Guidance on Sampling Design

Form Approved
OMB No. 0920-1346

GUIDANCE ON SELECTING A SAMPLE FOR A SCHOOL-BASED ORAL HEALTH SURVEY
MAY 2013, UPDATED JUNE 2015 AND JULY 2017
Is your state, territory or local health agency planning to conduct a school-based oral health survey?
If yes, then you undoubtedly have questions about how to select an appropriate sample. This topic is important
because proper sampling design and methods are crucial for valid population estimates and statistical
assessments of precision of estimates. The purpose of this document is to give you a basic framework for how a
sample of schools is selected. Although this document is geared towards states and territories, the techniques
are appropriate for other jurisdictions such as counties.
Because no one method is appropriate for all states/territories we encourage you to read this document then
contact ASTDD for additional guidance on selecting a sample for your state/territory.

This document is limited to a discussion of sampling. For additional information on how to conduct and use data
from a school-based oral health survey, please refer to the Basic Screening Survey (BSS) tools developed by the
Association of State and Territorial Dental Directors (ASTDD). These tools are available at the following website:
www.astdd.org/basic-screening-survey-tool/.
Do you want to submit the data to the National Oral Health Surveillance System (NOHSS)?
NOHSS (www.cdc.gov/oralhealthdata) is a collaborative effort between CDC's Division of Oral Health and ASTDD.
NOHSS is designed to monitor the burden of oral disease, use of the oral health care delivery system, and the
status of community water fluoridation on both a national and state level. NOHSS is designed to track oral
health surveillance indicators based on data sources and
surveillance capacity available to most states. The Council of State
If you follow the guidance provided
and Territorial Epidemiologists (CSTE) and the Chronic Disease
in this document your oral health
Directors (CDD) were instrumental in developing the framework
data will meet the specifications for
for chronic disease surveillance indicators, including the oral
inclusion in NOHSS.
health indicators in NOHSS.
Only data that meet the following specifications are included in the NOHSS data system:
• The data are from a statewide probability sample of elementary schools.
• If a complex sampling scheme is used, the data must be weighted for the sampling scheme.
• ASTDD strongly suggests that, at minimum, 3rd grade children be screened. Grades K-2 as well as Head
Start may also be screened and are included on the NOHSS website.
Why not have just one sampling plan for all states?
There are limitations to creating one single sample design for all states. States differ in size, geography, political
boundaries, population distribution, population demographics and in the make-up and arrangement of the
schools to be sampled. In addition to the basic BSS oral health indicators for the state population, state oral
health programs may have additional indicators or population subgroups of specific interest. Resources may also
vary, affecting the size and extent of BSS surveys, which in turn can affect the sample design. These differences
may require unique sample design features, limiting the degree to which a single predefined sampling plan fits
all situations. Given these considerations, some general guidelines for BSS survey sampling follow.

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What basic sampling guidelines should I follow?
The following guidelines are intended to aid states in designing sampling plans for oral health surveys using the
BSS methodology. These guidelines focus on choosing target populations and employing appropriate
stratification and cluster sample selection techniques. Schools represent natural clusters for sample selection.
Effective stratification, based on geographic area or the proportion of students participating in the National
School Lunch Program (NSLP) for example, can improve the statistical efficiency of sampling. Such stratification
can be implemented, along with appropriate cluster selection, in the sampling schemes described below. Using
common sampling techniques in combination with BSS methodology can improve the efficiency of state oral
health needs assessment surveys and improve precision and reduce bias in estimates and tracking of trends.
Standardizing methods of sampling can also increase comparability of BSS findings between states.
What sampling designs are appropriate for a school-based oral health survey?
There are many different types of sampling designs but some, such as simple random sampling, are not
appropriate for a school-based oral health survey. Following are types of sampling designs that are appropriate.
When implementing survey sampling methodology, follow these basic guidelines:
At a minimum, school surveys should include 3rd graders in public on-site schools. States can
determine if they want to include other types of schools such as private schools or schools
administered by the Bureau of Indian Education.
Sample designs for school oral health surveys should ensure good representation on socioeconomic
status (SES) through stratification (preferably implicit) on NSLP participation at the school level.
Replacement schools should be selected for schools that refuse to participate through a random
probability selection process from schools in the same stratum or sampling interval.
Selection probabilities and response rates should be tracked for use in calculating sampling weights
for data analysis.

