Statnote 39: The binomial distribution: comparing two proportions

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Abstract

Many populations consist of two classes only, e.g., alive or dead, present or absent, clean or dirty, infected or non-infected, and it is the proportion or percentage of observations that fall into one of these classes that is of interest to an investigator. An observation that falls into one of the two classes is considered a ‘success’ (S), and ‘p’ is defined as the proportion of observations falling into that class. If a random sample of size ‘n’ is obtained from a population, the probability of obtaining 0, 1, 2, 3, etc., successes is then given by the binomial distribution. The binomial distribution can be used as the basis of a number of statistical tests but is most useful when comparing two proportions. This statnote describes two such scenarios in which the binomial distribution is used to compare: (1) two proportions when the samples are independent and (2) two proportions when the samples are paired.

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Details

Original languageEnglish
Pages30-33
Number of pages4
Volume15
Issue number4
JournalMicrobiologist
Publication statusPublished - Dec 2014

    Keywords

  • Binomial distribution, Rules of probability, Comparing two proportions

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