For which one of the following situations would Kendall’s tau be appropriate?

a) The Mohs scale rates the hardness of minerals. If one mineral can scratch another, it is judged to be harder. (Diamond, the hardest mineral, is a 10.) Is hardness related to the weight of a  cm cube of the mineral?

b) Each member of a group of professional chefs rates the quality of a basket of organic vegetables on a 5-point scale. The same chefs then rate the quality of a basket of nonorganic vegetables on the same scale. Are the organic veggies rated higher?

c) During its initial release, is there an association between the number of downloads of a new smartphone game and the number of hours since it has been released?

d) The Richter scale measures the damage potential of earthquakes. Some scientists think it is best used for judging the relative size of earthquakes and not their absolute size. Are earthquakes around the Pacific “ring of fire” rim stronger in general than those around the Atlantic? Compare earthquakes over a recent 5 year period.

e) A dog’s intelligence can be judged roughly by how many times a new command must be repeated until it is learned. A researcher trained several dogs of each of 4 different breeds, teaching them 3 new commands. Are the breeds equally “intelligent?”