Each of these designs employ cluster sampling for efficiencies (sampling schools vs. random sample of children).
• Stratified random sampling: Separate the sampling frame into categories (e.g., counties, health regions,
urban/rural) and randomly select from each category.
o Proportionate – select a consistent fraction from each group to sample proportionally. The numbers
selected into the sample will be proportional to the numbers in the population groups (strata).
o Disproportionate – select at different rates from the groups, e.g., only 10% of the population is in a
particular category, but you are particularly interested in that category (e.g., rural counties) so you
sample at a higher rate to get better estimates. Oversampling would be used for strata in which
proportionate sampling might not result in selection of a large enough number to obtain sufficiently
precise population estimates.
• Systematic sampling: Sampling from a list using a selection interval and random start. For example,
sampling every 6th element from a list starting with a random number between 1 and 6.
o NOTE: Ordering the list by group (strata) and then using a systematic sample makes this method
equivalent to (or better than) a proportionate stratified sample because this implicit stratification
can be used with continuous variables (e.g., ordering schools by NSLP percentage) to provide finer
stratification and can be combined with probability proportional to size (PPS) sampling.
• Probability proportional to size (PPS) sampling: Sampling of clusters (schools) proportional to their size.
Proportional to size sampling is often employed in different stages of a multistage sample. For example,
in a survey of 3rd graders, school districts could be sampled according to total 3 rd grade enrollment size,
and then schools within selected districts could be sampled proportional to school 3 rd grade enrollment.
All children in targeted grades in selected schools can be included in the sample, but if a set number
(e.g., a typical class size of 25) is sampled within selected schools, the sample can become selfweighting, meaning the higher probability of selection for larger districts and schools is offset by the
lower probability of selecting children within the large schools so all children in the survey population
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have about the same probability of selection. This self-weighting is for probability of selection, and
doesn’t account for non-response (which will vary by school). Analysis weights may be needed to
account for non-response. PPS sampling can be advantageous because it ensures sufficient
representation of the larger clusters (schools). This may increase the efficiency of the survey logistically,
as larger clusters (schools) are often more geographically concentrated in urban areas, thus decreasing
survey travel time and costs.
What steps should I follow when selecting a sample?
Step 1. Determine which indicators will be collected. Refer to the BSS manual for a list of the recommended
indicators (www.astdd.org/basic-screening-survey-tool/).
Step 2. Identify your target population and any sub-populations of interest. For example, do you want oral
health estimates for 3rd grade children for the state as a whole or do you want oral health estimates for 3rd grade
children by region or by county? Other sub-populations of interest could include a particular geographic area,
racial/ethnic minorities, low-income or rural children.
Step 3. Define the survey population to include in your sampling frame considering the practical limitations for
accessing the entire target population. For example, you may decide to restrict your sampling frame to on-site
public schools with 20 or more children in 3rd grade. Restricting your sampling frame helps to assure that
resources aren’t wasted by going to schools with a very small number of participants.
Step 4. Determine your sample size based on the population level estimates desired (e.g. state, region, health
district, county) and the level of statistical precision desired. Following are some general approximate guidelines
to sample size determination.
a. BSS indicators are proportions or percent estimates (e.g. percent of children with untreated tooth
decay)
i. The simple random sampling formula for proportions is: v(p0) =(1-f) p0q0/n-1
ii. The most conservative calculation is to use estimated p 0 = 50%. This results in sample sizes
associated with the levels of desired precision outlined in Box 1.
b. Multiply the sample size by the estimated design effect, which
Box 1
reflects the effects of complex sample design vs. simple random
For 95% CI = +/- 10% n = 97
sampling on variance/precision estimation (often about 2).
For 95% CI = +/- 5% n = 384
c. NOTE: The same sample size calculations are appropriate for the
For 95% CI = +/- 3% n = 1,066
population level of interest. If you want regional level estimates and
there are 5 regions in the state, then you should multiply the sample size by 5 (n X 5). If county level
estimates are desired and there are 35 counties in the state, then you should multiply the sample size by
35 (n X 35). For example, if you decided that you wanted estimates with a 95% confidence interval of +/10% for 35 counties, you would need a sample size of 97 from each of the 35 counties, for a total sample
size of 35*97=3,395.
d. NOTE: Available resources often drive sample size determination to a greater extent than statistical
precision considerations. Available funds, time and number of trained screeners, which affect the
number of schools you are able to screen, may be the limiting factors in determining sample size.
Step 5. Prepare your sampling frame. Obtain an electronic list of schools from your state department of
education. At a minimum, the file should include school name, school ID code, district name, district ID code,
enrollment by grade, total enrollment, county or region, and number or percent of children participating in
NSLP. Other useful information includes enrollment by race/ethnicity which allows you to determine if the
sample is representative of the state in terms of race/ethnicity. To make contacting the school easier, it is also
useful to have the school’s address, phone number and email address.

