Survey of Smoking Behavior. Survey of Smoking Behavior. Survey of Smoking Behavior

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Harvey Cameron
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1 Sample HH from Frame HH One-Stage Cluster Survey Population Frame Sample Elements N =, N =, n = population smokes Sample HH from Frame HH Elementary units are different from sampling units Sampled HH but analyzing people Analysis is a ratio estimator, not a binomial variable Variable one (smokers) Analyzed as a ratio estimator Variable two (persons) Same number persons as SRS, 9 Average persons per HH = Number HH =, 8 Student's t Student's t for Confidence Interval Calculations 9 CL 9 CL 99 CL CL CL. 99 CL.76 Number Clusters z Two Scenarios with Sample HH from Frame HH Large and Small have the Same Percentage Smokers How do the findings in a cluster survey where the sample units and elements for analysis are different (i.e., estimating r) compare to a SRS a population where the sample units and elements for analysis are the same (i.e., estimating p)? Smokers are randomly distributed in Smokers within are as variable as among Smokers are not randomly distributed in Smokers within are more or less variable than among Sample Frame HH One Person HH Two Person HH Three Person HH Sample Frame with Random Distribution Persons are Smokers N = N = Average HH size = N = Four Person HH Five Person HH N = N =

2 Random Distribution s Same as SRS Smokers in Population HH Size not Associated with Sample HH from Frame HH Variable One Ratio estimator = Variable Two HH size = HH size = If there is no association between smoking (i.e., variable one) and HH size (i.e., variable two), then the analysis the ratio estimator behaves similar to the analysis a binomial variable in a SRS people rather than 7 Random Distribution s (same variability as SRS) 9 Confidence Intervals from all Possible Samples Cluster Sample with 9 Persons from 9 Sample Frame, with Persons 8 p surveys =. 7 6 te: nearly the same Average SE =. as SE =. for SRS shown earlier 6 confidence intervals did not bracket the true value * * * * * * P = Relation t value to z value Use t for Class Example Cluster Sampling and for Rapid Surveys t value 8 6 t =. for sample (i.e., 9 d.f.) z value = Sample Size minus One 8 tions Variability among Clusters Stated Size Variability HH size = HH size = HH size = HH size = 6 Variability Smokers among Less Variability among Clusters (i.e., ) than SRS HH Size not Associated with 9

3 Variability (i.e., less than SRS) Smokers among Clusters (i.e. ) 9 Confidence Intervals from all Possible Samples One-Stage Cluster Sample with 9 Persons 9 from Sample Frame, with Persons Average SE =. confidence intervals did not bracket the true value ** * * p surveys =.9 P = 7 6 Smokers among Clusters (i.e., ) 9 Confidence Intervals from all Possible Samples One-Stage Cluster Sample with 9 Persons 9 from Sample Frame, with Persons 8 p surveys =. Average SE =. P = 6 confidence intervals did not bracket the true value * * * * * * Same as Slide Medium Variability Smokers among Same Variability among Clusters (i.e., ) as SRS HH Size not Associated with Smokers among More Variable among Clusters (i.e., ) than SRS HH Size not Associated with Same as Slide tions Variability among Clusters Stated Size HH size = HH size = HH size = HH size = (i.e., greater than SRS) Smokers among Clusters (i.e., ) Confidence Intervals from all Possible Samples One-Stage Cluster Sample with 9 Persons from Sample Frame, with Persons p surveys =. P = Average SE = 9.8 confidence intervals did not bracket the true value * * * * *

4 te: this is different than the variance a proportion, or p q n Variance (p x q) Variance a Binomial Variable Smokers in a Group Five Persons p x q x. x.8. x.6.6 x..8 x. x Variability Among and Within Clusters (i.e., ) with person variability among clusters (i.e., ) is less variable than a SRS. Such variability is shown for the 6 in the sample that have persons. p q =. x.6 =. p q =. x.6 =. p q =.6 x. =. Variability HH size =. - - Number Smokers Much more heterogeneity (i.e., dissimilarity) within clusters variability among (i.e., between) clusters arises from high variability within clusters The variance the binomial variable smoking in a group five persons is greatest when - are smokers 6 p q =.6 x. =. p q =.6 x. =. p q =.8 x. =.6 9 Variability Among and Within Clusters (i.e., ) In the total population,, there are that are person In a typical survey smoking behavior involving, one-fifth (or 6) will be -person HH size = Sample HH from Frame HH What happens to the ratio estimator if cluster (i.e., HH) size is associated with smoking? p q = x = p q = x = p q = x = Ratio estimator = Variable One Variable Two smokers homogeneity (i.e., similarity) within clusters variability among (i.e., between) clusters arises from extremely low variability within clusters Does the ratio estimator analyzed for a HH survey still behave the same as a proportion analyzed for a SRS? HH = HH = Persons in large are more likely to smoke than persons in small p q = x = p q = x = p q = x = 7 Variability Among and Within Clusters (i.e., ) with person Medium variability among clusters (i.e., ) is the same variability as a SRS. Such variability is shown for the 6 in the sample that have persons. p q =. x.8 =.6 p q =. x.6 =. p q =.6 x. =. More heterogeneity (i.e., dissimilarity) within clusters Medium Variability HH size = Medium variability among (i.e., between) clusters arises from medium variability within clusters Sample HH from Frame HH Complete distortion variability smoking within Plus, smoking status varies dramatically with HH size Question to be answered Does this extreme situation bias the use a ratio estimator to determine the proportion who smoke? p q =.6 x. =. p q =.8 x. =.6 p q = x = 8

5 tions Variability where Cluster (i.e., HH) Size is Associated with Stated Size HH size = HH size = Summary Effects on SE and Mean What happens to the standard error and mean the ratio estimator as variability smoking changes among and within clusters (i.e., )? Type Survey SRS Among -- Variability Within -- SE (). Mean Smokers. Bias HH size = 8 HH size = 8 Medium Medium * Slight Through it all, the CI the ratio estimator still behaves like a 9 CI should behave * not associated with HH size ** associated with HH size Smokers among More Variable among Clusters (i.e., ) than SRS HH Size Associated with Reading Assignment 7 To be Discussed Next 6 8 Download from: 6 (i.e., greater than SRS) Smokers among Clusters (i.e., ) Confidence Intervals from all Possible Samples One-Stage Cluster Sample with 9 Persons from Sample Frame, with Persons p surveys =.8 Slight bias 7 6 confidence intervals did not bracket the true value * * * * * P = Average SE = 9.8

Survey of Smoking Behavior. Samples and Elements. Survey of Smoking Behavior. Samples and Elements

Survey of Smoking Behavior. Samples and Elements. Survey of Smoking Behavior. Samples and Elements s and Elements Units are Same as Elementary Units Frame Elements Analyzed as a binomial variable 9 Persons from, Frame Elements N =, N =, n = 9 Analyzed as a binomial variable HIV+ HIV- % population smokes