Question

You have been hired as a consultant by building contractor, who have been sued by the owners’ representatives of a large condominium project for shoddy construction work. In order to assess the damages for the various units, the owners’ association sent out a letter to owners and asked if people were willing to make their units available for destructive testing. Destructive testing was conducted in some of these units as a result of the responses. Based on the tests, the owners’ association inferred the damage over the entire condo complex.

(a) Do you think that the inference is valid in this case?

(b) Discuss how proper sampling should proceed in this situation

Answer 1

This is clearly a case of sample selection bias which leads to bias in the OLS estimator in general. It should be clear that inference cannot be conducted properly, since owners who suspect that their unit is faulty are much more likely to agree to destructive testing of their unit than those who have not experienced any problems. The proportion of units assumed to be faulty in the population is bound to be too large when derived through sampling of this type.
The proper sampling method would be to decide on the units to be tested through random sampling. A random number generator should be used to determine the sampled units. The owners' association must guarantee that the randomly selected units are available for destructive testing.