Proportions

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Contents

• Proportions and percentages
• Statistical tests for proportions
  • How do I determine a confidence interval for a proportion in SPSS?
  • I would like to report a different type of confidence interval. How can I calculate that?
  • Z-test for proportions

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Proportions and percentages

Statistical tests for proportions

How do I determine a confidence interval for a proportion in SPSS?

In SPSS, you can very easily determine a confidence interval for a proportion via Analyze -> Descriptives -> Proportion Confidence Intervals. You do not need a data file (.sav) for this and can enter the observed counts directly. You then get the confidence interval for a binomial distribution (Jeffrey's confidence interval, called "Bayesian" in the R package binom).

Via syntax, this function is even richer. You can also use it to compare two observed proportions, for example with the following SPSS syntax: PROPOR NUM=15 10 DENOM=450 500 /LEVEL ALPHA=.05.

The following SPSS syntax shows all the possibilities of the PROPOR function, including examples: PROPOR /HELP.

I would like to report a different type of confidence interval. How can I calculate that?

With the binom-package in R, you can determine many different types of confidence intervals.

If you don't yet have much experience with R, this R code should be enough to get you started:

install.packages(“binom”) require(binom) X = 5 # numerator; change this number to the number of <successes/cases/heads in a coin toss> N = 45 # denominator; change this number to the number of <patients treated/people examined/times a coin was tossed> binom.confint(X, N, conf.level = 0.95) help(binom)

Z-test for proportions

The z-test for proportions is a parametric test for binary/dichotomous variables, which allows you to compare/test an observed proportion in your sample against a pre-specified proportion (the null hypothesis).

However, this test is not suitable for extreme proportions (close to zero or one) or for small samples.

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