1. Introduction to Sampling for the Implementation of PATs
Materials Developed by
The IRIS Center at the University of Maryland

2. Advantages of Sampling
In most cases, do not want to survey EVERYONE
Why?
Too costly
Too time consuming
Too many resources needed

3. Advantages of Sampling
To make our work more cost-effective:
Interview the minimum number needed
Reduce:
time
cost
human error

4. Survey Sampling
According to sampling theory we can get valid results from studying only a fraction (a sample) of our clients, provided:
the sample is REPRESENTATIVE of the qualities of our client POPULATION, and
of sufficient SIZE to satisfy the assumptions of the statistical techniques used in our analysis

5. Simple Random Sampling
For the sample to be representative, it must be obtained randomly.
It is a simple random sample if each item in the population has an equal chance of being selected.

6. Types of Bias in Survey Process
Poor randomization is not the only cause of biased samples. Bias and error are more often introduced by:
poor group definition
interviewer error
inadequate records (incomplete or outdated client lists).

7. Longitudinal Design
Longitudinal studies compare multiple clients at multiple points in time (at least two points in time).
Often there is a baseline (when the client began the program) and an endline (two years later, for example).

8. Cross Sectional Design
Cross sectional studies compare multiple clients in the program at one point in time.
Ex: On October 1, 2005, program looks at:
Incoming clients
2-year clients
4-year clients

9. Calculating Sample Size: How Big is Big Enough?
Sample results are almost never identical to the
entire population
The larger the sample of clients, the greater the
likelihood that the statistical analysis will yield
“significant” results that closely resemble the
entire client population.

10. Calculating Sample Size
Different Views:
Statistician – maximalist – at least 500
Field researcher – minimalist – at least 35 to 50 for each subgroup we want to analyze and compare
USAID PAT – at least 300

11. Trade off: Larger sample is more accurate, but
Trade off: Larger sample is more accurate, but costs more in time and money
To make generalizations about entire population, need a total sample size of (depending on total population and confidence level desired)

12. Sample Size Calculator
Creative Research Systems:
Population Size
Confidence Level
Confidence Interval
Sample Size
1,000 5
95%
278
5,000
357
10,000
370
50,000
381
100,000
383
1,000,000
384

13. How to Sample Randomly?
RANDOM = giving each client an equal chance to be selected
This is done by:
drawing numbers, as in a lottery
numbering all clients and selecting numbers from a
random number table
systematically, by selecting every ‘nth’ case from a
complete list of clients
DANGER!!! The list may be biased by:
who is left out—Is the list up-to-date?

14. Steps in Taking a Simple Random Sample
Number a copy of the complete client list, and note the total number of clients (the last number)
Decide on your sample size
Create a list of random numbers
Use Excel or a random number table to select the sample, matching the numbers from the table with those on your numbered client list.

15. Cluster Sampling
To focus on specific subgroups, first classify the population into several subpopulations, called “strata,” then randomly sample from each stratum (subgroup).

16. Cluster Sampling
Is a way of selecting randomly, when you have a geographically dispersed population when time is limited.
This method can help reduce the time and cost in data collection.
Group the clients into clusters (could be branches or loan groups). Randomly choose the clusters. Then sample random individuals from only some randomly chosen clusters.

17. Stratified Sampling
Stratified survey sampling enables you to focus on specific groups (for example, women or rural people), ensuring that they will be represented in the sample. Although random survey sampling, done correctly, will give the researcher roughly proportional samples of all groups, disproportional stratified sampling will guarantee that a certain group is adequately represented.

18. Parametric Statistics
Assumes that the distribution of values for your variables are normal (Bell Curve), and also relatively similar to each other.
In parametric statistics, thirty is a “magic minimum number”--meaning that it is generally accepted as the minimum cell size for each stratum or subgroup of a simple sample.

19. Minimum for Each Subgroup
30 = ‘minimum magic number’ for each subgroup
To do any statistical analysis between subgroups, need a minimum of 30 in each subgroup in order to have any chance at all of finding ‘significant’ differences.
BUT, 30 is NOT enough for your total sample.
30 = ‘minimum magic number’ for each subgroup
To have a chance at finding statistically significant differences between subgroups of the sample, you need a minimum of 30 cases in each subgroup. BUT, 30 is not enough for your total sample.

20. If you want to compare between subgroups, you need 35 in each cell
Since the magic minimum number is 30, and you may have some missing values in some of your interview forms, for practical purposes, you need to always have a minimum number of 35 completed surveys for each cell of the sampling frame.