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NOTE: The National School Lunch Program is a federally assisted meal program operating in public and nonprofit
private schools and residential child care institutions. Each state may use a different name for this program. For
example, West Virginia refers to this as “percent needy”. The federal Healthy, Hunger-Free Kids Act of 2010
established a community eligibility provision (CEP) within the NSLP. This is a reimbursement option for eligible
educational agencies and schools that allows them to offer free school meals to all children in high poverty
schools without collecting household applications. In states where schools are using the CEP option, you may
need to obtain information on both NSLP and CEP. For additional information on CEP refer to
http://www.fns.usda.gov/school-meals/community-eligibility-provision.
Step 6. Stratify the sampling frame. This helps to ensure representation of population subgroups of interest or
importance and almost always improves precision of overall survey estimates.
a. Common stratification variables include:
i. Geographic factors such as county, region or health district
ii. Urban/rural status
iii. NSLP status of school
b. Most states use multiple levels of stratification. For example, a state may stratify by region, by
urban/rural within region, and by NSLP percent within urban/rural.
c. Stratification can be:
i. Explicit – sampling within each stratum
ii. Implicit – with systematic sampling from a list sorted by stratification variables
d. NOTE: ASTDD recommends that all states, at a minimum, use stratification (preferably implicit) by the
percent of children that participate in NSLP.
Step 7. Select the sample using one of the following general methods.
a. Probability proportional to size (PPS) sampling of schools. With PPS sampling, larger schools have a
higher probability of being selected. For a self-weighting analysis, screen a consistent number of
children (e.g. 1 or 2 classrooms) per school. PPS sampling with a consistent number of children screened
at each school can result in an efficient scheduling of screeners and ensures proportionate
representation of children from different sized clusters (i.e., large clusters are not under-represented).
b. Probability sampling of schools without regard to school size (non-PPS). With a non-PPS sampling of
schools, each school, regardless of size has an equal probability of being selected. For a self weighting
analysis, all children in the target grade should be screened. NOTE: The sample should be self weighting
within the strata but you will need to include an adjustment factor to account for differences in stratum
population sizes.
What are some examples of the sampling process?
Following are two examples to help you visualize the sampling process. The first example uses PPS sampling
while the second example uses a non-PPS sampling design. Both examples generate a sample that is implicitly
stratified by region, urban/rural status and percent of children participating in NSLP. If systematic sampling will
be part of your PPS sampling scheme, then a cumulative running total of school 3 rd grade child enrollment
should be included starting with the first school and adding through the entire sampling frame.
NOTE: The following examples use Excel for setting up the sampling frame and selecting the sample. Automated
procedures, such as SAS SurveySelect may present difficulties for sampling techniques such as systematic
selection from an ordered list to achieve implicit stratification and for selection of replacements for refusing
schools, which is very important in assuring that the final surveyed sample is representative of the population.

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Example #1: Systematic PPS sampling with implicit stratification by region, urban/rural status and F/R lunch
This example describes a PPS sampling strategy. In this example, larger schools have a higher probability of
selection. Based on available resources, the decision was made to include 70 schools in the “Utopia” oral health
survey of 3rd grade children. The following sampling steps were employed:
• The sampling frame list was sorted by region then by urban/rural status within each region
• Schools were then sorted by percent of children participating in NSLP within urban/rural school
categories.
Calculations used for systematic PPS sampling are as follows:
• Sampling interval for sampling = (total 3rd grade enrollment) / (# of schools to be screened)
o 53,320 / 70 = 761.7
• Random start = random number between 0 and interval (761.7) = 148.0
o This is the first school selection number
o There are a variety of methods for selecting a random number including, but not limited to, Excel
and www.random.org
• Select the school with the 148th child. Add the sampling interval (761.7) to 148 to get the next school
(909.7). Continue adding the sampling interval repeatedly until all 70 school selections are made.
148.0, 909.7, 1671.4, 2433.1, 3194.8, 3956.5, 4718.2, …
•

These numbers are matched to the cumulative enrollment numbers in the sampling list. The schools
with enrollment intervals containing the sample selection numbers are selected into the sample. The
sampling frame list and the selected schools are shown in Table 1.

