2004 National Youth Tobacco Survey 

Methodology Report 

Contract Number: 2003-Q-00775

Submitted to:

Office on Smoking and Health 

National Center for Chronic Disease Prevention 

and Health Promotion 

Centers for Disease Control and Prevention

Prepared by:

ORC Macro 

(Macro International Inc.)

Revised August 31, 2005
CHAPTER 1. INTRODUCTION 

The objective of the sampling design was to support estimation of tobacco use, attitudes towards 

tobacco use, cessation attempts, exposure to second-hand smoke, and environmental factors in a 

national population of students in grades 6 through 12. The study was designed to produce 

national estimates of these characteristics as measured by the NYTS questionnaire by school 

grade level (middle, high), by specific grade (6, 7, . . .12), by gender, and by race/ethnicity 

(African American, Hispanic, and Asian). 

The sampling frame encompasses all public, Catholic and other private schools in the United 

States. A stratified, three-stage sampling design involved selection of Primary Sampling Units 

(or PSUs), schools within PSUs, and intact classrooms within schools. Stratification was by 

Census Region and Metropolitan Statistical Area (MSA) status; in addition, the frame was 

stratified implicitly by state (i.e., the frame was sorted by state). Within each stratum, a PSU (a 

county, or a group of small counties, or portions of large counties) was chosen without 

replacement. In the subsequent sampling stages, schools and intact classrooms were selected 

probabilistically from sampled PSUs. 

At the first stage, 91 PSUs were selected. At the second stage, three schools were selected from

each sampled PSU. In addition, in a randomly selected subset of the 91 PSUs, one “small” 

school was selected (16 small schools in 16 sampled PSUs). 

Students in three racial/ethnic groups— African American, Hispanic and Asian—were 

oversampled by using a modified measure of size that increases the probability of selection of 

PSUs and schools with disproportionately high minority student enrollments. The measure of 

size was adjusted to equalize the expected sample size by grade. 

Chapter 2 provides a description of the 2004 NYTS sampling design. Chapter 3 describes the 

sampling methods. Chapter 4 describes data collection methods. Chapter 5 summarizes the 

methods used to weight the response data. This report also includes an appendix providing 

additional tabulations representing the weighting process (Appendix A). 

2
CHAPTER 2. NYTS SAMPLING DESIGN 

2.1 Study Objectives and Population 

The objective of the sampling design was to support estimation of tobacco use, attitudes towards 

tobacco use, cessation attempts, exposure to second-hand smoke, and environmental factors in a 

national population of students in grades 6 through 12. The study was designed to produce 

national estimates of these characteristics as measured by the NYTS questionnaire by school 

grade level (middle, high), by specific grade (6, 7, . . ., 12), by gender, and by race/ethnicity 

(African American, Hispanic, and Asian). It was also expected to produce additional estimates, 

such as by grade/gender and by race/ethnicity by school grade level. 

The universe for the study consisted of all public, Catholic, and other private school students 

enrolled in regular middle schools and high schools in grades 6 through 12 in the 50 states and the 

District of Columbia. Excluded are students enrolled in regular schools who are unable to complete 

the questionnaire without special assistance. Also excluded are students enrolled in alternative 

schools, special education schools, Department of Defense operated schools, and vocational schools 

that only serve students who are enrolled at another school. 

2.2 Designed Sample Sizes 

The sample was designed to satisfy the following requirements: 

1. 10,500 middle school students @ 3,500 per grade (grades 6-8) 

2. 14,000 high school students @ 3,500 per grade (grades 9-12) 

3. The sample design and size should be large enough to yield reliable estimates for the 

following: 

a. Individual grades (6, 7, 8, 9, 10, 11, and 12) 

b. Individual grades by gender (male/female) 

c. Race/ethnicity (African American, Hispanic, Asian, White) by middle school 

(grades 6-8) and high school (grades 9-12) 

To satisfy these precision requirements, the study required a final yield of approximately 24,500 

students. It was necessary to draw an initial sample that is considerably larger than this target 

number to compensate for school and student non-participation. While recognizing response 

rates attained in prior cycles of the NYTS (83% to 90% for schools and 91% to 93% for 

students), we assumed for sampling purposes more conservative rates of 82% for schools and 

85.5% for students, or a combined rate of approximately 70%. 

The sampling design specifies approximately equal sample sizes for each grade, so that gradespecific estimates may be made that meet the criteria above. Note that estimates for combined 

high-school grades are necessarily more precise than those for middle school grades because the 

sample sizes are larger for the combined high-school grades. 

The large projected sample size permits analysis by gender without any special considerations in 

the sampling plan. Gender subgroups cut across schools (usually) and across grades, and each 

gender group constitutes about half of the student sample, or an anticipated 12,250 students per 

3
group.

1

 Estimates by gender and grade have slightly larger standard errors than those for other 

key analysis groupings. While 95% confidence intervals will be within 3 percentage points for 

all other estimates, estimates by grade and gender will be within 5 percentage points. 

Another critical design parameter is the sample size per school. This requires striking a balance 

between the size distributions of schools and the burden that would be placed on schools if 

substantially larger student samples were drawn in larger schools. For consistency with prior 

cycles of NYTS, we maintained a target sample size of 125 students per school, which ordinarily 

amounts to random selection of 4 to 6 class sections (most typically 5). The actual number of 

classes selected depended on the average number of students per class section in the required 

subject selected as a frame from which to select classes. This approach generated approximately 

equal numbers of students selected across targeted grades. 

About 6.5 percent of U.S. students attend small schools defined as those having fewer than 125 

students across targeted grades. Proportional representation of these schools would yield 

approximately 18 small schools into the sample. The design ensured sufficient sample 

representation of small schools by creating separate strata for small schools, and allocating a 

specified number of units to these strata. 

The design was based on an average yield of 103.8 students per school across both small and 

large schools. (In small schools, all eligible students were selected into the sample.) This 

anticipated average yield was similar to the student yield attained in the 2002 NYTS, and 

conservatively, it was substantially lower than the student yield attained in the NYTS 1999 and 

2000. 

The sample design was constructed to support separate analysis for subsets of students, including 

high school and middle school students; 6th through 12th graders as separate groups; males and 

females, in total, by level, and by specific grade; and African American, Hispanics, and Asian 

students in total and by level.

High School and Middle School Estimates 

Estimates by school level are required to support separate analysis of students across senior high 

school grades (9, 10, 11, and 12) and across middle school grades (6, 7, 8). The problem presented 

by this requirement was that schools do not have consistent grade structures, so it is impossible to 

divide a sample of schools in a manner that also uniformly divides students by grade. For example, 

9th grade students are served by both 7-9 junior high schools and by 9-12 high schools. We also 

sought a simple sampling approach in order to be able to draw the sample in a concentrated time 

period. As a result, we rejected approaches that would require artificially slicing and melding 

schools (e.g., removing a 9th grade from a junior high school and attaching it to a high school for 

sampling purposes).

Another approach would have been to create a rule that would classify all schools as either 

“Middle” or “High” and select one of each from every PSU. However, after an examination of the 

 1 As shown in Kish (1965, Chapter 5), for example, design effects will be relatively small for subgroups that cut 

across clusters (i.e., schools); therefore, gender group estimates will have better precision than other groups than are 

less evenly dispersed across schools (e.g., racial/ethnic groups).

4
grade structure of schools by level in the sampling frame, it became apparent that any grouping of 

schools would result in certain grades being found frequently in both groupings. 

Further analysis revealed that the sample size requirements for the two grade-based domains of 

study (high/middle) could be satisfied through the use of an implicit stratification scheme. We

therefore chose an approach based on implicit stratification. Implicit stratification is a technique 

used in systematic sampling. Implicit stratification by grade was achieved by sorting the sampling 

frame (or list of schools) by grade (see Section 3.3). 

