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# Examples of cluster selection using probability proportional to size (PPS) and systematic sampling (SS)

### Box 6.1. Small-scale example of selecting clusters from a listing of PSUs using the PPS method

Step 1: Calculate the sampling interval (k) by dividing the total population by the number of clusters to be surveyed. In this example, the total population is 24 940, and the number of clusters to be surveyed is 30, thus the sampling interval is 24 940 ÷ 30 = 831 people. Always round down to the nearest whole integer.

Step 2: Use a random number table or generator to determine a random starting point between 1 and the sampling interval (k). In this example where the sampling interval is 831, the number 710 was randomly selected as the starting participant

Step 3: Based on the cumulative population column, individual n° 710 is found in the first cluster. In this example, the first cluster is in the PSU of Mina because it includes the population from individual 601 to individual 1300.

Step 4: Continue to assign clusters by adding 831 (k) cumulatively. For example, the second cluster will be in the PSU where the value 1541 is located (710 + 831 = 1541), which is Bolama. The third cluster is where the value 2372 is located (1541 + 831 = 2372), and so on. In PSUs with large populations, more than one cluster could be selected. Note that if two clusters are selected in the same PSU (in this case Hilandia), the survey team will divide the PSU area into two sections of approximately equal population size and treat each area as an independent cluster. Similarly, if three or more clusters were in a PSU (for example, Cococopa), the PSU would be divided into three or more sections (clusters) of approximately equal population size.

PSU # PSU Pop. Cum. Cluster PSU # PSU Pop. Cum. Cluster
1 Utural 600 600 26 Banvinai 400 10,730 13
2 Mina 700 1,300 1 27 Purantna 220 10,950
3 Bolama 350 1,650 2 28 Kegalni 140 11,090
4 Taluma 680 2,330 29 Hamali-Ura 80 11,170
5 War-Yali 430 2,760 3 30 Kameni 410 11,580 14
6 Galey 220 2,980 31 Kiroya 280 11,860
7 Tarum 40 3,020 32 Yanwela 330 12,190
8 Hamtato 150 3,170 4 33 Bagvi 440 12,630 15
9 Nayjaff 90 3,260 34 Atota 320 12,950
10 Nuviya 300 3,560 35 Kogouva 120 13,070 16
11 Cattical 430 3,990 5 36 Ahekpa 60 13,130
12 Paralai 150 4,140 5 37 Yondot 320 13,450
13 Egala-Kuru 380 4,520 38 Nozop 1,780 15,230 17,18
14 Uwanarpo 310 4,830 6 39 Mapazko 390 15,620 19
15 Hilandia 2,000 6,830 7,8 40 Lotohah 1,500 17,120 20
16 Assosa 750 7,580 9 41 Voattigan 960 18,080 21,22
17 Dimma 250 7,830 42 Plitok 420 18,500
18 Aisha 420 8,250 10 43 Dopoltan 270 18,770
19 Nam Yao 180 8,430 44 Cococopa 3,500 22,270 23,24,25,26,27
20 Mai Jarim 300 8,730 45 Famegzi 400 22,670
21 Pua 100 8,830 46 Jigpelay 210 22,880
22 Gambela 710 9,540 11 47 Mewoah 50 22,930
23 Fugnido 190 9,730 12 48 Odigla 350 23,280 28
24 Degeh Bur 150 9,880 12 49 Sanbati 1,440 24,720 29
25 Mezan 450 10,330 50 Andidwa 220 24,940 230

In this example, there are only 50 PSUs in the listing. In practice, the number of PSUs will be much larger. The spreadsheet and formula used to generate the table above are shown in the “How to select PSUs” online tool.

## Box 6.2. Small-scale example of systematic sampling of clusters from a listing of PSUs

Step 1: Obtain the list of the PSUs and number them from 1 to the total number of PSUs. In this example there are 50 PSUs.

Step 2: The number of PSUs to sample should have already been determined. In this example it is 20.

Step 3: Calculate the sampling interval (k) by dividing the total number of PSUs by the number to be sampled. In this example, there are 50 PSUs, of which 20 should be sampled, thus the sampling interval is k is 50 ÷ 20 = 2.5.

Step 4: Using a random number table or generator, select an integer between 1 and k . Whichever number is randomly selected, go to the PSU list and include that PSU as the first selected PSU. In this example, the first selected PSU is number 2.

Step 5: Select the subsequent PSUs by adding k to the selected PSU number, then round down to the nearest whole integer. In this example the second PSU would be 2 + 2.5 = 4.5, rounding down makes it PSU number 4, and the third selected PSU is 4.5 + 2.5 = 7. The fourth selected PSU is 7 + 2.5 =9.5, rounded down to 9. This table shows the 20 PSUs selected from PSUs numbered 1 to 50.

Number PSU name Selected Number PSU name Selected
1 Utural 26 Ban Vinai
2 Mina x-1 27 Puratna x-11
3 Bolama 28 Kegalni
4 Taluma x-2 29 Hamali-Ura x-12
5 War-Yelo 30 Kameni
6 Galey 31 Kiroya
7 Tarum x-3 32 Yanwela x-13
8 Hamtato 33 Bagvi
8 Hamtato 33 Bagvi
9 Nayjaff x-4 34 Atota x-14
10 Nuviya 35 Kogouva
11 Cattical 36 Ahekpa
12 Paralia x-5 37 Yondot x-15
13 Egala-Kuru 38 Nozop
14 Uwanarpol x-6 39 Mapazoko x-16
15 Hilandia 40 Lotohah
16 Assosa 41 Voattigan
17 Dimma x-7 42 Plitok x-17
18 Aisha 43 Dopltan
19 Nam Yao x-8 44 Cococopa x-18
20 Mai Jarim 45 Famegzi
21 Ppua 46 Jigpley
22 Gambela x-9 47 Mewoah x-19
23 Fugnido 48 Odigla
24 Degeh Bur x-10 49 Sanbita x-20
25 Mezan 50 Andidwa x

In this example, there are only 50 PSUs in the listing. In practice, the number of PSUs will be much larger. You can find the spreadsheet and formula used to generate the table above in the “How to select PSUs” online tool.