A biologist working in the Outback of Australia is studying the effects of land-use by tourists (campers, fishers, etc.) on vegetation cover in a river gorge of the outback. There is a river that runs along the centre of the gorge and there is also a road that runs parallel to the river. People move along the river and also along the road in these gorges. Certain areas are known to be used most often by tourists, while others are not. The biologist is therefore also interested in whether the effect of the usage (if any) on vegetation cover is different near the roads as opposed to near the rivers, and also whether there is a clear decrease in usage with distance from the thoroughfares (either river or road).

Factor 1: Usage, 2 levels (high use vs low use), fixed;

Factor 2: Transects, 6 levels, random, nested in factor 1;

Factor 3: Type of thoroughfare, 2 levels (river vs road), fixed;

Factor 4: Distance from thoroughfare, 10 levels (1m-10m), fixed;

n = 2 replicate quadrats per combination of factors

a. Write down the model for the above experimental design, making sure you define your notation and any relevant assumptions.

b. Determine the degrees of freedom (df) and the expected mean squares (EMS) for each term in the model. (Use a table of multipliers if you wish).

c.  Write down the F-ratio of appropriate mean squares that would be used to test each term in the model.