Types of Sampling Plans. Types of Sampling Plans. Sampling Procedures. Probability Samples -Simple Random sample -Stratified sample -Cluster sample

Transcription

1 Samplg Procedures Defe the Populato Idetfy the Samplg Frame Select a Samplg Procedure Determe the Sample Sze Select the Sample Elemets Collect the Data Types of Samplg Plas o-probablty Samples -Coveece sample -Judgmet sample -Quota sample Types of Samplg Plas Probablty Samples -Smple Radom sample -Stratfed sample -Cluster sample

2 Stratfed Samplg. Exclusve & Collectvely Exhaustve Subgroups Stratfcato varables?. Select Exclusve & Collectvely Exhaustve a depedet radom Sample each stratum Sample sze wth each stratum? Proportoate or dsproportoate? Example : Retal Sales of Folger s coffee Stratfcato varable?. Sze of store. Weeked or ot 3. Rego of the coutry The Purpose of Stratfed Samplg? A decrease the stadard error of a estmator. Decomposg Populato Varace Ex ( µ ) E[( x µ ) G ] P[ G ] + E[( x µ ) G ] P[ G ] E[( x µ ) ] + E[( x µ ) ] E[( x µ ) + ( µ µ )] + E[( x µ ) ] E[( x ) + ( ) ] + [( ) ] [ σ + E( µ µ ) ] + [ σ + E( µ µ ) ] µ µ µ E x µ

3 The Stadard Devato of Sample Mea Uder Stratfed Samplg Var( w x w x ) w w wvar( x) + ( ) + wvar x σ σ w σ wσ w + w + f proportoate (.., e w ; w) σ The Stadard Devato of Sample Mea Uder Smple Radom Samplg Var( x) σ w w w w σ + σ + ( µ µ ) + ( µ µ ) Stratum Example (Let 3) μ s s Smple Radom Samplg {6, 30 } {3,3,,} σ 6 Var( x) > x 8 σ ( 5) /6 Mea: µ( )/65 Varace: σ 36/66

4 Proportoate Stratfed Samplg Dsproportoate Samplg ( optmal allocato ) Let σ jσ j j Stratfed samplg results a decrease the stadard error of a estmator Var( w x w x ) w w + σ σ w w f f proportoate dsproportoate Optmal allocato acheves hgher effcecy. /3 < /

5 Stratum Aother Example {6, 30 } {7,7,9,9} μ 8 8 s Ca proportoate stratfed samplg reduce stadard devato of estmator? How about dsproportoate stratfed samplg? s Cluster Samplg. Exclusve & collectvely exhaustve group ( clusters). Radomly select some clusters amog them () Oe-stage cluster samplg: Use all elemets those selected groups. () Two-stage cluster samplg : Select a radom sample of elemets from wth the selected groups. Area Samplg. Lst all cty blocks, B. Choose a radom sample B from B 3. Select all elemets the chose blocks B oe-stage area samplg Two-stage Area Samplg Smple two-stage area samplg Each cluster has the same prob. of beg selected the frst stage. Probablty Proportoal to Sze (PPS) Each cluster has the prob. of beg selected proportoal to ts sze.

6 Example Block umber # of households Average Icome B ; Smple oe stage area samplg : Block umber 3 # of households Average Icome μ 0.6x x x000+0.x () Smple two-stage E( x) 850 () PPS : E(x) µ Example Joh, a sales maager, wats to estmate the curret retal sales for a brad. Accordg to past studes, the populato dstrbuto ad average retal sales based o the store sze ad the cty block umber were as follows:

7 Store sze Block# 3 Large 0 ($0,000) 0 ($0,000) 0 ($5,000) Small 0 ($5,000) 0 ($0,000) 0 ($5,000) Total Plaed sample proporto 0/00 Stratfed samplg or cluster samplg? If stratfed samplg ad sample sze 0, What s the approprate stratfcato varable? Total What s the sample sze for each stratum? If two-stage cluster samplg s used ad oly oe cluster wll be radomly selected, What s the crtero to form clusters? Two-stage Cluster Samplg Whe Clusters are of Uequal Sze Desred Sample Proporto p/ a: Desred # of Clusters Selected the st Stage A: Total # of Clusters b: Sample Sze wth Each Cluster Selected : # of Elemets Cluster

8 Smple Two-stage Cluster Samplg The Frst-stage Prob. p a/a The Secod-stage Prob. p p (a/a) Sample sze cluster I, p * p Probablty Proportoal to Sze a A where b ab * A b p A a Example Draw a sample of,000 households from a cty that cotas about 00,000 households dstrbuted amog 000 blocks of uequal but kow sze. The desred sample proporto /00 The desred # of clusters selected the st stage00 How do we coduct the two-stage cluster samplg?