Example #2: Systematic sampling with implicit stratification by region, urban/rural status and F/R lunch
This example describes a non-PPS sampling strategy. In this example, all schools (regardless of size) have the
same probability of selection. Based on available resources, the decision was made to include 70 schools in the
“Utopia” oral health survey of 3rd grade children. The following sampling steps were employed:
• The sampling frame list was sorted by region then by urban/rural status within each region
• Schools were then sorted by percent of children participating in NSLP within urban/rural school
categories.
Calculations used for systematic sampling are as follows:
• Sampling interval for sampling = (number of schools in sampling frame) / (# of schools to be screened)
o 700 / 70 = 10.0
• Random start = random number between 1 and interval (10) = 6
o This is the first school selection number
o There are a variety of methods for selecting a random number including, but not limited to, Excel
and www.random.org
• Select the 6th school. Add the sampling interval (10.0) to 6 to get the next school (16.0). Continue adding
the sampling interval repeatedly until all 70 school selections are made.
6.0, 16.0, 26.0, 36.0, 46.0, 56.0, 66.0, …
•
•

These numbers are matched to the sequential number of schools in the sampling list to identify the
schools selected into the sample. The sampling frame list and the selected schools are shown in Table 2.
NOTE: In this example, dividing the number of schools by the number to screen produced a whole
number. Please contact ASTDD if you need more information on how to select a non-PPS sample when
the sampling interval includes a decimal.

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What should I do if a school refuses to participate?
An important part of the sample design is the replacement of refusing clusters (schools). Refusals should be
replaced with similar probability methods as original selections. Selection of a replacement should be from the
same sampling interval as the refusing school so that the sampling interval is represented.
• If systematic PPS sampling was used in the original sample, a PPS method of replacement selection
should be used. Table 3 shows the method of replacement used in the Utopia PPS sampling example.
o The list of the final selections is created that includes enrollment size and start of the sampling
interval on the sampling frame list.
o The enrollment size of the refusing school is subtracted from the sampling interval size.
o A random number between 0-1 is generated and applied to the remaining sample interval, using the
sample interval start to determine the position of the replacement selection in the interval. The
following website can be used for selecting a random number between 0-1:
http://www.random.org/decimal-fractions/
o The original sample frame list is then viewed to see where this replacement number falls, to
determine the replacement school.
o NOTE: If your replacement number calculated is equal to or greater than the refusal school interval,
you have to add the enrollment number for the refusing school for your replacement selection
number (e.g. the second replacement in Table 3 - 133 is added for a final replacement number of
3531.2). This adjusts for the fact that the refusing school is no longer in the adjusted interval.
o Table 3 shows replacement numbers and calculations for two refusing schools that were originally
selected using PPS.
• If systematic non-PPS sampling was used in the original sample, a non-PPS method of replacement
selection should be used. Table 4 shows the method of replacement used in the Utopia non-PPS
sampling example.
o Determine the range of the sampling interval for the refusing school.
o Select a random number between the lowest and highest school number in the interval. If you get a
number matching the refusing school, just generate another number.
o The school with that number is the replacement.
Will I need specialized software to analyze the data?
Yes, you will need to use statistical software designed to address the statistical ramifications of complex
probability sample designs, specifically stratification and cluster sampling. Appropriate software packages
include, but are not limited to, SUDAAN and survey analysis procedures in SAS, Stata, SPSS, Epi Info and R.
Where can I get additional help?
ASTDD can help you with the sample selection process. Please contact us if you have any questions.
Association of State & Territorial Dental Directors
Kathy Phipps, Data and Surveillance Coordinator
Phone: 805-776-3393, Email: [email protected]
Acknowledgements
Supported by Cooperative Agreement NU5U8DP004919 from the Centers for Disease Control and Prevention. Its
contents are solely the responsibility of the authors and do not necessarily represent the official views of CDC.
ASTDD would like to thank Michael Manz, Kathy Phipps and Laurie Barker for their assistance in developing and
reviewing this guidance.

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References and additional resources
• Kalton G (1983). Introduction to survey sampling, Sage, Beverly Hills, CA.
• Kish L (1965). Survey Sampling, John Wiley & Sons, New York.
• Heeringa SG, West BT, Berglund PA (2010). Applied survey data analysis, Chapman and Hall, London.