Gender Group Estimates

The large sample size permitted analysis by gender without any special considerations in the 

sampling plan. During the class selection process we avoided wherever possible, all-male or allfemale classes (unless it was a single-gender school). 

Racial Group Estimates 

In order to support the analysis of the data for African American, Hispanics, and Asian students

separately, and by grade level (middle and high), adequate sample sizes were required for subgroups 

defined by a) grade level by racial grouping, or b) gender by racial grouping. 

Sample sizes were not designed to support detailed analyses by gender and grade level within 

racial/ethnic subgroups (e.g., middle school Hispanic males). 

The design used selection with probabilities proportional to size (PPS) sampling methods with a 

weighted measure of size that increased the chances of selecting PSUs and schools with 

relatively high minority enrollments, thereby increasing the likelihood of selecting classrooms 

with relatively high concentrations of targeted minority students. 

An analysis of precision levels for these racial/ethnic group estimates from prior cycles of the 

NYTS indicated that this approach would produce estimates with a Confidence Interval (CI) of 

+3% in all but one case, and +5% in all cases. Table 1 presents the number of cases underlying 

these estimates for the prior cycles of the NYTS, as well as our target sample sizes by subgroup 

for this cycle. Even for Asians at the middle school and high school levels, 95% confidence 

intervals (CIs) were projected to be within plus or minus 3 percentage points, with the exception 

of one estimate that yields CIs within 5 percentage points. 

Table 1. Expected Racial/Ethnic Group Sample Sizes 

2000 NYTS Sample 2002 NYTS Sample 2004 NYTS (expected)

Sample

Key Racial/

Ethnic 

Subgroup Group Size % of Sample Group Size % of Sample Group Size % of Sample

Asian 2,158 6.07% 1,698 6.49% 1,593 6.50% 

Hispanics 7,445 20.96% 5,647 22.12% 5,420 22.12% 

African 

Americans 

5,750 16.18% 5,051 19.69% 4,826 19.67% 

Total student 

sample size 

35,828 26,108 24,500

5
Small Schools 

In small schools, defined as schools with fewer than 125 students across the targeted grades for 

which the school was selected, it was not possible to select the targeted 125 students per school. 

Although there are a large number of these schools, they account for a small proportion of the 

student universe. Further, they are more expensive per student survey as they incur all of the 

costs involved with recruiting a school and dispatching a field data collector, but produce 

somewhat smaller samples. 

Our strategy treated the small schools as a stratum to be sampled and surveyed in addition to the 

“main” survey sample. We computed a sample allocation to the small school stratum that would 

result in proportional representation of students enrolled in small schools as part of the national 

sample. This created a target number of schools that were selected from the same PSUs used in 

the main sample draw. Our coverage of the middle and high strata was guaranteed by the main 

sample draw; the supplemental draw guaranteed coverage of the small school segment of the 

population. 

2.3 Actual Sample Yield and Participation Rates 

Participation rates for this survey were high: 93% of the selected schools and 88% of selected 

students participated. Detailed numbers are provided below in Table 2. 

Table 2. Participation Rates and Number of Participants

Initial Sample Sizes No. Participants Participation Rate 

Schools 

 

 288

 

267 93%

Students 31,774 27,933 88%

6
CHAPTER 3. SAMPLING METHODS 

The sampling frame included public, Catholic, and other private schools in the 50 states and the 

District of Columbia with at least one grade in the 6 through 12th grade range. The sampling 

process employed a three-stage cluster design stratified explicitly by geography and MSA status. 

Within each stratum, a PSU (a county or a group of small counties or part of a very large county) 

was chosen without replacement from which a probabilistic selection of schools and students was 

subsequently made. Schools within each PSU were implicitly stratified by the highest and lowest 

eligible grade present, geographic location, and eligible enrollment. 

3.1 Measure of Size

The sampling approach utilized probability proportional to size (pps) sampling methods, in which 

the probability of a PSU being selected was proportional to the “size” of the PSU. This section 

describes the measure of size used. 

One way of accomplishing oversampling of African American, Hispanic, and Asian students was 

to use a modified measure of population size during the pps sample selection steps. A function of

the form raA + rbB + rhH + roO is sought where the r's are the weighting factors for the Asian,

African American, Hispanic and Other populations (A, B, H, and O, respectively). This function 

can increase the chances of schools with relatively large minority enrollments entering the sample.

The effectiveness of a weighted measure of size in achieving oversampling is dependent upon the

distributions of African American, Hispanic, and Asian students in schools. For example, if U.S. 

schools had identical percentages of minorities in every school, then the sample of students from

any sample of schools would mirror the national percentages and use of a weighted measure of size 

would fail to oversample minority students. We know this is not the case, however, and a weighted

measure of size has been used in the national YRBS since its inception and also in prior cycles of 

NYTS. 

The weighted measure of size also was modified by the ratio of a given grade’s enrollment to the 

12th grade enrollment. This had the effect of equalizing the size of the grade level enrollment so as

to more equally distribute the sample across grades. 

The weighting function used was. 

(1.0 9.0 5.0 16.0 )

grades i i i i i i

Size = ∑ ER O + H + B + A ∈

where i denotes the grade, ER denotes the enrollment ratio for the ith grade, and Ai, Bi ,Hi , and Oi

denote the minority enrollment for that grade as described above.

This weighted measure of size for large schools was summed to compute stratum and PSU sizes. 

Disproportionate weighting had the effect of increasing the allocation of the sample to 

high-minority strata and increasing the chances of PSUs with high minority concentrations in these 

strata being included in the sample.

7
3.2 Stage 1 – Selection of PSUs 

PSU Definition 

In defining PSUs, several issues were considered: 

•

•

•

•

•

•

Each PSU should be large enough to contain the requisite number of schools and students by 

grade. 

Each PSU should not be so large as to be selected with certainty 

Each PSU should be compact geographically so that field staff can go from school to school

easily. 

There should be recent data available to characterize the PSUs. 

PSU definitions should be consistent with secondary sampling unit (school) definitions. 

Generally, counties were equivalent to PSUs, except where low population counties were combined

in order to provide sufficient numbers of schools and students. In addition, very large counties were

sub-divided to minimize certainty PSUs. 

County population figures were aggregated from school enrollment data for the grades of interest. 

Enrollment data were obtained from the most recent Common Core of Data from the National 

Center for Education Statistics and the current school and school district data files of Quality 

Education Data, Inc. (QED). 

The NYTS 2004 PSU definitions were consistent with those used in previous NYTS cycles. 

PSUs were created using special software developed by Macro that ensures that each PSU has the 

correct number of schools and students; map data were also used to ensure that each PSU was 

compact geographically. 

Stratification and Selection of PSUs 

The PSUs were organized into 8 strata, based on urban/rural location and regional division. PSUs

were classified as “urban” if they were in one of the 54 largest MSAs in the U.S.; otherwise, they

were considered “rural.” 

At the first stage, 91 sample PSUs were selected. The sample PSUs were allocated to the strata in

proportion to weighted enrollments (measures of size). At the second stage, three schools were 

selected from each sampled PSU. In addition, in a subset of the PSUs, one “small” school was 

selected (16 small schools in 16 sub-sample PSUs). 

In each stratum, the PSUs were sorted by five-digit zip code (an implicit geographic stratification) 

and selected with probability proportional to size as follows: 

A sampling interval was computed by dividing the sum of the measures of size for the PSUs in a 

stratum by the number of PSUs to be selected. 

Any PSUs larger than the 80% of the sampling interval was split into sub-PSU using a process that

assigned schools randomly to equally sized groups. These sub-PSU were then sampled.

8
• The PSU sample was drawn using a systematic pps sampling method. 

3.3 Stage 2 – Selection of Schools 

Schools in selected PSUs were assigned to one of the two school strata if they had at least one

eligible grade. Schools were classified as “large” if they had 125 or more students across all

targeted grades for which the school was selected; otherwise, schools were classified as small.

