StatTools : Sample Size for Population Parameter Estimation Explained

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Related link :
Sample Size Introduction and Explanation Page
Sample Size to Establish Population Proportions Explanation, Calculations, and Tables Page
Sample Size to Establish Population Means Expalnation and Tables Page
Sample Size to Establish Population Standard Deviation Program Page
Sample Size to Establish Population Standard Deviation Explanations and Tables Page

Introduction Population Mean Population Standard Deviation Population Proportion References
To evaluate a population parameter is probably the most common research activity anywhere. It is the basis of market research, political polling, disease prevalence survey, economic activity, quality of schools, and so on.

Increasingly, the statistics involved are used also in quality control situations, where data obtained from sampling are matched against a bench mark value. The Quality Statistics Explained Page will expand on this use of this statistics.

To design a proper survey to evaluate a population parameter involves many technical issues, such as how to select the right population, what is the most appropriate measurement or question to ask, how to control bias, and so on.

This site addresses only the single issue of estimating sample size requirement during the planning stage, and once the data is obtained, to estimate the accuracy of the results.

Glossary : There are a number of terms used in all population parameter estimations.

  • Parameter value is what we set out to establish.
  • Error is the width of uncertainty
  • Confidence interval is the range within which the true parameter value is likely to be. It is Value ±Error
  • Percent of confidence interval is the percent of time the results we obtained will likely to fall within the confidence interval, should we repeated the survey many time with the same sample size. This represents how sure we can be that the result is within the confidence interval. The most commonly used is the 95% confidence interval, which means that 95% of the time we will get a result within the confidence interval if we were to repeat the survey (or 95% sure).

There are therefore two calculations.

  1. At the planning stage, we define the confidence interval we required, and hence the error tolerable, from these we can estimate the sample size required to do the job.
  2. When all the data has been collected, we know the central value, the variation, and the sample size, from these we can estimate the error, and hence the confidence interval of the results we have.