NAEP Technical DocumentationExample of a Partially Balanced Incomplete Block (pBIB) Design

The full sample of students is divided into 16 equivalent groups, and each group of students is assigned one of the 16 test booklets. In this design, each cognitive block appears twice in each of the two possible positions, just as in a balanced incomplete block (BIB) design. However, unlike a BIB design, this partially balanced incomplete block design does not require each block to be paired an equal number of times with every other block (Johnson 1992). In this example, each block containing items from a content area is paired with every other block of items from the same content area, but paired with only one block of items from the other content area. Blocks A, B, C, and D contain items from Content Area 1, and blocks E, F, G, and H contain items from Content Area 2. The last table on this page provides a visual representation: within a content area, each block is paired with every other block (see the shaded table cells). The unshaded cells are pairings across content areas for which a complete pairing was not important.

The first six booklet versions pair Content Area 1 blocks, and the second six booklet versions pair Content Area 2 blocks. In the final four booklet versions, each block is paired with a block of items from the other content area.

Example of a pBIB design
Booklet version	Position 1 cognitive block	Position 2 cognitive block
1	A	C
2	B	A
3	C	D
4	D	B
5	A	D
6	B	C
7	H	E
8	E	F
9	F	G
10	G	H
11	G	E
12	H	F
13	C	G
14	D	H
15	E	B
16	F	A
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP).

Number of times each block appears in each position in a pBIB design
Cognitive block	Position 1	Position 2
A	2	2
B	2	2
C	2	2
D	2	2
E	2	2
F	2	2
G	2	2
H	2	2
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP).

Number of times pairs of blocks appear together in a pBIB design
Items	A	B	C	D	E	F	G	H
A	†
B	1	†
C	1	1	†
D	1	1	1	†
E	0	1	0	0	†
F	1	0	0	0	1	†
G	0	0	1	0	1	1	†
H	0	0	0	1	1	1	1	†
† Not applicable. Any given block never appears twice in the same booklet. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP).

Last updated 11 February 2009 (RF)

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