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An Introduction to Experimental Design ANOVA and ANCOVA

4 Some initial examples and challenge questions

In this section, we will review a field based experimental design example. There are challenge questions to answer.

We will also introduce tools to generate randomised experimental designs - this is a good trick to have up your sleeves!

4.1 Designing your first experiment

You are challenged to design an Arctic field manipulation experiment to evaluate UV-B radiation and increased \(CO_{2}\) impacts on plant growth.

Context: an arctic tundra study

  • Increasing ultraviolet-B (+UV-B) radiation from ozone depletion (the arctic ozone hole)
  • Increasing atmospheric \(CO_{2}\) (\(+CO_{2}\)) from anthropogenic emissions
  • For plants: +UV-B potentially harmful, +CO2 potentially beneficial

Hypotheses

  • Elevated (+) UV-B radiation will reduce the growth of arctic plants
  • Elevated (+) \(CO_{2}\) will increase the growth of arctic plants

The resources available to you are constrained. The arctic research station has given permission for 16 plots (each 2m x 2m) in the natural vegetation nearby.

  • One +UV-B plot (2m x 2m) costs £4000 (this provides the UV-B lamps, frame, power and control system, wooden walkways around the plots)
  • One \(+CO_{2}\) plot (2m x 2m) costs £6000 (this provides a \(CO_{2}\) release system, \(CO_{2}\) control and covers \(CO_{2}\) purchase costs, wooden walkways around the plots)
  • One control plot (2m x 2m) costs £200 (marking posts, wooden walkways around the plots)

You have a budget of £61,000

Design an experiment to test the hypotheses (i.e. the design of the plots and treatments including replication, not what measurements you will take - which will be plant growth rates….). Think hard about this. How many treatments do you have? How many plots/treatment would you like to allocate? Is this possible? Will this be a balanced design, given your max budget? If it isn’t, what rule can you use to allocate them replicates to treatments?

Write an answer down, before moving to the next section (this is part of the DO THIS package of challenges). We’ll provide the answer separately!