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Table 1: Systematic PPS sampling with implicit stratification by region, urban/rural and NSLP participation
Region

Urban/
Rural

1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2

Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Rural
Rural
Rural

School Name
KEOWEE
WALHALLA
RAVENEL
LAKEVIEW
NINETY SIX
NORTHSIDE
MCCORMICK
FAIR-OAK
HICKORY TAVERN
HOLLYWOOD
CHEROKEE TRAIL
PINECREST
MERRYWOOD
DIAMOND HILL
SPRINGFIELD
TAMASSEE-SALEM
WESTMINSTER
HODGES
LAURENS
GRAY COURT OWINGS
E B MORSE
CLINTON
WESTWOOD
ORCHARD PARK
WARE SHOALS PRIMARY
JOANNA-WOODSON
JAMES M BROWN
OAKLAND
BLUE RIDGE ELEMENTARY
WATERLOO
EASTSIDE
WOODFIELDS
SALUDA
MATHEWS
JOHN C CALHOUN
FORD
MIDWAY SCHL
WREN
WRIGHT
POWDERSVILLE
CONCORD
HUNT MEADOWS
MT LEBANON
MERRIWETHER
SPEARMAN
LA FRANCE
BELTON
STARR
CENTERVILLE
WEST PELZER
HONEA PATH
CEDAR GROVE
PALMETTO
TOWNVILLE
W E PARKER
MCLEES
IVA
CALHOUN ACADEMY
WHITEHALL
NEW PROSPECT
JOHNSTON
HOMELAND PARK
PENDLETON
FLAT ROCK .
NEVITT FOREST SCHOOL
DOUGLAS
VARENNES ACADEMY
SPARTANBURG
LOCKHART
BUFFALO

National School Lunch
Program Percent
37.1%
39.8%
52.3%
52.4%
52.7%
52.8%
53.9%
55.7%
56.8%
57.2%
57.8%
60.0%
60.1%
60.3%
60.9%
61.7%
67.2%
67.5%
67.7%
68.7%
68.7%
69.0%
69.8%
71.5%
72.0%
72.2%
73.9%
74.8%
76.6%
77.5%
78.9%
80.8%
81.0%
83.3%
89.9%
92.8%
16.7%
26.5%
28.6%
31.2%
31.5%
39.8%
41.9%
48.4%
51.3%
51.3%
52.2%
53.2%
55.5%
55.6%
55.6%
55.9%
61.9%
63.5%
64.9%
65.1%
67.2%
67.6%
69.9%
72.3%
73.5%
74.7%
74.7%
76.5%
80.7%
82.4%
90.8%
43.2%
58.8%
70.9%

Cumulative
3rd Grade
Enrollment

3rd Grade
Enrollment
38
92
91
94
130
95
56
117
61
66
53
100
90
38
89
41
62
36
92
58
95
87
120
61
55
50
98
78
90
37
67
97
107
84
36
81
142
100
28
173
133
75
55
120
60
52
160
57
117
69
97
90
90
36
88
118
70
120
75
66
49
52
52
67
66
48
65
45
23
103

Selected
School
38
130
221
315
445
540
596
713
774
840
893
993
1,083
1,121
1,210
1,251
1,313
1,349
1,441
1,499
1,594
1,681
1,801
1,862
1,917
1,967
2,065
2,143
2,233
2,270
2,337
2,434
2,541
2,625
2,661
2,742
2,884
2,984
3,012
3,185
3,318
3,393
3,448
3,568
3,628
3,680
3,840
3,897
4,014
4,083
4,180
4,270
4,360
4,396
4,484
4,602
4,672
4,792
4,867
4,933
4,982
5,034
5,086
5,153
5,219
5,267
5,332
5,377
5,400
5,503

148.0

909.7

1,671.4

2,433.1

3,194.8

3,956.5

4,718.2

* In PPS sampling, the number of children in the sampling interval is the same for each interval; in this example 761.7. This number will be used to calculate the weight factor.

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Table 2: Systematic sampling (non-PPS) with implicit stratification by region, urban/rural status and NSLP participation
Region
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2

Urban/
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Rural
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Urban
Rural
Rural
Rural

School Name
KEOWEE
WALHALLA
RAVENEL
LAKEVIEW
NINETY SIX
NORTHSIDE
MCCORMICK
FAIR-OAK
HICKORY TAVERN
HOLLYWOOD
CHEROKEE TRAIL
PINECREST
MERRYWOOD
DIAMOND HILL
SPRINGFIELD
TAMASSEE-SALEM
WESTMINSTER
HODGES
LAURENS
GRAY COURT OWINGS
E B MORSE
CLINTON
WESTWOOD
ORCHARD PARK
WARE SHOALS
JOANNA-WOODSON
JAMES M BROWN
OAKLAND
BLUE RIDGE
WATERLOO
EASTSIDE
WOODFIELDS
SALUDA
MATHEWS
JOHN C CALHOUN
FORD
MIDWAY
WREN
WRIGHT
POWDERSVILLE
CONCORD
HUNT MEADOWS
MT LEBANON
MERRIWETHER
SPEARMAN
LA FRANCE
BELTON
STARR
CENTERVILLE
WEST PELZER
HONEA PATH
CEDAR GROVE
PALMETTO
TOWNVILLE
W E PARKER
MCLEES
IVA
CALHOUN ACADEMY
WHITEHALL
NEW PROSPECT
JOHNSTON
HOMELAND PARK
PENDLETON
FLAT ROCK
NEVITT FOREST
DOUGLAS
VARENNES ACADEMY
SPARTANBURG
LOCKHART
BUFFALO