Refusing schools were not replaced. The sample sizes anticipated a certain amount of nonparticipation by allowing for refusals in calculating the number of schools initially drawn. 

Schools in a PSU were sorted by highest grade, lowest grade, zip code and enrollment; a 

systematic, random sample of three schools was then taken from this sorted school frame. 

Sorting the frame is a form of implicit stratification that helps ensure that the sample represents 

different geographic areas and the full range of eligible grades available in the schools in each 

PSU. We attempted to select approximately equal sample sizes for each grade, so that gradespecific estimates may be made. 

 

Large Schools 

Three large schools were selected per PSU with probability proportional to the weighted measure of

size of the school, using a systematic sampling procedure with a random start. Prior to sampling, 

schools were sorted by the highest eligible grade, then lowest eligible grade, then geographic 

location, and finally by eligible enrollment. This sort implicitly stratified the sample by high 

school/middle school grades. 

Small Schools 

In the small school stratum, we calculated the percentage of students that should come from small 

schools to reflect the representation of students from small schools as a proportion of all students. 

The small school sample had approximately the same number of students as their proportion in the 

population. We randomly selected a sub-sample of the selected PSUs equal in number to the 

number of small schools to be selected. One small school per sub-sampled PSU was selected with 

probability proportional to size, using the weighted measure of size. 

9
3.4 Stage 3 – Selection of Classes 

The method of selecting students varied somewhat from school to school, depending upon the 

organization of that school. To ensure that all students had one and only one chance of being 

selected to participate, classes ordinarily were chosen from required core courses such as English, 

social studies, math, or science. Among middle school students (and in a few states from among 

high school students), physical education and/or health also were considered core courses. In some

schools, it was extremely difficult to develop an appropriate frame. Therefore, in small number of 

schools, classes were selected by using a time of day when all students had class, and randomly

selecting from all classes held at this time (usually second period). As a variation on this approach, 

in some schools homerooms were used as the frame for class selection. Homerooms are particularly 

good choices because the homeroom teacher usually has a strong relationship with students and can 

be particularly helpful in securing parental consent and student cooperation. However, relatively 

few schools have homerooms meeting of sufficient duration to conduct the survey. 

The target number of students to be selected within a given school remained constant at 125; this

number was smaller in schools with fewer than 125 students across the grades of interest. The 

number of classes to be selected varied slightly depending on the average class size. The number of

students to be selected was calculated by dividing the total enrollment at the grades of interest by the

number of class sections available in the chosen core subject area or at the selected time period. 

This resulted in the number of sections to be selected. An Excel program was used to select class 

sections using systematic sampling procedures. Using the average classroom size, this process 

consistently targeted the number of classes needed to meet or exceed the 125 student requirement. 

Of course, in practice, because average class sizes were employed, the number of students actually

selected in each school varied from this 125 student target. Ordinarily, 4 to 6 class sections were 

selected in large schools, with 5 class sections being the norm. 

All students in a selected classroom who could complete the survey without special assistance were 

considered eligible and offered the opportunity to participate in the survey. Refusing students were

not replaced. Non-response at the student level was accounted for in the sample size using an 

average per class yield that assumed student response rates derived from historical experience with 

the NYTS. 

 

3.5 Probabilities of Selection 

This section describes the probabilities of selection associated with the various sampling stages. 

These probabilities will provide the basis for the sampling weights discussed in Chapter 5. 

If ni is the number of PSUs to be selected from stratum i, Si is the size of stratum i, and Sij is the size

of PSU j in stratum i (in all cases "size" refers to our measure of size), then the probability of

selection of PSU i is niSij/Si. For the two schools to be selected in stratum i, Sijk is the size of school

k in PSU j in stratum i, and then the conditional probability of selection of the school given the

selection of the PSU is 3Sijk/Sij. If Cijk is the number of classes in school ijk and m is the number of 

classes to be selected, then the conditional probability of selection of a class is m/Cijk. Since all

10
students were selected, the conditional probability of selection of a student given the selection of the 

class is unity. 

The overall probability of selection of a student in stratum i is the product of the conditional 

probabilities of selection:

Equation 1:

⎟

⎟

⎟

⎠

⎞

⎜

⎜

⎜

⎝

⎛

⎟

⎟

⎟

⎠

⎞

⎜

⎜

⎜

⎝

⎛

ij ijk

ijk

i

i ij

C

m

S

S

S

n S 3

We note that if the number of classes were exactly proportional to the size of the school, then the 

probability of selection for a student would be constant throughout each stratum. This sort of 

“self-weighting” sample tends to be statistically efficient. The probabilities of selection were the 

same for all students in a given school, regardless of their ethnicity, but varied across schools 

depending upon the racial/ethnic mix of the schools and their surrounding regions. 

11
CHAPTER 4: DATA COLLECTION

The management of the NYTS 2004 data collection process combined recruitment and 

scheduling of schools for data collectors all over the country with ongoing cycles of mailings to 

schools in preparation for data collection. In addition, Macro hired and trained field staff and 

provided careful, supportive management over the course of the project. 

4.1 Recruitment and Scheduling Schools 

Schools representing 35 states were selected to participate in the NYTS 2004 (not all states are 

represented because the design did not control for this). Recruitment began in August of 2003 

with calls to State Departments of Education and Health. Letters of support were obtained from

State agencies and used in mailings to districts and schools. District and school recruitment 

began in September of 2003. Once schools agreed to participate, approximately 5 classes 

(typically 125 students) were randomly selected along with a date for data collection. The date 

was selected to optimize the efficiency of data collection while accommodating school 

schedules. In selecting a date, Macro considered convenience to the school and its calendar 

while also trying to group schools from the same school district or PSU together. Recruiters used 

an electronic calendar on a secure, shared drive to facilitate communication and avoid scheduling 

two schools for the same data collector on the same day. 

4.2 Mailings to Schools 

Once schools had been recruited, classes selected, and a date scheduled, each school received a 

packet of pre-survey materials. These materials included all the information necessary to prepare 

the school for data collection. Most importantly the teacher’s packets contained the parental 

permission forms that had to be given out to all students in the selected classes prior to data 

collection. The timing of these pre-survey packet mailings was determined in part by the type of

permission form selected by the school. If a school selected passive parental permission forms, 

or forms returned only if the parents do not want their child to participate, these would be sent 

approximately one week prior to the scheduled date of data collection. If the school selected 

active parental permission forms, or forms that must be returned with the parent’s signature in 

order for the child to participate, these packets were sent out at least two weeks prior to the 

scheduled date of data collection. Macro followed up with the schools to answer questions and 

make sure materials were received and distributed to selected classes and students.

4.3 Hiring and Training Data Collectors 

Data collectors were recruited from a pool of previously trained data collectors as well as from

retired teachers associations, school health networks, and a variety of health education electronic 

lists. Of the 12 data collectors hired, six were returning to work on their third, fourth, or even 

seventh Macro school-based survey. Data collector training was conducted on March 4 through 

6, 2004. 

12
4.4 Management and Support of Data Collectors in the Field 

On a weekly basis, data collectors received mailings containing their assignments for the coming 

week, travel and logistics to get them where they needed to be, and delivered their must read 

weekly bulletin. Weekly bulletins underlined key performance issues, corrected misconceptions, 

provided consistent direction on any procedural changes, and kept everyone abreast of the latest 

must have information among the NYTS group (data collectors, Macro, and CDC/OSH staff). In 

addition to these mailings, boxes of survey supplies were sent to data collectors at their next 

week’s site. These boxes contained all supplies necessary for completing the data collection: 

questionnaires, envelopes, field forms, and pencils. 

In addition to receiving multiple mailings, supervisors remained in close contact with the data 

collectors by phone and email, including daily contact during the first week and no less than 

twice-weekly contact thereafter. These contacts also reviewed performance, provided reminders, 

and gave emotional support. In addition, these phone calls gave data collectors the opportunities 

to ask questions, provided feedback from schools, and discussed difficult or rewarding data 

collection experiences. 

