1 / 11

Sample size determinations

Sample size determinations. (Session 11). Learning Objectives. By the end of this session, you will be able to explain how sample size calculations are done when using simple random sampling when the main objective is one of estimating a mean or a proportion

calder
Download Presentation

Sample size determinations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Sample size determinations (Session 11)

  2. Learning Objectives By the end of this session, you will be able to • explain how sample size calculations are done when using simple random sampling when the main objective is one of estimating a mean or a proportion • derive the required sample size from first principles for a simple scenario

  3. Traditional view • As indicated in Session 03, statistical theory closely follows the objective of needing to produce estimates of population characteristics • Sample size formulae generally relate to this objective • Note however, that such formulae relate to very simple scenarios… • Here we discuss formulae applicable when the objective is one of estimating a mean or a proportion – see Session 12 for more general issues…

  4. An example We use an example to illustrate… • Consider Example of survey described in Practical 6, question 2. • Aim was to determine the mean area of land per farm, of subsistence farmers, using a simple random sample of farms • Suppose for a future survey of a similar nature, it is required to estimate the mean area of a farm to within 20 acres of the true value with more than 95% confidence • How do we determine the sample size?

  5. Sample size for estimating a mean Require sample size n so that But we know Hence we need n so that

  6. Sample size for estimating a mean Above expression implies we need to have i.e. i.e. Using N=379, and the previous estimate of s2=6671, get n54.8. Thus use n=55.

  7. Formula for sample size: with fpc The general formula for sample size is: Incorporates the finite population correction (fpc). Here d=minimum difference required from true mean, z is the value from z tables to get (1- )100% confidence, and S is the population variance using a suitable estimate.

  8. Formula for sample size: ignoring fpc If the finite population correction can be ignored, this formula simplifies to: Note that the main difficulty in using this expression is that it requires an estimate of the population variance. See separate handout for some hints on how this may be overcome.

  9. Sample size for a proportion The sample size formula when estimating a population proportion is: where Here P is the population proportion which is unknown. So require some approximate knowledge of P, or use P(1-P)=¼ which is its maximum value.

  10. References Lemeshow, S., Hosmer, D.W., Klar, J. and Lwanga, S.K. (1990) Adequacy of Sample Size in Health Studies. W.H.O./Wiley, 0 471 92517 9. SSC (2001) Case Studies of Good Statistical Practice. Case Study 5 & 8. The University of Reading Statistical Services Centre Guideline Series for DFID, available at http://www.rdg.ac.uk/ssc/workareas/development/case_studies.html

  11. Practical work follows…

More Related