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Design of Experiments

Peter Ralph

7 October 2021 – Advanced Biological Statistics

Experimental design

Goals of an experiment

What do we want to know?

How do we measure it?

This can be done by observation or experiment.

What’s an experiment?

An experiment is a study in which the values of important variables (e.g., group membership, dosage) are determined by the experimenters.

Otherwise, it is an observational study.

Note that controlling the set-up doesn’t necessarily make it a good experiment.

A biological example to get us started

Say you perform an experiment on two different strains of stickleback fish, one from an ocean population (RS) and one from a freshwater lake (BP) by making them microbe free. Microbes in the gut are known to interact with the gut epithelium in ways that lead to a proper maturation of the immune system.

Experimental setup: You decide to carry out an experiment by treating multiple fish from each strain so that some of them have a conventional microbiota, and some of them are inoculated with only one bacterial species. You then measure the levels of gene expression in the stickleback gut using RNA-seq. Because you have a suspicion that the sex of the fish might be important, you track it too.

stickleback experiment

terms related to experiments

from Logan, Biostatistical Design and Analysis Using R

What makes a good study?

  • Will we have the power to detect the effect of interest?

    • What are the sources of noise?
    • How big do we expect the effect to be?

  • How generalizable will the results be?

    • How representative is the sample? Of what group?

  • What are possible causal explanations?

    • What are possible confounding factors?

Considerations

  1. Where do the samples come from?
  2. Sample size, replication, and balance across groups
  3. Controls: setting up good comparisons
  4. Randomization!

For (2), remember that \[\begin{equation} \text{(margin of error)} \propto \frac{\sigma}{\sqrt{n}} . \end{equation}\]

Toxoplasma gondii infection rates and measures of aggregate neuroticism:

country prevalence N18 country prevalence N18
Argentina 52.7 51.3 Japan 12.3 50.7
Australia 28.0 48.6 Netherlands 24.5 48.6
Austria 36.0 48.3 Norway 8.6 47.4
Belgium 46.8 49.6 Peru 32.9 48.5
Brazil 66.9 53.7 Poland 46.5 50.7
China 24.3 53.1 South Korea 4.3 48.4
Croatia 37.4 49.3 Slovenia 30.9 50.6
Czech Rep 26.6 51.4 Spain 22.7 49.7
Denmark 22.0 50.3 Sweden 12.5 46.3
Ethiopia 16.4 48.8 Switzerland 36.7 47.5
France 45.0 52.7 Thailand 11.2 48.9
Germany 42.7 48.1 Turkey 46.8 51.4
Hungary 58.9 53.8 UK 6.6 50.1
Indonesia 46.2 50.0 USA 12.3 48.1
Ireland 25.0 50.1 Yugoslavia 66.8 51.1
Italy 32.6 52.6 NA NA

Lafferty 2006, Can the common brain parasite, Toxoplasma gondii, influence human culture?

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