4.5 Survey Administration 

Survey administration in the schools began immediately after data collector training on March 8 

and continued until June 22, 2004. Each data collector visited an average of 3 schools per week. 

While the details of each data collection varied, there were 6 steps followed in every school 

including: (1) Precontact call with the principal or lead contact prior to arrival at the school; (2) 

Entry meeting with the principal or lead contact; (3) Entry meeting with teacher or group of 

teachers prior to survey administration; (4) Survey administration; (5) Post-survey meeting with 

the teacher or teachers; and (6) Post-survey meeting with the principal or lead contact prior to 

leaving the school. Most survey administrations could be completed in one day, while at other 

times, due to the number of classes selected or alternating block schedules, the data collector 

needed to return for a second day. Procedures were designed to protect students’ privacy by 

assuring that student participation was anonymous and voluntary. Students completed a self 

administered, scannable questionnaire. 

4.6 Makeup Sessions 

Macro followed essentially the same make-up procedures followed on previous cycles of the 

NYTS. In each class, if students were eligible to participate but were absent on the day of the 

survey, a Make Up List was completed. Copies of the Make Up List were given to the 

applicable teacher and to the principal/lead contact; one also was kept by the data collector. 

Every effort was made to have the data collector return at least once to each visited school to 

conduct a make-up session if necessary. However, sometimes there was no opportunity for the 

data collector to return to a school prior to leaving for the next site; or, coming back while the 

data collector was still in the area was too soon for a make-up session. In these and other 

similar situations, teachers were asked to administer makeup surveys and send them back to 

Macro in business reply envelopes. These supplementary makeups closely followed the national 

YRBS model for teacher-administered make-up sessions. This ensured comparability of data 

and protected respondent anonymity while at the same time maximizing response rates. 

13
After data collection was completed in a school, data collectors sent thank you letters to each of 

the participating teachers and the principal/lead contact. This allowed the data collector an 

opportunity to connect once more with the staff at the school, inquire as to the status of makeups 

expected, and encourage further participation. 

4.7 School and Student Participation Rates

Participation rates for this survey were high and generally comparable to participation rates 

achieved in the 1999 and 2000 cycles of NYTS. Of the 288 eligible schools, 267 (93%) 

participated in the 2004 NYTS. Among the 31,744 sampled youths enrolled at the 267 

participating schools, 27,933 (88%) participated. This resulted in a combined overall response 

rate of 82%. 

14
CHAPTER 5. WEIGHTING 

This section describes the procedures used to weight the data collected in NYTS 2004. The process 

involved the steps outlined below: 

•

•

•

•

•

Sampling Weights 

Non-response Adjustments 

Adjusting Weights for National Estimates 

Weight Trimming 

Post-stratification to National Estimates of Racial Percentages by Grade 

This section focuses on the development of the weights for the student response data. The school 

profile data was weighted using the sampling weight for the corresponding school. The final data

set was weighted to reflect the initial probabilities of selection and non-response patterns, to 

mitigate large variations in sampling weights, and to post-stratify the data to known control 

characteristics. 

5.1 Sampling Weights 

The basic weights were computed on a case-by-case basis as the reciprocal of the probability of 

selection of that case. A base weight, or sampling weight, incorporating adjustments for nonresponse and scaling to total school enrollment at the student level, was computed in three stages. 

PSU-level Probabilities 

The PSU component of the sampling weight was computed by the sampling program as part of the

sampling process, with certainty PSU handled as described in section 3.2. The resulting weight is: 

Equation 2:

ij i

i P

ij n S

S W =

For small schools, the PSU component of the weight was multiplied by the ratio of the number of 

PSUs to the number of PSUs selected to have a small school drawn, or 16. 

Table A-1 in Appendix A shows the number of PSUs formed in each stratum and the number of 

PSUs sampled in each stratum. Table A-2 (Appendix A) gives, for each sampled PSU, the total 

large school size measure for the stratum and for the PSU, the PSU-level sampling weight after 

removal of certainty PSUs, and the number of times the PSU was taken into the sample. 

School-level Probabilities

The school level component of the sampling weight also was computed by the sampling program, 

accounting for schools selected with certainty as described in section 3.3. The weight was computed 

as in Equation 3 with Table A-3 (Appendix A) giving the school measure of size and the school 

15
component of the sampling weight. Note that for schools identified as small schools, only one 

school was selected per PSU. 

Equation 3:

ijk

ij

S

ijk S

S

W

3 =

Student-level Probabilities 

The student level component of the sampling weight was computed to include a post-stratification 

adjustment to total school enrollment. If rijk is the number of responding students in the school k, 

PSU j, stratum i, and Eijk is the school enrollment in eligible grades, then the weight of student l

adjusted for non-response is: 

Equation 4:

r

E W = ijk

R ijk

ijkl

5.2 Non-response Adjustments 

An overall adjustment for school non-response was made by stratum, adjusting the sum of the 

student weights to the weighted measure of size of that stratum. This adjustment was made

separately for large and small schools.

Equation 5:

⎟

⎟

⎟

⎠

⎞

⎜

⎜

⎜

⎝

⎛

∑

∑

∈

W W S

W W S

F = P

ij ijk

S

ijk

k Stratum irespondents

ijk

P

ij

S

ijk

k

i ,l arg e

The final weight of student l is . School response rates by strata and PSU, and the

resulting non-response adjustment factors, are detailed in Table 3. For small schools, a similar 

adjustment was computed using the entire small school sample as the adjusting class as shown in 

Equation 6 below. 

R

ijkl

P

ij

S Fi,l arg eWijkW W

Equation 6:

W W S

W W S

F =

ijk

P

ij

S

ijk k smallsamplerespondents

ijk

P

ij

S

ijk

i j k

small

∑

∑

∈

, ,

16
5.3 Adjusting Weights for National Estimates 

The results of the weighting steps just described were a set of weights useful for producing accurate

estimates by stratum. However, because weighted measures of size were used, development of

national estimates required a re-weighting of the strata to total enrollment. This provides two 

benefits – the weights are adjusted to represent strata in the correct proportions, and simultaneously 

adjusted to control totals. The adjustment for strata i was computed as: 

Equation 7:

∑

=

i

i

i

W

E Af

i

where Ei = enrollment totals for grades 6 - 12 and Wi is the sum of all adjusted weights for

respondents in stratum i.

Table 4 gives the enrollment, weight and adjustment for each stratum. Adjustments were made 

based on the total enrollment in all eligible grades. 

5.4 Weight Trimming 

Extreme variation in sampling weights can cause inflated sampling variances and offset the 

precision gained from a well-designed sampling plan. This variation can occur, for example, if the 

number of respondents in a particular school is very low, causing a large non-response adjustment 

factor to be computed. One strategy to compensate for this is to trim extreme weights and distribute 

the trimmed weight among the untrimmed weights. The method we used is based on a similar

procedure done for the National Assessment of Educational Progress (NAEP)2

. The trimming was

an iterative procedure. In each iteration an optimal weight, Wo, was calculated from the sum of the 

squared weights in the sample. Then, each weight, Wi, was marked and trimmed if it exceeded that

optimal weight. The trimmed weight was summed within grade and spread out proportionally over 

the unmarked cases in the grade. The process was allowed to iterate until trimming produced a 

change in the design effect due to weighting of less than one percent. Weight trimming was done 

within stratum.

Wok is determined by the following: 

Equation 8: ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ ∑ n

w W = c

2

k

n

k=1

2

1

ok

The constant c was set so that a maximum of three percent of the weight would be trimmed on the 

first iteration of the trimming process in each stratum. 

 2 Potter, F. “A Study of Procedures to Identify and Trim Extreme Sample Weights”, Proceedings of the Section on

Survey Research Methods, American Statistical Association, pp. 225-230. , 1990.

