ICAR AICE-JRF/SRF Incomplete Block Designs & Design Construction: practice questions

1 · General block design: C-matrix, connectedness and balance · medium

What is the adjusted total Q_i of treatment i in a block design?

1. T_i plus the sum of the totals of blocks not containing treatment i
2. T_i minus the sum of (block total / block size) over its blocks
3. T_i minus (grand mean x r_i), ignoring which blocks held treatment i
4. T_i divided by the number of blocks in which treatment i appears

2 · General block design: C-matrix, connectedness and balance · medium

Which term describes a design in which no treatment occurs more than once in a block?

1. Binary
2. Equireplicate
3. Resolvable
4. Proper

3 · Intra-block analysis and recovery of inter-block information · medium

In the intra-block analysis of a block design with n plots, b blocks and v treatments, how many error degrees of freedom are there?

1. n - b - v
2. n - v
3. (b - 1)(v - 1)
4. n - b - v + 1

4 · Construction of BIBDs: finite fields, difference sets and MOLS · hard

Why is {0, 1, 2} modulo 7 not a difference set?

1. It has three elements, but a difference set needs four
2. It contains the element zero, which is not allowed
3. Its elements are consecutive, so it gives a Latin square
4. Differences 1 and 6 occur twice; 3 and 4 never occur

5 · Partially balanced incomplete block designs with two associate classes · easy

Why were PBIBDs introduced?

1. PBIBDs remove the need for any blocking in field trials
2. PBIBDs usually give every pair of treatments the same variance
3. BIBDs exist for few parameter sets and need many replicates
4. BIBDs cannot be analysed by the intra-block method at all

6 · Partially balanced incomplete block designs with two associate classes · medium

In a triangular PBIBD with parameter q, how many first associates does each treatment have?

1. q - 1
2. (q - 2)(q - 3)/2
3. q(q - 1)/2
4. 2(q - 2)

7 · Lattice designs: square, rectangular and cubic · easy

A square lattice for 25 varieties uses blocks of what size?

1. 25
2. 6
3. 5
4. 10

8 · Youden squares and row-column designs · medium

In a Youden square, why can row effects be removed without adjusting treatments?

1. Row effects are always assumed to be zero in the model
2. Each treatment is in every row, so rows are orthogonal
3. Rows are random effects and never enter the analysis
4. Rows contain only one treatment each, so they have no effect

9 · Efficiency factors of incomplete block designs · medium

In an equireplicate incomplete block design with efficiency factor E, what is the average variance of an elementary contrast?

1. sigma^2 / (r E)
2. 2 sigma^2 / (r E)
3. 2 sigma^2 E / r
4. 2 sigma^2 / r

10 · Efficiency factors of incomplete block designs · medium

What is the efficiency factor of the unreduced BIBD with v = 4 and k = 2?

1. 0.500
2. 0.667
3. 1.000
4. 0.750