Contemporary Frequentist Views of the $2\times2$ Binomial Trial
2017
The 2 × 2 table is the simplest of data structures yet it is of immense
practical importance. It is also just complex enough to provide a theoretical
testing ground for general frequentist methods. Yet after 70 years
of debate, its correct analysis is still not settled. Rather than recount the entire
history, our review is motivated by contemporary developments in likelihood
and testing theory as well as computational advances. We will look at
both conditional and unconditional tests. Within the conditional framework,
we explain the relationship of Fisher’s test with variants such as mid-p and
Liebermeister’s test, as well as modern developments in likelihood theory,
such as p
∗ and approximate conditioning. Within an unconditional framework,
we consider four modern methods of correcting approximate tests to
properly control size by accounting for the unknown value of the nuisance
parameter: maximisation (M), partial maximisation (B), estimation (E) and
estimation followed by maximisation (E+M). Under the conditional model,
we recommend Fisher’s test. For the unconditional model, amongst standard
approximate methods, Liebermeister’s tests come closest to controlling size.
However, our best recommendation is the E procedure applied to the signed
root likelihood statistic, as this performs very well in terms of size and power
and is easily computed. We support our assertions with a numerical study.
Keywords:
- Correction
- Source
- Cite
- Save
- Machine Reading By IdeaReader
17
References
7
Citations
NaN
KQI