17
Let Wik and Wok be the weight for the ith case and the optimum weight for the kth iteration, 

respectively, and define Tik as 1 if Wik is greater than or equal to Wok, and zero otherwise. Then the 

trimmed weight for the k + 1 iteration is defined as follows: 

Equation 9:

⎪

⎪

⎪

⎭

⎪

⎪

⎪

⎬

⎫

⎪

⎪

⎪

⎩

⎪

⎪

⎪

⎨

⎧

⎥

⎥

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ ⎟

⎠

⎞ ⎜

⎝

⎛

≥

∑

∑

if W <W

W (1-t )

W

W

W 1-t

W if W W

W = ik ok

ik ik

n

i=1

ik

ik

ok

ik

n

i=1

ok ik ok

i,k+1

Table 5 presents the results of the weight trimming. 

5.5 Post-stratification 

National estimates of the racial/ethnic student distribution by race/ethnicity and grade within 

stratum were obtained from the QED database, which has five racial/ethnic categories: White, 

African American, Hispanic, Asian and Pacific Islander, and Native American. Weights were poststratified to national estimates of enrollment obtained from the QED database within the crossclassification of grade and race/ethnicity. 

Given a national estimate of Ra and a weighted population estimate of Pa for race/grade combination 

a, the simple post-stratification factor would be the ratio of Ra to Pa for each race and grade. 

However, this process sets weights for the respondents giving “Other” and “Missing” responses to 

either the grade or race questions to zero. Missing responses were imputed using a hot-deck method, 

with adjustable imputation classes prior to the post-stratification step. 

Table 6 gives for each post-stratification cell, the percentage of weight, the percentage of 

enrollment, and the post-stratification adjustment. 

Table 3. School Response Rate by Stratum 

Table 3

School Responding Schools Sampled Schools 

Size

Stratum 

Weighted Size

Measure 

Count Weighted Size

Measure 

Count 

Percent 

Responding

NonResponse

Adjustment

1N 2,712,926.62 20 2,851,884.61 21 95.238 1.05122

1U 7,167,044.95 27 7,954,082.93 30 90.000 1.10981

2N 4,196,430.27 34 4,328,590.76 35 97.143 1.03149

2U 5,116,443.67 24 5,749,268.20 27 88.889 1.12368

3N 13,412,088.64 60 13,412,088.64 60 100.000 1.00000

3U 9,361,456.11 32 10,535,059.82 36 88.889 1.12537

4N 6,452,981.18 24 7,307,078.27 27 88.889 1.13236

4U 12,670,485.30 31 14,707,580.86 36 86.111 1.16077

Large 

Overall 61,089,856.74 252 66,845,634.10 272

Small 3,879,402.21 15 4,097,141.18 16 93.75 1.05613

18
Table 4. Enrollment Weight Adjustment

Table 4

Stratum Enrollments Adjustment

Frame 

(Control)

Estimated 

(Weighted Responses)

1N 1,817,515.66 2,246,092.51 0.80919

1U 2,827,559.08 2,691,499.92 1.05055

2N 3,419,268.25 2,804,530.28 1.21919

2U 2,585,788.29 3,223,772.03 0.80210

3N 5,600,778.96 4,397,780.00 1.27355

3U 3,446,121.09 3,019,407.35 1.14132

4N 2,412,222.41 2,146,928.16 1.12357

4U 3,422,019.51 3,667,373.52 0.93310

Total 25,531,273.24 24,197.383.77

Table 5. Trimming

Table 5

Stratum Trim Number Trim Weight Adjusting Weight Variance Design

Factor Cases Iteration Optimal Factor Trimmed Weight Effect

1N 10.9 2,506 Initial 5507.49 1.00000 2159.45 1398534.11 3.6577

Final 4155.16 1.00161 2380.18 1053750.67 3.0025

1U 3.0 2,638 Initial 4107.47 1.00000 2332.38 743374.61 1.6468

Final 2200.84 1.00281 2200.84 461641.31 1.4017

2N 10.0 3,976 Initial 144049.88 1.00000 1688.49 36730994.75 50.6535

Final 4038.61 1.00413 2499.55 875981.59 2.1842

2U 10.0 2,780 Initial 11731.91 1.00000 1564.27 2635417.64 4.0451

Final 4375.79 1.00139 1905.52 1043976.76 2.2063

3N 5.5 6,319 Initial 5368.46 1.00000 1511.10 610737.58 1.7773

Final 2467.31 1.00245 1626.44 315902.26 1.4021

3U 3.1 3,506 Initial 2916.31 1.00000 2111.44 663054.60 1.6861

Final 2140.74 1.00199 2140.74 509817.43 1.5275

4N 7.5 2,596 Initial 5944.09 1.00000 3049.97 1877514.12 3.1737

Final 4268.11 1.00119 3277.82 1562386.90 2.8088

4U 10.0 3,612 Initial 25503.59 1.00000 973.84 10380038.98 12.5614

Final 3952.07 1.00325 1655.41 650089.61 1.7241

19
Table 6

Adjusting Class Percent Students Number 

Cases

Post-stratification 

Race/Ethnicity Grade Control Adjustment

(Population)

Estimate 

(Weighted 

Responses)