21. Handling Sampling Problems in the Field
If you cannot interview the client who is sampled
(not available, refusal, etc.)
Sample ‘at least’ an extra 40% and have
alternates available to be interviewed in each
area (subgroup)
Help ensure that you complete 35
questionnaires for each subgroup (if you plan to
do additional analysis and compare subgroups)
Make better use of the interviewers’ time
Cannot interview the client who is sampled
(not at home; sick; refusal; etc.)
.We have sampled 25% extra for these situations
.We need a minimum number from each area
45 Coast Mountains Plain
Your team will need to do more than the minimum numbers because some of the forms will prove to be not useable and we must have the minimum numbers for statistical purposes

22. Example of a Sampling Frame
Survey Sample
Region 1
Region 2
Region 3
Total
Clients interviewed
112
100 88
300
Substitute sample (approx 40%) 45 40 35
120
157
140
123
420

23. What if there are not enough with the 40% extra?
Check with the sample tracking coordinator to give you new
names
B. If there is not time, the field supervisor must adjust in the
field
1) Use random number table and select clients from master
list that have not already been selected
2) If you do not have a random number table, can ask
someone to pick a number between # and ## at random
Do NOT introduce bias
3) Write down the changes that you made and how you did it
A. Check with the sample tracking coordinator to give you new names
B. If there is not time, the field unit coordinator must adjust in the field while keeping bias out. Should have a complete client list and a random number table.
1). Take the random number table and choose the ones on your center list that have not been selected
2). If you do not have a random number table, choose random numbers in your head and then see which clients are selected
Do NOT introduce bias by just choosing the closest person or the nicest looking person or the person who has a store with cold drinks
3) write down the changes that you made and how you did it and give it to the sample tracking coordinator that afternoon.

24. An excerpt from a Random Number Table
Can use:

25. Random walk sampling -- less expensive but more prone to bias
IF YOU DON’T HAVE A CLIENT LIST
Random walk sampling -- less expensive but more prone to bias
Watch out for “tarmac bias”, selecting only
houses that are easily accessible from the
road

26. Example of BDS Sampling
Investigative emphasis: final beneficiaries.
Will use three subsectors (irrigation, cashews, potable water).
Will focus only on end users of the technologies.
Will focus on region surrounding Ziguinchor.

27. Example of Business Development Services Sampling
Sample size = 200
Casamance region is the focus
Program has three sub-sectors
Sample in each sub-sector stratified according to major differences between types of clients
Irrigation – individual owners and group owners
Cashew processing – shellers and peelers
Potable water – tubewells and rope pumps (rural and
peri-urban)
Of the total country of Senegal, the regions where the largest concentration of clients and USAID dollars was Casamance.
The program is divided into three main sub-sectors: irrigation pumps, cashew processing, and potable water pumps.
The percentage of clients interviewed in each sub-sector will be relative to the percentage of the total program budget dedicated to each sub-sector

28. Example of BDS Sampling
Generate a list of the direct clients and divide by
subgroup
# of clients per stratum or subgroup depends on
percentage the stratum constitutes in sector
Select clients using a random number list
Each direct client will provide information to the
interviewers so that they can create a list of end
users from which some will be chosen according to
a predetermined random number list.
Program will generate a list of the direct clients and disaggregate using the strata identified
The number of clients to be interviewed in each strata will be calculated with respect to the percentage that group constitutes in its sector
A sample of direct clients will be chosen using a random number list.
Each direct client will provide information to the interviewers so that they can create a list of end users from which some will be chosen according to a predetermined random number list.
Irrigation: Individual owners will provide names of other users. 10 groups will provide names of group members from which a minimum of 2 from each will be chosen.
Cashew processing: Unit owners will provide a list of workers.
Potable water: 15 rope pump owners, disaggregated by urban and rural locations, will provide a list of households using the pumps.

29. BDS Sampling Framework Example
Subsector
Irrigation
Cashew
Potable Water
Total
Total Number of Beneficiaries
5,500
800
3,500
9,800
Percentage of Total Beneficiary Population
56% 9%
35%
100%
Total Number of Beneficiaries to be interviewed for PAT implementation (based on % extra, or 420)
235 38
147
420
Type of Client
Individual
Group
Shellers
Peelers
Tubewell
Rope Pump
Percentage of Total
65%
45%
55%
10%
90%
Number to be interviewed
153 82 17 21 15
132
Rural
Urban
30%
70% 40 92