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## Interdisciplinaria

*versión On-line* ISSN 1668-7027

#### Resumen

NEWCOMBE, Robert G.
y
MERINO SOTO, Cesar. Confidence intervals for estimations of proportions and their differences.* Interdisciplinaria* [online].
2006,
vol.23, n.2, pp. 141-154.
ISSN 1668-7027.

It's nowadays accepted by many journals in diverse areas of health and social sciences, that confidence intervals give more descriptive information and they are better than hypothesis tests to express uncertainty resulting from limited sample size. The tool confidence intervals is a very useful descriptive frame to the researcher and to the consumer of statistical results, and their value as statistical summary is very important in descriptive and comparative studies. During decades, hypothesis tests have been the main support of statistical inference in comparative studies, whereas in comparative-descriptive research in social sciences, the method of analysis for categorical variables has been unusual. In fact, good methods to calculate confidence intervals for proportions and their differences, have not been generally available to researchers. Moreover, these methods have not been popular because they remain in statistical articles and away from non specialized users in mathematical knowledge. In this article methods based in works of Newcombe (1998a, 1998b, 1998c) and Wilson (1927) are reported. They overcome traditional methods for the proportion confidence intervals calculation. Although this calculation is moderately simple, we took advantage of the computational technology to facilitate the process of calculus and to diminish errors. An Excel spreadsheet is now available, in Spanish, English and Welsh versions. Also equivalent versions were developed in the language of macros for SPSS and Minitab, which are all available in the internet address mentioned within the text of the article. These devices enable researchers to calculate the intervals using proven good methods; these methods come from the score method, which is derived from Wilson's work (1927). The typical situation for calculating intervals of confidence for proportions comes from a single sample of participants, and/or from a comparison between dependent and independent samples.The score method takes advantage of the calculation of a simple proportion, to extend it to the comparison between dependent and independent proportions. The rationality of this extension is intuitive and is applied easily by means of the computer programs mentioned previously. Examples of confidence intervals calculus for a simple proportion and differences of proportions are presented and a discussion about their careful use in the context of research design is developed. Particularly, confidence intervals appear to be one of the most useful forms to express the uncertainty in research findings, since the necessity to design studies using a limited sample from the population, makes that the appropriate interpretation of the intervals becomes a point of learning and agreement that the authors put in relevance. Finally, the reader must have in mind that the estimation of the intervals does not give information in absolute terms, because it likewise offers a probability of containing the population value of interest (proportion). On the other hand, trying to reach the exact results is only one part of the problem. There are other important aspects as the choice of the statistical analysis and the study design, and within this last one, the sampling process, that continues being a prevalent source of weakness in research literature. If the specific sample is biased towards the population that we are trying to study (for example, certain population segment can be more motivated to fill in questionnaires or to participate in studies, in which case we are in front of a self-selected sample) or towards our expectations, every calculus that will be done will be biased. We hope that the readers of this article are aware and benefit of the usefulness of this old wine in new bottle method.

**Palabras llave
:
**Confidence intervals; Proportions; Differences; Statistical method.