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Test for one proportion

Description

The Test for one proportion in the Tests menu can be used to test the hypothesis that an observed proportion is equal to a pre-specified proportion.

This test is not performed on data in the spreadsheet, but on statistics you enter in a dialog box.

Required input

  • Observed proportion (%): the observed proportion, expressed as a percentage.
  • Sample size: the sample size or total number of observations.
  • Null Hypothesis value (%): the pre-specified proportion (the value to compare the observed proportion to), expressed as a percentage.

Test for one proportion

When all data have been entered click Test.

Results

The program displays:

  • the 95% Confidence Interval (CI) for the observed proportion
  • z statistic and associated P-value.

If the P-value is less than 0.05, the hypothesis that the observed proportion is equal to the pre-specified proportion value is rejected, and the alternative hypothesis that there is a significant difference between the two proportions can be accepted.

In the Comment input field you can enter a comment or conclusion that will be included on the printed report.

Computational notes

P-value

The significance level, or P-value, is calculated using a general z-test (Altman, 1991):

z-value for single proportion$$ z = \frac {p - p_{exp}} { se(p)} $$

where p is the observed proportion; pexp is the Null hypothesis (or expected) proportion; and se(p) is the standard error of the expected proportion:

Standard error of a proportion$$ se(p) = \sqrt{ \frac {p_{exp} (1 - p_{exp})} {n}} $$

The P-value is the area of the normal distribution that falls outside ±z (see Values of the Normal distribution table).

Normal distribution

Confidence interval

MedCalc calculates the "exact" Clopper-Pearson confidence interval for the observed proportion (Clopper & Pearson, 1934; Fleis et al., 2003).

Literature

  • Altman DG (1991) Practical statistics for medical research. London: Chapman and Hall.
  • Clopper C, Pearson ES (1934) The use of confidence or fiducial limits illustrated in the case of the binomial. Biometrika 26:404–413.
  • Fleiss JL, Levin B, Paik MC (2003) Statistical methods for rates and proportions, 3rd ed. Hoboken: John Wiley & Sons. (p. 26)