NSLP Percent
37.1%
39.8%
52.3%
52.4%
52.7%
52.8%
53.9%
55.7%
56.8%
57.2%
57.8%
60.0%
60.1%
60.3%
60.9%
61.7%
67.2%
67.5%
67.7%
68.7%
68.7%
69.0%
69.8%
71.5%
72.0%
72.2%
73.9%
74.8%
76.6%
77.5%
78.9%
80.8%
81.0%
83.3%
89.9%
92.8%
16.7%
26.5%
28.6%
31.2%
31.5%
39.8%
41.9%
48.4%
51.3%
51.3%
52.2%
53.2%
55.5%
55.6%
55.6%
55.9%
61.9%
63.5%
64.9%
65.1%
67.2%
67.6%
69.9%
72.3%
73.5%
74.7%
74.7%
76.5%
80.7%
82.4%
90.8%
43.2%
58.8%
70.9%

3rd Grade
Enrollment
38
92
91
94
130
95
56
117
61
66
53
100
90
38
89
41
62
36
92
58
95
87
120
61
55
50
98
78
90
37
67
97
107
84
36
81
142
100
28
173
133
75
55
120
60
52
160
57
117
69
97
90
90
36
88
118
70
120
75
66
49
52
52
67
66
48
65
45
23
103

Sequential School
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70

Sampling
Interval #
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
6
6
6
6
6
6
6
6
6
6
7
7
7
7
7
7
7
7
7
7

# of Children in
Sampling Interval*

Selected
School

6

840

16

659

26

771

36

915

46

898

56

850

66

570

* The number of children in the sampling interval will be used to calculate the weight factor.

July 2017

9

Table 3: Example of refusal replacement for systematic PPS sample selection
A
School Name

NSLP%

KEOWEE
WALHALLA
RAVENEL
LAKEVIEW
NINETY SIX
NORTHSIDE
MCCORMICK
FAIR-OAK
HICKORY TAVERN
HOLLYWOOD
CHEROKEE TRAIL
PINECREST
MERRYWOOD
DIAMOND HILL
SPRINGFIELD
TAMASSEE-SALEM
WESTMINSTER
HODGES
LAURENS
GRAY COURT OWINGS
E B MORSE
CLINTON
WESTWOOD
ORCHARD PARK
WARE SHOALS
JOANNA-WOODSON
JAMES M BROWN
OAKLAND
BLUE RIDGE
WATERLOO
EASTSIDE
WOODFIELDS
SALUDA
MATHEWS
JOHN C CALHOUN
FORD
MIDWAY SCHL
WREN
WRIGHT
POWDERSVILLE
CONCORD
HUNT MEADOWS
MT LEBANON
MERRIWETHER
SPEARMAN
LA FRANCE
BELTON
STARR
CENTERVILLE
WEST PELZER
HONEA PATH
CEDAR GROVE
PALMETTO
TOWNVILLE
W E PARKER
MCLEES
IVA
CALHOUN ACADEMY
WHITEHALL
NEW PROSPECT
JOHNSTON
HOMELAND PARK
PENDLETON
FLAT ROCK .
NEVITT FOREST
DOUGLAS

37.1%
39.8%
52.3%
52.4%
52.7%
52.8%
53.9%
55.7%
56.8%
57.2%
57.8%
60.0%
60.1%
60.3%
60.9%
61.7%
67.2%
67.5%
67.7%
68.7%
68.7%
69.0%
69.8%
71.5%
72.0%
72.2%
73.9%
74.8%
76.6%
77.5%
78.9%
80.8%
81.0%
83.3%
89.9%
92.8%
16.7%
26.5%
28.6%
31.2%
31.5%
39.8%
41.9%
48.4%
51.3%
51.3%
52.2%
53.2%
55.5%
55.6%
55.6%
55.9%
61.9%
63.5%
64.9%
65.1%
67.2%
67.6%
69.9%
72.3%
73.5%
74.7%
74.7%
76.5%
80.7%
82.4%

