How to Estimate the True Proportion

••• wutwhanfoto/iStock/GettyImages

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.

    Warnings

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

Related Articles

How to Calculate the Confidence Interval of the Mean
How to Calculate Sample Size Formula
How to Calculate Sample Size from a Confidence Interval
How to Figure Survey Percentages
How to Calculate Odds Ratio on a Contingency Table
How to Calculate a T-Score
How to Calculate a T-Statistic
How to Calculate a Demographic Percentage
How to Calculate Standard Error of The Mean
How to Change a Ratio Into a Decimal
How to Calculate P-hat
How to Calculate Relative Standard Error
How to Calculate Skew
How to Calculate Unexplained Variance
How to Calculate CV Values
How to Calculate a P-Value
How to Calculate Incidence & Prevalence
How to Calculate Relative Dispersion
How to Calculate Statistical Difference
What Is the Meaning of Sample Size?