Experimental Design
Swidbert R. Ott
This week’s ILOs
As on Blackboard
- Recognize pseudoreplication in experimental designs, and design experiments that are based on independent replicates.
- Explain the importance of independent replication and consequences of pseudoreplication in relation to SSQ, Mean Squares, \(F\)-ratios and \(P\)-values.
- Recognize systematic designs and sources of bias, and use full randomisation in your designs.
- Apply blocking as a design method, assess its importance in a given study, and interpret models that implement blocked designs.
- Assess the orthogonality of data, and identify the consequences of a departure from orthogonality for the analysis.
Quick warm-up
Come up with a pseudo-replication scenario (other than lecture examples).
- Can be whatever you like;
- Give enough detail to briefly describe the setting.
Anxious Mice
- To test a new anxiolytic, Nofearin, you measure fearfulness in mice.
- You have ethics approval for using a total of 24 mice.
- You suspect that male mice are generally more fearful, so you want to use both male and female mice in your test.
Come up with…
- the worst possible design that you can think of…;
- a design that is orthogonal and balanced;
- a design that is orthogonal but unbalanced.
Write down the main issue with non-orthogonality.
Design Template
| F | M | |
|---|---|---|
| Nofearin | \(n_1\) | \(n_2\) |
| Placebo | \(n_3\) | \(n_4\) |
where
\[n_1 + n_2 + n_3 + n_4 = 24\]
Non-orthogonal designs
Totally confounded / non-orthogonal:
| F | M | |
|---|---|---|
| Nofearin | 12 | 0 |
| Placebo | 0 | 12 |
Severely non-orthogonal: treatment and sex share information
| F | M | |
|---|---|---|
| Nofearin | 9 | 3 |
| Placebo | 3 | 9 |
Orthogonal designs
Balanced
| F | M | |
|---|---|---|
| Nofearin | 6 | 6 |
| Placebo | 6 | 6 |
Unbalanced for sex
| F | M | |
|---|---|---|
| Nofearin | 3 | 9 |
| Placebo | 3 | 9 |
Model for non-orthogonal case
| F | M | |
|---|---|---|
| Nofearin | 9 | 3 |
| Placebo | 3 | 9 |
- Write model code
lm(). - What is the disadvantage over orthogonal design?
More Anxious Mice
- You want to test Nofearin against a placebo control in mice.
- You have ethics approval for using a total of 24 mice.
- No mouse mum has 24 babies in a litter… in your out-bred strain, you can expect litters of 8 or more.
What to do – for now, ignoring sex?
- If your litters turn out to be 9, 8 and 11 mice?
- If your litters come out as 10, 7 and 8 mice?
Block by litter
| Litter A | Litter B | Litter C | |
|---|---|---|---|
| Nofearin | 4 | 4 | 4 |
| Placebo | 4 | 4 | 4 |
What if the litter sizes come out as A = 10, B = 7, C = 8 mice?
| Litter A | Litter B | Litter C | |
|---|---|---|---|
| Nofearin | 5 | 3 | 4 |
| Placebo | 5 | 3 | 4 |
Link to another concept?
Assume you have two litters, A and B, of 12 mice each. Litter A gets Nofearin, litter B gets placebo. If you ignore litter in your analysis (e.g., simple t-test), what concept is applicable?
Pseudo-replication: replicates are not independent.
| Litter A | Litter B | |
|---|---|---|
| Nofearin | 12 | 0 |
| Placebo | 0 | 12 |
(in this design from hell, you can’t factor in litter…)
Model Output
options(contrasts = rep ("contr.sum", 2)) # global
m.1 <- lm(fear ~ litter + treat, data = Anx)
s.1 <- summary(m.1)
signif(s.1$coefficients, 2) Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.50 0.19 29.00 1.1e-17
litter1 0.24 0.27 0.89 3.8e-01
litter2 -0.72 0.27 -2.60 1.6e-02
treat1 -0.51 0.19 -2.70 1.5e-02- What is the fear level in the Nofearin-treated mice?
- What is the difference in fear level between Nofearin and Placebo?
Plotted
Intercept
Intercept +/- treat1 effect
BS2004 Revision lecture W3