African American 06th 2.5473 2.7876 808 0.9138

African American 07th 2.4936 3.2555 952 0.7660

African American 08th 2.3976 3.2577 925 0.7360

African American 09th 2.6177 2.6356 802 0.9932

African American 10th 2.0809 2.0394 585 1.0203

African American 11th 1.7338 2.2713 658 0.7633

African American 12th 1.5340 1.9567 569 0.7840

Native American 06th 0.1625 0.6548 165 0.2482

Native American 07th 0.1632 0.5845 147 0.2792

Native American 08th 0.1563 0.4832 126 0.3236

Native American 09th 0.1621 0.3478 94 0.4660

Native American 10th 0.1416 0.2362 65 0.6089

Native American 11th 0.1243 0.1670 44 0.7445

Native American 12th 0.1142 0.1592 37 0.7175

Asian 06th 0.6335 0.8012 252 0.7907

Asian 07th 0.6317 0.7378 282 0.8562

Asian 08th 0.6121 0.7023 249 0.8715

Asian 09th 0.7136 0.7903 311 0.9029

Asian 10th 0.6381 0.6866 243 0.9293

Asian 11th 0.5705 0.5568 193 1.0245

Asian 12th 0.5130 0.4649 167 1.1034

White 06th 9.8013 9.1639 2239 1.0695

White 07th 9.8177 8.8543 2163 1.1088

White 08th 9.6656 8.6892 2093 1.1124

White 09th 10.3459 8.0674 1782 1.2824

White 10th 9.3866 7.2399 1718 1.2965

White 11th 8.5246 6.1781 1383 1.3798

White 12th 2.5869 4.8374 1106 1.6334

Hispanic 06th 2.3315 3.4715 1276 0.6716

Hispanic 07th 2.2585 3.5978 1255 0.6278

Hispanic 08th 2.1730 3.3606 1181 0.6466

Hispanic 09th 2.2630 3.5118 1395 0.6443 

Hispanic 10th 1.8526 2.8814 1029 0.6429

Hispanic 11th 1.5704 2.3899 833 0.6571

Hispanic 12th 1.3663 2.1838 806 0.6256

20
APPENDIX A. Additional Tables 

Table A-1 Stratum Summary 

Table A-1

Stratum Stratum Size Measure PSU Count 

Frame Sampled 

1N 3,084,333.96 118 7

1U 8,530,082.18 54 10

2N 4,890,946.31 376 12

2U 6,119,821.02 61 9

3N 14,009,471.54 454 20

3U 10,961,113.52 85 12

4N 8,102,645.44 133 9

4U 15,701,018.14 35 12

21
Table A-2 PSU Sampling 

Table A-2

Stratum PSU Size Measure Expected Number 

Draws 

Sampling

Weight

Subsampled 

For 

Small 

Schools 

1U 421010 520345.37 0.61001 1.6393 Yes

1U 360050 585249.47 0.68610 1.4575 No

1U 360470 445998.78 0.52285 1.9126 Yes

1U 360610 567580.70 0.66539 1.5029 No

1U 250230 81894.92 0.09601 10.416 No

1U 250270 131831.96 0.15455 6.470 No

1U 340070 125509.23 0.14714 6.7964 No

1U 340130 249173.71 0.29211 3.4233 No

1U 360810 441411.63 0.51748 1.9325 No

1U 361030 290960.13 0.34110 2.9317 No

1N 340170 245836.86 0.55794 1.7923 Yes

1N 420490 37692.99 0.08555 11.6897 No

1N 420770 74237.53 0.16848 5.9353 No

1N 090090 168940.49 0.38342 2.608 Yes

1N 330110 53597.00 0.12164 8.2210 No

1N 360650 28086.87 0.06374 15.6877 No

1N 360830 17899.70 0.04062 24.6160 Yes

2U 170311 452197.48 0.66502 1.504 No

2U 170312 464639.64 0.68331 1.463 Yes

2U 170313 442519.16 0.65078 1.537 No

2U 170890 120245.44 0.17684 5.655 No

2U 180970 161442.34 0.23742 4.212 No

2U 261630 469842.10 0.69096 1.447 No

2U 270030 41818.46 0.06150 16.260 No

2U 291830 33919.60 0.04988 20.0468 No

2U 390350 281240.38 0.41360 2.4178 No

2N 550730 30918.43 0.07586 13.1824 No

2N 390950 86986.37 0.21342 4.6855 Yes

2N 391390 14708.76 0.03609 27.7099 Yes

2N 171230 7761.18 0.01904 52.515 No

2N 180350 12649.27 0.03104 32.222 No

2N 180890 125874.20 0.30883 3.238 No

2N 190190 3926.67 0.00963 103.798 No

2N 201350 5153.60 0.01264 79.086 No

2N 260210 31538.21 0.07738 12.923 No

2N 260810 112157.51 0.27518 3.634 No

2N 290190 17035.75 0.04180 23.9249 No

2N 270670 8714.34 0.02138 46.7711 No

3U 120110 489983.25 0.53642 1.864 No

3U 120970 359560.45 0.39364 2.540 No

3U 132550 101681.48 0.11132 8.983 No

3U 240050 150770.45 0.16506 6.058 No

3U 240330 296833.36 0.32497 3.077 No

3U 370590 26915.08 0.02947 33.9373 No

3N 280510 14186.34 0.02025 49.3766 No

3N 010110 73441.07 0.10484 9.538 No

22
Table A-2

3N 100050 25108.04 0.03584 27.898 No

3N 120250 533213.14 0.76122 1.314 No

3N 120251 548576.46 0.78315 1.277 Yes

3N 120870 79604.78 0.11364 8.799 No

3N 120890 189139.68 0.27002 3.703 No

3N 132510 79402.76 0.11336 8.822 No

3N 210670 36289.54 0.05181 19.302 Yes

3N 220730 35389.55 0.05052 19.793 No

3N 371630 27635.89 0.03945 25.3465 No

3N 401090 140312.24 0.20031 4.9922 No

3N 450450 68567.86 0.09789 10.2158 No

3N 470470 334457.16 0.47747 2.0944 No

3N 480050 22193.96 0.03168 31.5614 No

3N 484890 293223.71 0.41861 2.3889 Yes

3N 481630 93773.36 0.13387 7.4699 No

3N 481750 40717.32 0.05813 17.2033 No

3N 483830 109723.53 0.15664 6.3840 No

3N 511430 10695.22 0.01527 65.4941 No

3U 481130 888888.33 0.97314 1.0276 No

3U 482010 482910.46 0.52868 1.8915 No

3U 482011 490164.93 0.53662 1.8635 No

3U 484390 457630.45 0.50100 1.9960 No

3U 484930 750090.45 0.82118 1.2178 Yes

3U 511770 56929.89 0.06233 16.0448 No

4U 040130 887871.70 0.67858 1.474 Yes

4U 060170 80604.77 0.06160 16.233 Yes

4U 060371 885857.36 0.67704 1.477 No

4U 060372 892906.57 0.68243 1.465 No

4U 060373 859110.91 0.65660 1.523 No

4U 060374 866098.07 0.66194 1.511 No

4U 060375 871956.39 0.66642 1.501 No

4U 060591 669999.46 0.51207 1.953 No

4U 060730 1199311.45 0.91661 1.091 No

4U 060810 312855.65 0.23911 4.182 No

4U 060850 865087.36 0.66117 1.512 No

4U 080010 116657.34 0.08916 11.216 No

4N 530530 173317.17 0.19251 5.1945 Yes

4N 040230 298277.69 0.33131 3.018 No

4N 060150 14012.15 0.01556 64.251 No

4N 060190 547942.84 0.60863 1.643 Yes

4N 060310 112116.67 0.12453 8.030 No

4N 060470 138616.63 0.15397 6.495 No

4N 080170 121933.75 0.13544 7.383 No

4N 150031 561845.64 0.62407 1.602 No

4N 350250 110124.87 0.12232 8.1752 No

23
Table A-3 School Selection 

Table A-3

Stratum PSU School ID School Size

Class

School Size

Measure

Expected

Number of 

Draws

Sampling

Weight

1N 090090 00235859 Small 198.60 0.01914 52.245

1N 090090 00240111 Large 2982.17 0.05642 17.724

1N 090090 00244692 Large 1550.13 0.02933 34.097

1N 090090 00247773 Large 3158.39 0.05976 16.735

1N 330110 00853795 Large 316.79 0.01916 52.194

1N 330110 00856708 Large 4040.54 0.24438 4.092

1N 330110 00860055 Large 207.32 0.01254 79.753

1N 340170 00861616 Small 490.07 0.02183 45.816

1N 340170 00885375 Large 16873.43 0.22661 4.413

1N 340170 00893411 Large 13524.92 0.18164 5.505

1N 340170 00902712 Large 2442.24 0.03280 30.489

1N 360650 00950733 Large 787.44 0.09690 10.320

1N 360650 00991408 Large 309.29 0.03806 26.275

1N 360650 03241430 Large 2194.16 0.27000 3.704

1N 360830 00923583 Large 1014.34 0.17969 5.565

