### Abstract Paper (PDF)

Wallis (2013) provides an account of an empirical evaluation of Binomial confidence intervals and contingency test formulae. The main take-home message of that article was that it is possible to evaluate statistical methods objectively and provide advice to researchers that is based on an objective computational assessment.

In this article we develop the evaluation of that article further by re-weighting estimates of error using Binomial and Fisher weighting, which is equivalent to an ‘exhaustive Monte-Carlo simulation’. We also develop an argument concerning key attributes of difference intervals: that we are not merely concerned with when differences are zero (conventionally equivalent to a significance test) but also accurate estimation when difference may be non-zero (necessary for plotting data and comparing differences).

### 1. Introduction

All statistical procedures may be evaluated in terms of the rate of two distinct types of error.

**Type I errors**(false positives): this is evidence of so-called ‘radical’ or ‘anti-conservative’ behaviour, i.e.*rejecting*null hypotheses which should not have been rejected, and**Type II errors**(false negatives): this is evidence of ‘conservative’ behaviour, i.e.*retaining or failing to reject*null hypotheses unnecessarily.

It is customary to treat these errors separately because the consequences of rejecting and retaining a null hypothesis are qualitatively distinct. Continue reading “Further evaluation of Binomial confidence intervals”