3rd
Enroll.
38
92
91
94
130
95
56
117
61
66
53
100
90
38
89
41
62
36
92
58
95
87
120
61
55
50
98
78
90
37
67
97
107
84
36
81
142
100
28
173
133
75
55
120
60
52
160
57
117
69
97
90
90
36
88
118
70
120
75
66
49
52
52
67
66
48

Cumulative
3rd Grade
Enroll.
38
130
221
315
445
540
596
713
774
840
893
993
1,083
1,121
1,210
1,251
1,313
1,349
1,441
1,499
1,594
1,681
1,801
1,862
1,917
1,967
2,065
2,143
2,233
2,270
2,337
2,434
2,541
2,625
2,661
2,742
2,884
2,984
3,012
3,185
3,318
3,393
3,448
3,568
3,628
3,680
3,840
3,897
4,014
4,083
4,180
4,270
4,360
4,396
4,484
4,602
4,672
4,792
4,867
4,933
4,982
5,034
5,086
5,153
5,219
5,267

B
Original
Selection
Number

Status

Originally selected school Pinecrest refused.

148.0

C: New interval start = B Minus Random Start #
909.7 – 148.0 = 761.7

874.2
909.7

Replacement
Refused

D: New interval size = Sampling Interval Minus A
761.7 – 100 = 661.7
E: Random number between 0 and 1 = 0.17
New selection number = C + (D*E)
761.7 + (661.7 * 0.17) = 874.2
Replacement school: Cherokee Trail

1,671.4

2,433.1

Originally selected school Concord refused.
C: New interval start = B Minus Random Start #
3194.1 – 148.0 = 3046.1
3,194.8

Refused

3,531.2

Replacement

3,956.5

D: New interval size = Sampling Interval Minus A
761.7 – 133 = 628.7
E: Random number between 0 and 1 = 0.56
New selection number = C+(D*E)
3046.1 + (628.7 * 0.56) = 3398.2+133=3531.2
Replacement school: Merriwether

4,718.2

* If your replacement number is equal to or greater than the refusal school interval, you have to add the enrollment number for the refusing school to
your replacement selection number (in this case 133 is added for a final replacement number of 3,533). This adjusts for the fact that the refusing school
is no longer in the adjusted interval.

July 2017

10

Table 4: Example of refusal replacement for systematic non-PPS sample selection
School Name

NSLP%

KEOWEE
WALHALLA
RAVENEL
LAKEVIEW
NINETY SIX
NORTHSIDE
MCCORMICK
FAIR-OAK
HICKORY TAVERN
HOLLYWOOD
CHEROKEE TRAIL
PINECREST
MERRYWOOD
DIAMOND HILL
SPRINGFIELD
TAMASSEE-SALEM
WESTMINSTER
HODGES
LAURENS
GRAY COURT OWINGS
E B MORSE
CLINTON
WESTWOOD
ORCHARD PARK
WARE SHOALS
JOANNA-WOODSON
JAMES M BROWN
OAKLAND
BLUE RIDGE
WATERLOO
EASTSIDE
WOODFIELDS
SALUDA
MATHEWS
JOHN C CALHOUN
FORD
MIDWAY
WREN
WRIGHT
POWDERSVILLE
CONCORD
HUNT MEADOWS
MT LEBANON
MERRIWETHER
SPEARMAN
LA FRANCE
BELTON
STARR
CENTERVILLE
WEST PELZER
HONEA PATH
CEDAR GROVE
PALMETTO
TOWNVILLE
W E PARKER
MCLEES
IVA
CALHOUN ACADEMY
WHITEHALL
NEW PROSPECT
JOHNSTON
HOMELAND PARK
PENDLETON
FLAT ROCK
NEVITT FOREST
DOUGLAS
VARENNES ACADEMY
SPARTANBURG
LOCKHART
BUFFALO

37.1%
39.8%
52.3%
52.4%
52.7%
52.8%
53.9%
55.7%
56.8%
57.2%
57.8%
60.0%
60.1%
60.3%
60.9%
61.7%
67.2%
67.5%
67.7%
68.7%
68.7%
69.0%
69.8%
71.5%
72.0%
72.2%
73.9%
74.8%
76.6%
77.5%
78.9%
80.8%
81.0%
83.3%
89.9%
92.8%
16.7%
26.5%
28.6%
31.2%
31.5%
39.8%
41.9%
48.4%
51.3%
51.3%
52.2%
53.2%
55.5%
55.6%
55.6%
55.9%
61.9%
63.5%
64.9%
65.1%
67.2%
67.6%
69.9%
72.3%
73.5%
74.7%
74.7%
76.5%
80.7%
82.4%
90.8%
43.2%
58.8%
70.9%