1N 360830 00955527 Large 1777.06 0.31480 3.177

1N 360830 00955571 Large 1170.60 0.20737 4.822

1N 360830 00962793 Small 92.38 0.09577 10.442

1N 420490 01217271 Large 423.81 0.03660 27.325

1N 420490 01218898 Large 800.88 0.06916 14.460

1N 420490 01222204 Large 597.65 0.05161 19.377

1N 420770 01203633 Large 5067.36 0.21245 4.707

1N 420770 01203699 Large 10785.89 0.45220 2.211

1N 420770 01232642 Large 1865.68 0.07822 12.784

1U 250230 00599464 Large 1184.65 0.04689 21.326

1U 250230 00610107 Large 13629.45 0.53948 1.854

1U 250230 00612727 Large 825.50 0.03267 30.605

1U 250270 00612658 Large 1656.27 0.04230 23.639

1U 250270 00617736 Large 3252.62 0.08308 12.037

1U 250270 00623524 Large 1120.40 0.02862 34.945

1U 340070 00872468 Large 3692.74 0.09598 10.418

1U 340070 00874396 Large 1695.53 0.04407 22.690

1U 340070 00875312 Large 6096.72 0.15847 6.310

1U 340130 00863704 Large 2098.97 0.02794 35.796

1U 340130 00893069 Large 4539.35 0.06042 16.552

1U 340130 06113992 Large 1092.52 0.01454 68.772

1U 360050 00922138 Large 827.85 0.00439 227.637

1U 360050 00972622 Large 14954.47 0.07936 12.602

1U 360050 00974175 Large 8015.38 0.04253 23.511

1U 360470 00980429 Large 4678.81 0.03295 30.348

1U 360470 00983587 Large 15852.14 0.11164 8.957

1U 360470 00984412 Small 542.82 0.02712 36.875

1U 360470 05485714 Large 3831.59 0.02698 37.059

1U 360610 00939174 Large 1244.23 0.00715 139.920

1U 360610 00974186 Large 19152.08 0.11001 9.090

1U 360610 00976966 Large 15579.95 0.08949 11.174

24
Table A-3

Stratum PSU School ID School Size

Class

School Size

Measure

Expected

Number of 

Draws

Sampling

Weight

1U 360810 00973932 Large 25817.02 0.19024 5.257

1U 360810 00980928 Large 4845.67 0.03571 28.006

1U 360810 04043335 Large 6395.88 0.04713 21.218

1U 361030 00964167 Large 1114.55 0.01195 83.693

1U 361030 00964666 Large 1978.40 0.02121 47.149

1U 361030 00970308 Large 4543.56 0.04871 20.530

1U 421010 01188409 Large 2056.58 0.01237 80.857

1U 421010 01236137 Small 480.82 0.02239 44.672

1U 421010 01236181 Large 15424.20 0.09276 10.781

1U 421010 01236942 Large 2992.56 0.01800 55.567

2N 171230 00355337 Large 238.78 0.10225 9.780

2N 171230 00381855 Large 2216.05 0.94895 1.054

2N 171230 00381913 Large 910.58 0.38992 2.565

2N 180350 00443869 Large 2394.13 0.58370 1.713

2N 180350 00443993 Large 1489.28 0.36310 2.754

2N 180350 05750966 Large 465.38 0.11346 8.813

2N 180890 00423376 Large 2277.15 0.05898 16.955

2N 180890 00435927 Large 3088.58 0.08000 12.501

2N 180890 00444104 Large 1644.15 0.04258 23.483

2N 190190 00472663 Large 600.83 0.51345 1.948

2N 190190 00473441 Large 251.62 0.21503 4.651

2N 190190 05949337 Large 170.04 0.14531 6.882

2N 201350 00498014 Large 1678.03 1.37713 0.726

2N 201350 00498025 Large 926.16 0.76009 1.316

2N 260210 00651198 Large 928.21 0.10051 9.949

2N 260210 00652191 Large 848.63 0.09189 10.883

2N 260210 00652952 Large 576.25 0.06240 16.026

2N 260810 00654337 Large 954.19 0.02771 36.090

2N 260810 00666466 Large 1749.36 0.05080 19.685

2N 260810 00672797 Large 1460.55 0.04241 23.578

2N 270670 00712426 Large 363.86 0.12815 7.803

2N 270670 00717989 Large 657.48 0.23156 4.318

2N 270670 00718009 Large 937.70 0.33026 3.028

2N 290190 00757037 Large 4735.84 0.84787 1.179

2N 290190 00783271 Large 455.76 0.08160 12.256

2N 290190 04214879 Large 1830.71 0.32776 3.051

2N 390950 01087637 Large 2395.66 0.09895 10.106

2N 390950 01087976 Large 246.44 0.01018 98.242

2N 390950 01088018 Small 462.67 0.03223 31.024

2N 390950 01088266 Large 2905.69 0.12002 8.332

2N 391390 01080405 Large 1226.66 0.26305 3.802

2N 391390 01113691 Large 1145.03 0.24555 4.073

2N 391390 01113895 Large 1010.09 0.21661 4.617

2N 391390 01905392 Small 39.50 0.05493 18.205

2N 550730 01544786 Large 4261.87 0.45396 2.203

2N 550730 01544888 Large 4349.22 0.46326 2.159

2N 550730 04129654 Large 4224.07 0.44993 2.223

2U 170311 00401567 Large 848.26 0.00618 161.916

2U 170311 00407773 Large 2751.64 0.02003 49.915

2U 170311 00412772 Large 7125.11 0.05188 19.277

2U 170312 00359706 Small 268.73 0.00725 137.943

25
Table A-3

Stratum PSU School ID School Size

Class

School Size

Measure

Expected

Number of 

Draws

Sampling

Weight

2U 170312 00366236 Large 3628.99 0.02546 39.274

2U 170312 00398916 Large 5652.57 0.03966 25.214

2U 170312 90173544 Large 6665.57 0.04677 21.382

2U 170313 00365822 Large 978.36 0.00722 138.592

2U 170313 00371257 Large 7768.00 0.05729 17.455

2U 170313 00417486 Large 172.15 0.00127 787.630

2U 170890 00357797 Large 3247.11 0.08823 11.333

2U 170890 00358382 Large 2292.36 0.06229 16.054

2U 170890 00378343 Large 2021.36 0.05493 18.206

2U 180970 00438382 Large 1105.68 0.02139 46.750

2U 180970 00447014 Large 2355.15 0.04556 21.948

2U 180970 00447386 Large 8438.96 0.16326 6.125

2U 261630 00660646 Large 4054.23 0.02777 36.012

2U 261630 00690433 Large 2036.78 0.01395 71.683

2U 261630 00692328 Large 3259.49 0.02232 44.793

2U 270030 00706398 Large 3722.89 0.27354 3.656

2U 270030 00706401 Large 4140.24 0.30420 3.287

2U 270030 05450485 Large 1486.00 0.10918 9.159

2U 291830 00752152 Large 637.66 0.05768 17.338

2U 291830 00760979 Large 1677.16 0.15170 6.592

2U 291830 00784344 Large 1660.24 0.15017 6.659

2U 390350 01058242 Large 343.27 0.00390 256.515

2U 390350 01071751 Large 4855.10 0.05514 18.137

2U 390350 03237172 Large 748.20 0.00850 117.689

3N 010110 00006396 Large 3426.75 0.15605 6.408

3N 010110 00017218 Large 1631.69 0.07431 13.458

3N 010110 00017466 Large 4789.73 0.21812 4.585

3N 100050 00251757 Large 1133.30 0.13871 7.210

3N 100050 00251837 Large 1978.64 0.24217 4.129

3N 100050 00252193 Large 2118.01 0.25922 3.858

3N 120250 00273588 Large 9408.35 0.05414 18.470

3N 120250 00273963 Large 17246.15 0.09924 10.076

3N 120250 00274049 Large 22772.37 0.13105 7.631

3N 120251 00272857 Large 7952.56 0.04449 22.474

3N 120251 00273861 Large 12755.83 0.07137 14.012

3N 120251 00274752 Large 8005.57 0.04479 22.326

3N 120251 04157003 Small 634.18 0.05120 19.533

3N 120870 00271944 Large 6346.11 0.24427 4.094

3N 120870 00278837 Large 4561.95 0.17559 5.695

3N 120870 00278892 Large 2944.30 0.11333 8.824

3N 120890 00275869 Large 2723.10 0.04394 22.757

3N 120890 00277094 Large 5786.49 0.09338 10.709

3N 120890 05743766 Large 4861.99 0.07846 12.746

3N 132510 00320971 Large 1959.75 0.07445 13.433

