V k 1
t
the amount of test variance that is construct related, it should be reported whenever a particular
inventory is used.
Coefficients Alpha, Beta and Omega - 1

Components of variance associated with a test score include general test variance, group variance,
specific item variance, and error variance.

General Group Specific Error
Reliable Variance
Common Shared Variance

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