9860

Stratification as a Device for Variance Reduction

Stratification is a commonly used device for variance reduction in statistical estimation problems. A judicious choice of the strata may lead to substantial reductions in the variance of the estimator. In this Demonstration, the estimation of the mean of a truncated gamma distribution with parameters [2, 5], adequately normalized, is considered.
Once the strata limits are established, the variance of the estimator depends also on the sample allocation, that is, the sample size allocated to each stratum. This Demonstration affords a simple way to look at the behavior of the variance as a function of strata definition and sample allocation. This variance is compared with the variance in simple random sampling (simple r.s.), that is, the sampling scheme with the same total sample size and no stratification. Moving the sliders for strata definition and sample sizes yields the change in the value of the variance depicted on the scale placed at the right of the distribution plot.
Contrary to common belief, an inadequate stratification may lead to variances greater than those obtained in simple random sampling.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+