Different experimental designs

• Exam #3 this Friday
  • W&S: Ch. 11-15 (excl. 14); R&C: Ch. 3
  • You may bring a formula sheet (2 sided is fine)!!
  • Lab today and tomorrow - review/study session!
• Guest lecturer on Monday - attendance is required.
  • Jelena Pantel will be presenting on her research program - she uses lots of statistics!!

Eliminate bias

Reduce sampling error

To reduce bias (increase accuracy):

• Controls
• Randomization
• Blinding

To reduce sampling error (increase precision):

• Replication
• Balance
• Blocking

Positive control: Oh yeah, well is it better than a handgun?

• Concurrent control
  • Negative control (probably what you're familiar with)
  • Positive control (compare to best method available)
• Historical control
  • When a researcher says “Ain't nobody got time/money for that!”

Key takeaway:

“Careful statement of the hypothesis under test makes it easy to determine what type of control your experiment requires.”
- Ruxton & Colegrave

“These procedures are designed to remove the perception that unconscious bias might taint the results of a study.”

- Ruxton & Colegrave

\[ \mathrm{SE}_{\bar{Y}_{1}-\bar{Y}_{2}} = \sqrt{s_{p}^{2}\left(\frac{1}{n_{1}} + \frac{1}{n_{2}}\right)} \]

“If you know and can measure some factor of experimental units that is likely to explain a substantial fraction of between-subject variation then it can be effective to block on that factor.”
- Ruxton & Colegrave

“Don't block on a factor unless you have a clear expectation that that factor substantially increases between-individual variation.”
- Ruxton & Colegrave

Examples of type of statistics used:

• Paired \( t \)-test (one categorical fixed effect with two levels)
• Two-way fixed effects ANOVA (two categorical fixed effects with more than two levels; one variable is of interest, the other covariate is used to partition variation)
• Two-way mixed effects (two categorical, one fixed effect of interest, and one random effect covariate used to partition variation)
• ANCOVA (one categorical fixed effect of interest, and one numerical covariate): This essentially performs simultaneous regression in the levels of the categorical fixed effect.

Read Whitlock & Schluter, Chapter 14: Designing experiments.