Difference between Independent Proportions and the Square- and-Add Approach

• Published in: Confidence Intervals for Proportions and Related Measures of Effect Size pp. 156 - 189
• Main Author: Newcombe, Robert Gordon
• Format: Book Chapter
• Language: English
• Published: United Kingdom CRC Press 2013; Taylor & Francis Group
• Subjects: BIOLOGY, LIFE SCIENCES; Probability & statistics; Psychological methodology; Cc; Score Interval; Independent Groups; Arr; Parameter Space Points; Minimum Coverage Probability; CI; Sentinel Node; Pi Pi Pi; Wilson Score Interval; Cell Frequencies; Coverage Probability; Wald Interval; Eastern Co-operative Oncology Group; Bayesian Interval; Distal Non-coverage; Confidence Region; Wilson Interval; Independent Proportions; Wilson Method; Wilson Score Method; ECOG; Pi Pi; Single Proportion
• ISBN: 9781439812785; 1439812780
• DOI: 10.1201/b12670-12

The 2 × 2 contingency table is very widely used to display the comparison between two independently sampled proportions or the association between two binary variables. Table 7.1 shows three representations of the 2 × 2 contingency table used to compare a binary outcome variable between two independent groups 1 and 2. In this chapter, and also in Chapter 10 which deals with the ratio of independent proportions, we are assuming that the column totals, m and n, are fixed. For example, the data could come from a randomised trial in which m subjects are allocated to treatment 1 and n subjects are allocated to treatment 2. In statistical parlance, inferences are conditional on the two marginal totals, m and n. This contrasts with the situation in a cross-sectional study, in which often only the table total is fixed. In Chapter 8 we consider a very different 2 × 2 table representing paired binary data.