July 2017

3rd
Enroll.
38
92
91
94
130
95
56
117
61
66
53
100
90
38
89
41
62
36
92
58
95
87
120
61
55
50
98
78
90
37
67
97
107
84
36
81
142
100
28
173
133
75
55
120
60
52
160
57
117
69
97
90
90
36
88
118
70
120
75
66
49
52
52
67
66
48
65
45
23
103

Sequential
School #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70

Sampling
Interval #
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
6
6
6
6
6
6
6
6
6
6
7
7
7
7
7
7
7
7
7
7

Selected
School

Status

6

Selected school Tamassee-Salem refused.
15
16

Replacement
Refused

Refusing school is in interval 11-20. Select
random number in interval 11-20 = 15
Replacement is school 15, Springfield.

26

36

46

50

Refused

Replacement

Selected school La France refused.
Refusing school is in interval 41-50. Select
random number in interval 11-20 = 50
Replacement is school 50, West Pelzer.

56

66

11

Glossary
Cluster sampling: Sampling groups rather than individuals. This is practically always necessary to gain
efficiencies in survey logistics, i.e. larger samples can be assessed for lower cost. For example, in surveys of
schoolchildren, multistage cluster sampling is typically employed, e.g. sampling school districts, then schools
within the selected districts, then possibly classes within selected schools. Cluster sampling effectively reduces
your sample size to the extent that individuals in clusters are more similar than individuals between clusters,
that is, confidence intervals are usually wider for given sample size in cluster sampling than if simple random
sampling were employed (see Design effect). The specific issue is intracluster or intraclass correlation, which is
accounted for in statistical programs designed for analysis of survey data employing complex sample designs
(e.g. SUDAAN, and survey analysis procedures in SAS and Stata). The degree of intracluster correlation varies by
the outcome analyzed, differing for different outcomes measured in the same survey. An obvious example of
cluster sampling in a 3rd grade survey is the selection of schools, with screening of children from selected
schools.
Design effect: The ratio of the variance of the estimator based on the employed complex sample design to the
variance of the estimator based on a simple random sample of the same size.
Nonresponse: Nonresponse can be associated with nonresponse bias (refusing children differing from
participating children in the survey variables of interest), which is difficult to assess and can vary depending on
the population and the variable. To the extent that response rates differ from school to school, the ultimate
probability of being in the survey sample will differ, even when schools are sampled with equal probability.
Oversampling: Sampling groups at different rates within a population. This is done when you are interested in
getting good estimates of a particular subpopulation (e.g. low SES) or when you are particularly interested in
estimates and comparisons for subgroups of the population, e.g. different regions of a state, rather than just
maximizing precision of overall population estimates. With set resources, oversampling will likely have a small
effect on loss of precision (i.e. wider confidence interval) of overall population estimates and estimates of the
groups that end up under-sampled. NOTE: this can occur when pursuing county level data in a state survey with
limited resources, where the resulting sampling will likely oversample low population rural counties and undersample high population urban counties.
Probability sampling: Sampling using some form of random selection where every element in the survey
population has a known or calculable non-zero chance of selection. Probability sampling is necessary for valid
estimates of statistical precision.
Purposive (“expert choice”) Sampling: Using knowledge of a population to pick or select the elements for the
sample that the sampler thinks represents the target population. This may be preferable to probability sampling
where a small number of elements are to be selected or where there is an increased potential for sampling error
with random methods. However, purposive sampling can introduce bias and does not allow for statistical
precision estimation. Quota Sampling is a variation of this, where specified numbers of subcategories of the
population are purposively selected in proportion to population numbers in an attempt to achieve better
representation of the population.
Stratification: Dividing the population into groups and sampling separately from the groups. This improves your
sample to the extent that individuals in the groups are more similar than individuals between groups. Clusters
are sampled from all defined strata, ensuring that all strata are represented in the survey sample. Stratification
will usually improve precision of population estimates from survey data. Improvements in estimate precision
from stratification, however, are usually outweighed by losses in precision due to intracluster correlation
associated with cluster sampling.
Weights: Generally the inverse of the probability of selection and survey participation (consented and
information collected), which in effect is the number of children in the target population that each person in the
sample represents. This direct method is weighting based on sample design and includes adjustment for nonresponse. Post-weighting can also be employed, adjusting the survey sample to known population parameters.

July 2017

12