To continue, we need to define a couple of terms. The first is a probability density function and the second is a sampling distribution.A probability density function expresses a particular function in terms of integrals. Thus for a frequency distribution smoothed (over repeated sampling) to form a curve as shown below, the area under the [...]
A hypothesis is a supposition made as a basis for research or reasoning without regard for its truth. So says the Oxford dictionary. What starts the hypothesis testing process is just such a supposition. In the justice system example we made, there is a supposition on the part of law enforcement that the apprehended person [...]
When discussing hypothesis testing, I have, from time to time, used the example of the criminal justice system to act as a metaphor for the logic and philosophical issues involved. It remains a good way to pose the logical dilemmas and the types of errors involved and to also discuss the idea of a system [...]
