FAQ/BinomialConfidence - CBU statistics Wiki

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Confidence Interval for Binomial Proportions

The binomial test (e.g. under the NONPARAMETRIC STATISTICS menu in SPSS) may be used to test if a proportion equals a particular constant (usually 0.5) however it does not provide a confidence interval for the magnitude of this difference. (See also the Graduate Statistics Talk on [:StatsCourse2010:Categorical Data Analysis]).

Newcombe (1998) suggests using alternatives to the usual Wald procedure to obtain confidence intervals for a proportion, particularly for proportions less than 0.2 or greater than 0.8. He suggests the exact binomial method and Wilson’s (1927) method provide slightly better coverage. Confidence intervals for both Wald, Wilson and Agresti-Coull methods may be computed by using [attachment:BinomialCIs_wald_rev.xls this spreadsheet]. The latter two are recommended for a single proportion by Brown, Cai and DasGupta (2001).

A limited range of CIs (Pearson-Clopper, Jeffreys and Wald) can be obtained in SPSS using the binomial test as below:

incomp

count

1

23

2

12

 

WEIGHT BY COUNT.
NPTESTS 
  /ONESAMPLE TEST (incomp) 
    BINOMIAL(TESTVALUE=0.5 JEFFREYS SUCCESSCATEGORICAL=FIRST SUCCESSCONTINUOUS=CUTPOINT(MIDPOINT)) 
  /MISSING SCOPE=ANALYSIS USERMISSING=EXCLUDE
  /CRITERIA ALPHA=0.05 CILEVEL=95.
WEIGHT OFF.

You can also obtain confidence intervals for the difference in two proportions [http://www.quantitativeskills.com/sisa/statistics/t-test.htm here.] Formulae used for the difference in proportions in 2x2 tables are described [:FAQ/ChiEqual: here].

  • [:FAQ/BinomialConfidence/2gp:Confidence interval for differences in two independent binomial proportions]
  • [:FAQ/BinomialConfidence/2gpp:Confidence interval for differences in two paired binomial proportions]

References

Brown LD, Cai TT and DasGupta A (2001) Interval estimation for a binomial proportion. Statistical Science 16 101-133.

Newcombe RG. (1998) Two sided confidence intervals for the single proportion: Comparison of seven methods. Statistics in Medicine 1998;17:857-872

Newcombe RG (2012) Confidence intervals for proportions and related measures of effect size. Chapman and Hall:London. (This book also contains details of web links to easy-to-use EXCEL programs located on the CRC press website which will work out the confidence intervals mentioned in the text).

Wilson EB (1927) Probable inference, the law of succession, and statistical inference. J Am Stat Assoc 22, 209-212.

Last updated on 12 February, 2008