1. Dr.N.K.Tyagi, 30-09-20101 SAMPLE SIZE The average in the form of estimate ‘p’ or mean should be of known along with its precision and tolerable error, they are indicated by  &  respectively. Then the relationship in these errors and SE(p) is as under:  p=Z 1-  SE(p)= Z 1-   (pq/n)  ((N-n)/N)  2 p 2 =Z 2 1-  (pq/n)((N-n)/N) Hence, n=Z 2 1-  Npq/(N  2 p 2 + Z 2 1-  pq)

2. Dr.N.K.Tyagi, 30-09-20102 In case N is not known or n is sufficiently large then:  p=Z 1-  SE(p)= Z 1-   (pq/n)  2 p 2 =Z 2 1-  (pq/n) Hence, n=Z 2 1-  q/(  2 p), where,  is type-I error i.e. level of significance and usually taken 0.05 (95% CI) and  is type-II error and decided by the administrator as a tolerable error usually taken 10-20%.

3. Dr.N.K.Tyagi, 30-09-20103 In case, sampling design is other than SRS then Design Effect (DE) should be multiplied to estimated sample size. As usually in disease surveys the sampling design is cluster sample and DE is taken as 1.5 to 2. Further, while deciding sample size the care should be taken for sample coverage, which is usually 90%, hence, the sample size again should be multiplied by (1/0.9).

4. Dr.N.K.Tyagi, 30-09-20104 While, computing the SE(p) or SE of mean the sampling design should be kept in mind because the formulae for different sampling designs are different.

5. Dr.N.K.Tyagi, 30-09-20105 The computation of n by n=Z 2 1-  /  2 *(q/p), at  =0.05 (i.e. 95% CI) the value of Z is 1.96 and  =10% for p=20%: n=1.96 2 /0.1 2 X 80/20 =1536.64 In case the sampling design is a cluster sampling and design effect (DE) is taken as 2, then the sample size: n=Z 2 1-  /  2 *(q/p) X DE and n=1536.64 X 2=3073,

6. Dr.N.K.Tyagi, 30-09-20106 Further, if sample coverage is taken as 90% then the sample size: n=Z 2 1-  /  2 *(q/p) X DE/0.9=3415 When, many investigations are carried out to decide the case then the sample size in the similar way should be corrected for coverage of each investigation.

7. Dr.N.K.Tyagi, 30-09-20107 Sample size at CI=95%,DE=2 & Sample coverage=90% P/B0.100.200.300.400.50 0.053073313659796851223415 0.107683341519921281854 0.1534151518885569379 0.201921854498320213

8. Dr.N.K.Tyagi, 30-09-20108 In cluster sampling if prevalence is less than 10 per 100, then the variance for cluster prevalence is taken as ‘p’, as it follows Poisson distribution. In this case the V(p)=p/n, where ‘p’ is the prevalence of sample of size ‘n’ considering sampling design as ‘simple random’.

9. Dr.N.K.Tyagi, 30-09-20109 In case the prevalence in clusters is available then the SE(p)=  V(p), and V(p), for sample clusters =(N-n)/(NnM 2 ) X (∑m i 2 (p i -P) 2 /(N-1), where ‘N’ is the total number of clusters from whom the sample of ‘n’ clusters were drawn, ‘M’ is the average cluster size and ‘m i ’ is the size of ‘i th ’ cluster, ‘p’ is the prevalence of the disease in given cluster and ‘P’ the total prevalence of the disease considering ‘random sampling’. The no. of clusters should be maximized.

10. Dr.N.K.Tyagi, 30-09-201010 In case of stratified sampling with proportional allocation the V(p sample ) is: V(p sample )=(  i 2 /(∑  i ) 2 )V(p i ), where  i are the proportion of population and V(p i ) the variance computed for ith stratum. Further, for both cluster and stratified sampling the sample size is computed as in simple random sampling, taking appropriate V(p).

11. Dr.N.K.Tyagi, 30-09-201011 Sample size for quantitative data The sample size (n) for quantitative data can be computed by using mean (  ) and SE of  i.e. SD/  n. n= DE X Z 2 1-  SD 2 / (  2  2 )

12. Dr.N.K.Tyagi, 30-09-201012 SAMPLING Is a process to select (draw) a specified proportion of the population for the study, with a purpose to investigate the characteristics of the population.

13. Dr.N.K.Tyagi, 30-09-201013 Benefits Reduced cost, Greater speed, Greater scope, Greater accuracy. Examples: NFHS, RCH, NSS, etc.

14. Dr.N.K.Tyagi, 30-09-201014 Steps in sample survey Objective of the survey, Population to be sampled, Data to be collected, Degree of Precision Desired, Methods of measurement, Sampling units/Population Frame, Selection of sample, The pretest, Organization of the work, Analysis and interpretation of the results, Generalization of the results. Information gained for future surveys,

15. Dr.N.K.Tyagi, 30-09-201015 The sample size estimation for proportions: The sample estimate ‘p’ of population parameter ‘P’ depends on: Value of ‘P’, Repeatability of sample estimate ‘p’ as is measured by SE(p)=  (N-n)/(N-1)  PQ/n

16. Dr.N.K.Tyagi, 30-09-201016 Types of Studies Cross-sectional studies, Longitudinal studies, Prospective studies, Retrospective studies, Case control studies, Cohort studies, Experimental or control studies, Quasi experimental studies, Single & double blind studies

17. Dr.N.K.Tyagi, 30-09-201017 These topics, though do not come under the head of sampling procedures, but demand special attention because poor work in any of the front ruins the entire survey, whatsoever, the care is taken in sampling.

18. Dr.N.K.Tyagi, 30-09-201018 The role of sampling in drawing conclusions and their generalization: The constants e.g. mean, SD, proportions, ratios, correlation etc, computed from a sample provide information about the sample and are known as descriptive statistics. Their, generalization about population is known as inference or inductive statistics. This generalization of results from sample to population; or from descriptive to inductive is achieved on the strength of the sampling procedures.

19. Dr.N.K.Tyagi, 30-09-201019 Simple Random Sampling (SRS) is a method of selecting ‘n’ units out of the ‘N’ such that every one of the NCn distinct samples has an equal chance of being drawn.

20. Dr.N.K.Tyagi, 30-09-201020 Stratified sampling, Systematic sampling, Cluster sampling, Double sampling, Interpenetrating sampling Inverse sampling Sequential sampling