The Selection Process Between the Sampling Probabilities Plans

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Examples for beginners Examples for advanced users

POSDEM

Example for beginners 1: obtain technical record and a list of units to investigate.

Example for beginners 2: choose the methods with minor variance.


Example for beginners 1: obtain technical record and a list of units to investigate.

You need to obtain a sample, not superior to the 5% of the total, in order to begin an investigation of the set of clients by sampling.

For this you have a data base with the following information:

Total number of companies   400 
Variable of classification  Social capital 
Variable of interest  Purchases in the company the previous year 
 

Solution

The data in the program are introduced by means of the option "Data." Inside the option "Sampling," you may select the method "Systematic with constant interval" and lastly obtain in the menu of "Listings," the units that are going to be in the sample and another ones that they could be used like substitutes for the case of absences and negative. In the screen "Report" you have prepared your technical record and the units that they should be investigated.

Results

Technical record of the Survey: Data of the design

Population frame used: Companies clients of the firm.

Variable of study: Purchases in the firm the previous year

Auxiliary variable: social Capital

Method of sampling: Systematic With Constant Interval

Size of population = 400

Size of sample = 20

Sampling fraction = 5%

Mean for population = 90.9825

Typical deviation (n-1)= 1503.6463

Typical deviation of the estimator = 4.5755

Sampling error CV% = 5.03%

Up limits of confidence = 99.9504

Low limits of confidence = 82.0146 

Variance for Swor = 71.4232

Variance for Sstr 26.7522

Variance for Ssic = 20.9348

Units to investigate that have been selected the number 9 like aleatory of selection and using sampling systematic with constant interval:

Population frame used: Companies clients of the firm

Variable of study: Purchases in the firm the previous year

Auxiliary variable: Social Capital

Sample (9)

Units 

Sample (14)

Reservations (1) 

Sample (5)

Reservations (2) 

14 
29  34  25 
49  54  45 
69  74  65 
89  94  85 
109  114  105 
129  134  125 
149  154  145 
169  174  165 
189  194  185 
209  214  205 
229  234  225 
249  254  245 
269  274  265 
289  294  285 
309  314  305 
329  334  325 
349  354  345 
369  374  365 
389  394  385 
 

The values of the sample (9) identify the units, in this case companies that should be investigated in the survey. The other two columns represent the identifications of those substitutes or reservations units, that they will investigate only in case taht it is not possible investigate the unit originally selected.

Parameters:

Mean of population = 90.9825

Typical deviation (n-1) = 1503.6463

Typical deviation of the estimator = 4.5755

Sample size = 20


Example for beginners 2: choose the methods with minor variance.

Now you are asked to select of all the available methods the one with minor variance.

Solution

In the option "Configuration" we selected all the methods. Later in "Calculations" we opted for the option" Variances for selection of methods." In the window "Reports" we have the recommendation, from the system, to choose the method .

Results

Available methods  V (x)  Efficiency (wor)  Efficiency (str) 
Sampling without replacement (S.R.)  71.4232  100.0000  266.9810 
Sampling [estratified] with an unit  26.7522  37.4559  100.0000 
Systematic interval [cte]. (SIC)  20.9348  29.3110  78.2547 
Systematic interval [var]. 1 (SIV1)  23.3163  32.6453  87.1567 
Systematic interval [var]. 2 (SIV2)  57.8629  81.0142  216.2924 
Systematic centered (CLS)  7.4256  10.3967  27.7571 
Systematic centered [int]. [var]. 1 (CLSIV1)  0.0156  0.0219  0.0584 
Systematic centered [int]. [var]. 2 (CLSIV2)  28.2412  39.5407  105.5661 
Systematic correction of Yachts (CY)  19.5264  27.3390  72.9900 
Systematic balanced (BSS)  30.4178  42.5881  113.7023 
Systematic modified (MSS)  21.9673  30.7566  82.1142 
Prob. unequals with replacement and [pps] (WRPPS)  44.2157  61.9067  165.2791 
Prob. unequals without replacement and pps (WORPPS)  24.5422  34.3617  91.7391 
Prob. unequals with partial replacement and pps (WRPPPS)  28.0061  39.2115  104.6872 
Two conglomerate constant interval (2CIC)  20.9348  29.3110  78.2547 
Two conglomerate variable interval (2CIV)  28.0226  39.2345  104.7488 
Two balanced conglomerate (2CBSS)  16.5591  23.1844  61.8980 
Two modified conglomerate (2CMSS)  21.9673  30.7566  82.1142 
 

Comment

In the report the program recommends use the method of two balanced conglomerate, that presents the minor variances and that it is 16.5. The centered methods are not recommended for considerations of great variability of the methods that should study in the most advanced examples.

The same report recommends:

  • In the comparison use the methods: balanced, systematic with variable interval and with partial replacement and pps.
  • If is necessary calculate the variances of the estimator with the data of a single sample, then the system recommen the method with partial replacement and proportional probabilities to the size, because there are developed formulas in order to esteem the variances correctly.
Recommended methods  V (x) 
1.- Sampling estratified with an unit  26.7522 
2.- Systematic interval [var]. 1 (SIV1)  23.3163 
3.- Systematic balanced (BSS)  30.4178 
4.- Prob. unequals with partial replacement and pps (WRPPPS)  27.6371 
 

From this table we observe that, in the case of not needing to calculate the errors of sampling with the data of a single sample, the better method will be the systematic with variable interval. Also could be observe that the variances of the method (4) present a certain variability consequence of not calculating the whole sampling space and to base the calculations in a representation of the same. Lastly, the software, recommended the systematic sampling with variable interval.