# SADC Course in Statistics Sample size determinations (Session 11)

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SADC Course in Statistics Sample size determinations (Session 11)

To put your footer here go to View > Header and Footer 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

To put your footer here go to View > Header and Footer 3 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… Traditional view

To put your footer here go to View > Header and Footer 4 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? An example

To put your footer here go to View > Header and Footer 5 Require sample size n so that But we know Hence we need n so that Sample size for estimating a mean

To put your footer here go to View > Header and Footer 6 Above expression implies we need to have i.e. Using N=379, and the previous estimate of s 2 =6671, get n54.8. Thus use n=55. Sample size for estimating a mean

To put your footer here go to View > Header and Footer 7 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. Formula for sample size: with fpc

To put your footer here go to View > Header and Footer 8 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. Formula for sample size: ignoring fpc

To put your footer here go to View > Header and Footer 9 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. Sample size for a proportion

To put your footer here go to View > Header and Footer 10 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/c ase_studies.html http://www.rdg.ac.uk/ssc/workareas/development/c ase_studies.html References

To put your footer here go to View > Header and Footer 11 Practical work follows…