ASRB NET Factorial Experiments, Confounding, Split- & Strip-Plot Designs: practice questions

1 · Factorial experiments: main effects and interactions · medium

In a 3 x 4 factorial (A at 3 levels, B at 4) in an RCBD with 3 replications and error mean square MSE, what is the standard error of the difference between two A means?

1. The square root of (2 MSE / 9)
2. The square root of (2 MSE / 4)
3. The square root of (2 MSE / 12)
4. The square root of (2 MSE / 3)

2 · Total and partial confounding · hard

Confounding AB and ABC in a 2^3 in four blocks of two would be a bad choice because:

1. AB and ABC cannot both be confounded in a 2^3 for any block size
2. Four blocks of two leave no degrees of freedom for any main effect
3. Their generalised interaction ABC^2 is confounded with replicates
4. Their generalised interaction C, a main effect, is also confounded

3 · Fractional factorials and aliasing · medium

A significant contrast in a 2^(4-1) (I = ABCD) estimates AC + BD. How can the two effects be separated?

1. Assume both effects are equal and halve the estimate
2. Test the contrast against a larger error mean square
3. Repeat the same half fraction with more replicates
4. Run the complementary or fold-over fraction

4 · Strip-plot (split-block) designs · medium

How are the two factors randomised in a strip-plot design?

1. Each factor is randomised to its strips independently in every block
2. Both factors are randomised together over all intersection plots
3. Each factor occurs once in every row and column of the block
4. The second factor is randomised within each plot of the first factor

5 · Strip-plot (split-block) designs · medium

A trial crosses four irrigation methods (channels across the block) with three tillage methods (tractor passes along the block). Which design fits?

1. A completely randomised design over the 12 combinations of plots
2. A Latin square with irrigation as rows and tillage as columns
3. A split-plot design with tillage randomised inside each irrigation plot
4. A strip-plot design with irrigation and tillage in perpendicular strips

6 · Factorials with extra (control) treatments · medium

A 3 x 3 factorial plus one control is in an RCBD. How are the 9 treatment degrees of freedom split?

1. Control vs rest 2, A 2, B 2, A x B 3
2. A 3, B 3, A x B 3, with the control in A
3. Control vs rest 1, A 3, B 3, A x B 2
4. Control vs rest 1, A 2, B 2, A x B 4

7 · Factorials with extra (control) treatments · hard

A 2 x 2 factorial plus one control in an RCBD with 4 replications: how many error degrees of freedom are there?

1. 15
2. 16
3. 12
4. 9

8 · Crossover (changeover) designs · easy

In a crossover design, each experimental unit:

1. Receives all treatments at once on different parts of its body
2. Receives a sequence of different treatments in successive periods
3. Receives one treatment for the whole trial, chosen at random
4. Receives the same treatment repeatedly in every period of the trial

9 · Crossover (changeover) designs · medium

Why are crossover designs efficient in animal experiments?

1. They avoid the need for any randomisation of treatment order
2. Between-animal variation is removed from treatment comparisons
3. Each animal needs to be measured only once during the trial
4. They allow carry-over effects to be ignored in the analysis

10 · Factorial experiments: main effects and interactions · easy

A factorial set of treatments can be laid out in which designs?

1. Only a Latin square design
2. Any basic design: CRD, RCBD or Latin square
3. Only a split-plot design
4. Only a completely randomised design