Question

Sampling design is highly important for the validity of statistical tests. Consider the following sampling design: The Great Lakes is an important resource for fisheries and biodiversity, and contains many different species of fish, invertebrates, and plants. A researcher wants to determine whether the mean size of fish in the Great Lakes (Lakes Superior, Eerie, Ontario, Michigan, and Huron) is greater than 1m in length. To do so, he samples 10 lake trout in each of three locations in Lake Superior (30 individuals total). He uses a one sample t-test with a critical value of t_0.05(2),29.

Identify all the flaws in this sampling design.

Answer 1

Given sampling design is flawed by: spatial psuedoreplicaiton.

if he is interested in all fish he should sample more than just lake trout.
if he is interested in the full great lakes , he should sample all the lakes.

.

But In the question ,Each site constitutes only one sample and uses T-test.
Each site (which is a group of 10) must therefore be averaged before the test, reducing the sample size to 3 and Degrees of Freedom to 3-1 is 2.
So, Not a very strong test.