How to Estimate the True Proportion

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The proportion of something is the number of observations that meet a certain criterion, divided by the total number of observations. For example, the proportion of males in the population of Americans is the number of American males divided by the number of Americans. The population proportion is this for the entire population. This can rarely be calculated exactly, so it must be estimated.

    Get a random sample of the population. If your sample is not random, estimates of the proportion (and other quantities) may be biased. For example, if you want to estimate the proportion of boys in an elementary school, you could assign a number to each student, then randomly pick a sample by choosing random numbers. The bigger your sample, the more accurate your estimate will be.

    Find the number of observations that meet the criterion in your sample. In our example, we would find how many of the children in our sample were boys.

    Divide this number by the total number of observations in the sample. This is the estimated proportion.

    To see how good this estimate is, the standard formula for a 95 percent confidence interval is p +- 1.96(pq/n) ^ .5, where p is the proportion found in step 3, q = 1 - p, and n is the number of observations.


    • The standard estimate of the confidence interval is not always accurate; for more information, see the article by Agresti et al.


  • "Dictionary of Statistics", Brian Everitt, 1998
  • "American Statistician", Approximate is Better than Exact for Interval Estimation of Binomial Proportions, Alan Agresti et al., 1998
  • "Statistics", David Freedman et al, 2007

About the Author

Peter Flom is a statistician and a learning-disabled adult. He has been writing for many years and has been published in many academic journals in fields such as psychology, drug addiction, epidemiology and others. He holds a Ph.D. in psychometrics from Fordham University.