 
WJR Frequency Table: Cluster
Differences
Required
Difference Between Single Cluster Scores and Mean Cluster Score at 5%
Level of Statistical Significance and Frequencies of Such Differences 

Average of 7
Clusters 


Significance
Level 

Cumulative % 
Cluster 

.05 

1% 
2% 
5% 
10% 
15% 
20% 
25% 
Longterm
retrieval 

9.40 

42 
38 
31 
25 
22 
19 
17 
Shortterm
memory 

13.03 

39 
35 
28 
24 
21 
18 
16 
Processing
Speed 

13.51 

35 
32 
27 
22 
19 
17 
16 
Auditory
Processing 

12.20 

43 
40 
33 
28 
24 
22 
19 
Visual
Processing 

15.85 

48 
44 
37 
31 
27 
23 
21 
Comprehension
Knowledge 

9.94 

34 
31 
26 
21 
18 
16 
14 
Fluid
Reasoning 

9.28 

40 
37 
30 
26 
22 
19 
17 
Note:
The differences required for statistical significance are based on the
average standard errors of measurement across all ages and calculated with
the following formula provided by Davis (1959): Difference score = Z
SQRT[(SEmt^2)/K^2+[(K2)/K](SEmi^2)], where Z is the normal curve value
associated with the desired significance level derived with the Bonferroni
correction for multiple comparisons, K is the number of tests in the
comparison, SEmt^2 is the sum of the squared standard errors of
measurement for all tests in the comparison, and SEmi^2 is the squared
standard error of measurement for the test of interest.
John and Ron thank Dr. Woodcock for his very generous granting of access to
portions of the WJR standardization data and for his kind permission to post these tables. 
Woodcock, R. W., & Mather, N. (1989). WJR Tests of Cognitive Ability Standard and Supplemental Batteries: Examiner's Manual. In R. W. Woodcock &
M. B. Johnson, WoodcockJohnson PsychoEducational BatteryRevised. Chicago: Riverside Publishing Co. All rights reserved. 
