 
 WJR Frequency Table: Cluster vs.
BCA
 Differences
Required
Difference Between Cluster Score and BCA (Ext) Score at 5% Level of
Statistical Significance and Frequencies of Such Differences 



Difference
Score 
Cumulative % 
BCA
vs Cluster 


1% 
2% 
5% 
10% 
15% 
20% 
25% 
BCA(Ext) 

Glr 
8.57 

33 
30 
25 
21 
18 
16 
15 


Gsm 
11.57 

32 
28 
24 
20 
18 
16 
14 


Gs 
11.98 

38 
34 
29 
24 
21 
19 
17 


Ga 
10.88 

34 
30 
24 
20 
18 
16 
15 


Gv 
13.95 

39 
35 
29 
24 
22 
19 
17 


Gc 
9.01 

29 
26 
21 
18 
16 
14 
12 


Gf 
8.47 

31 
28 
23 
19 
16 
15 
13 












Required
Difference Between Cluster Score and BCA (Std) Score at 5% Level of
Statistical Significance and Frequencies of Such Differences 



Difference
Score

Cumulative % 
BCA
vs Cluster 


1% 
2% 
5% 
10% 
15% 
20% 
25% 
BCA(Std) 

MFN 
10.23 

37 
34 
28 
23 
20 
18 
16 


MFS 
10.72 

32 
29 
24 
21 
18 
16 
15 


VM 
14.82 

41 
35 
30 
25 
22 
19 
17 


IncW 
13.44 

40 
36 
30 
25 
22 
19 
18 


VCl 
17.09 

42 
38 
32 
27 
23 
21 
19 


PVoc 
12.01 

33 
30 
25 
21 
18 
16 
14 


A/S 
10.60 

36 
32 
26 
22 
19 
17 
15 
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. 