3N 132510 00321385 Large 1983.53 0.07535 13.272

3N 132510 05448691 Large 4715.60 0.17913 5.582

3N 210670 00515246 Small 156.38 0.37418 2.672

3N 210670 00522956 Large 1561.39 0.13058 7.658

3N 210670 00522967 Large 3217.13 0.26905 3.717

3N 210670 02939591 Large 3847.02 0.32173 3.108

3N 220730 00553113 Large 3830.79 0.37519 2.665

26
Table A-3

Stratum PSU School ID School Size

Class

School Size

Measure

Expected

Number of 

Draws

Sampling

Weight

3N 220730 00553135 Large 2117.35 0.20738 4.822

3N 220730 00553168 Large 3300.05 0.32321 3.094

3N 280510 00739481 Large 768.74 0.16908 5.9145

3N 280510 00741413 Large 3528.22 0.77599 1.2887

3N 280510 02040289 Large 163.66 0.03599 27.7819

3N 371630 01015468 Large 800.38 0.08833 11.3214

3N 371630 01033068 Large 555.49 0.06130 16.3126

3N 371630 01035928 Large 1523.62 0.16814 5.9473

3N 401090 01147563 Large 5479.10 0.12231 8.1760

3N 401090 01147803 Large 2790.52 0.06229 16.0534

3N 401090 01148319 Large 3878.66 0.08658 11.5497

3N 450450 01272721 Large 2897.97 0.12864 7.7733

3N 450450 01272925 Large 2385.13 0.10588 9.4447

3N 450450 01932349 Large 607.85 0.02698 37.0599

3N 470470 01310871 Large 2757.28 0.02630 38.0233

3N 470470 01311354 Large 5774.62 0.05508 18.1554

3N 470470 01312201 Large 3469.57 0.03309 30.2172

3N 480050 01377892 Large 7268.17 0.98808 1.0121

3N 480050 01377906 Large 6381.29 0.86751 1.1527

3N 480050 01409634 Large 224.93 0.03058 32.7031

3N 481630 01346853 Large 2038.59 0.07144 13.9983

3N 481630 01352878 Large 22139.56 0.77582 1.2890

3N 481630 01387539 Large 4191.48 0.14688 6.8083

3N 481750 01361077 Large 1512.98 0.11390 8.7796

3N 481750 01404749 Large 8925.79 0.67195 1.4882

3N 481750 01404793 Large 6438.56 0.48471 2.0631

3N 483830 01353419 Large 4308.52 0.14235 7.0251

3N 483830 01353601 Large 11162.30 0.36879 2.7116

3N 483830 01381209 Large 8221.40 0.27162 3.6816

3N 484890 01328517 Small 219.03 0.05054 19.7864

3N 484890 01339766 Large 20107.37 0.20881 4.7891

3N 484890 01378036 Large 2557.26 0.02656 37.6561

3N 484890 01392298 Large 5671.96 0.05890 16.9776

3N 511430 01451132 Large 1198.86 0.34297 2.9157

3N 511430 01451267 Large 1478.56 0.42298 2.3642

3N 511430 01451369 Large 1560.67 0.44647 2.2398

3U 120110 00269254 Large 8863.74 0.05530 18.0825

3U 120110 00269403 Large 10754.27 0.06710 14.9038

3U 120110 00271081 Large 6203.93 0.03871 25.8351

3U 120970 00286586 Large 6299.44 0.05289 18.9064

3U 120970 03267276 Large 18327.97 0.15389 6.4983

3U 120970 05746993 Large 6868.86 0.05767 17.3391

3U 132550 00306469 Large 3548.97 0.10500 9.5240

3U 132550 00306516 Large 7367.87 0.21798 4.5875

3U 132550 00314491 Large 5012.75 0.14830 6.7429

3U 240050 00586943 Large 5528.38 0.11257 8.8832

3U 240050 00587142 Large 1794.58 0.03654 27.3655

3U 240050 00587186 Large 5763.31 0.11736 8.5211

3U 240330 00594502 Large 13888.58 0.16810 5.9487

3U 240330 00594761 Large 2147.43 0.02599 38.4734

3U 240330 00595583 Large 8556.03 0.10356 9.6562

27
Table A-3

Stratum PSU School ID School Size

Class

School Size

Measure

Expected

Number of 

Draws

Sampling

Weight

3U 370590 01035076 Large 1196.14 0.13706 7.2963

3U 370590 01035225 Large 2193.92 0.25138 3.978

3U 370590 01035291 Large 2051.64 0.23508 4.254

3U 481130 01348227 Large 8847.26 0.03300 30.304

3U 481130 01350291 Large 9511.48 0.03548 28.187

3U 481130 01408018 Large 3154.35 0.01177 84.995

3U 482010 01366734 Large 8909.93 0.05635 17.745

3U 482010 05492110 Large 2273.06 0.01438 69.556

3U 482010 06115333 Large 32533.73 0.20577 4.860

3U 482011 01331122 Large 13363.65 0.08312 12.031

3U 482011 01367013 Large 11989.05 0.07457 13.410

3U 482011 01399679 Large 13847.89 0.08613 11.610

3U 484390 01333877 Large 4608.56 0.03242 30.842

3U 484390 03260260 Large 2811.98 0.01978 50.547

3U 484390 04140441 Large 1546.62 0.01088 91.902

3U 484930 01322311 Large 2605.10 0.01064 93.977

3U 484930 01399395 Large 9699.25 0.03962 25.241

3U 484930 03270427 Large 16444.87 0.06717 14.887

3U 484930 05510651 Small 467.83 0.02993 33.408

3U 511770 01440517 Large 2862.44 0.15170 6.592

3U 511770 02874896 Large 2443.44 0.12949 7.722

3U 511770 06124031 Large 1622.56 0.08599 11.629

4N 040230 00033783 Large 1839.07 0.01949 51.321

4N 040230 00045868 Large 7844.49 0.08311 12.032

4N 040230 02110601 Large 8858.99 0.09386 10.654

4N 060150 00113987 Large 1651.60 0.46544 2.149

4N 060150 00113998 Large 3031.33 0.85426 1.171

4N 060150 02932439 Large 180.57 0.05089 19.651

4N 060190 00110013 Large 4474.87 0.02768 36.124

4N 060190 00122288 Large 29002.53 0.17941 5.574

4N 060190 00149732 Large 1287.37 0.00796 125.567

4N 060190 00181878 Small 891.00 0.01415 70.695

4N 060310 00100242 Large 3072.59 0.09340 10.706

4N 060310 00108037 Large 1376.12 0.04183 23.904

4N 060310 00163859 Large 5695.18 0.17313 5.776

4N 060470 00150023 Large 13643.63 0.30794 3.247

4N 060470 00150045 Large 18222.84 0.41129 2.431

4N 060470 04139935 Large 6690.94 0.15101 6.622

4N 080170 00214588 Large 3970.35 0.10235 9.770

4N 080170 05739782 Large 3651.55 0.09413 10.623

4N 080170 90070759 Large 1205.31 0.03107 32.184

4N 150031 00326769 Large 11113.88 0.06669 14.994

4N 150031 00327751 Large 25257.52 0.15157 6.598

4N 150031 05956253 Large 13153.61 0.07894 12.669

4N 350250 00917387 Large 5148.49 0.15643 6.393

4N 350250 00917467 Large 7241.23 0.22001 4.545

4N 350250 00917616 Large 1102.41 0.03349 29.856

4N 530530 01478642 Large 819.49 0.01505 66.435

4N 530530 01478711 Large 2495.02 0.04583 21.820

4N 530530 01484951 Large 7566.19 0.13898 7.196

4N 530530 03268145 Small 294.12 0.02944 33.962

28
Table A-3

Stratum PSU School ID School Size

Class

School Size

Measure

Expected

Number of 

Draws

Sampling

Weight

4U 040130 00032848 Small 163.98 0.00218 458.892

4U 040130 02868645 Large 353.42 0.00130 766.430

4U 040130 03239170 Large 6706.82 0.02476 40.388

4U 040130 03239216 Large 3596.89 0.01328 75.308

4U 060170 02940654 Small 182.75 0.03127 31.977

4U 060170 04139040 Large 6411.74 0.25729 3.887

4U 060170 05442827 Large 3574.52 0.14344 6.972

4U 060170 90069687 Large 2218.50 0.08902 11.233

4U 060371 00116707 Large 22177.47 0.07908 12.646

4U 060371 00136687 Large 37468.93 0.13360 7.485

4U 060371 00138356 Large 16434.40 0.05860 17.065

4U 060372 00136392 Large 28150.46 0.09946 10.055

4U 060372 00139735 Large 15458.76 0.05462 18.310

4U 060372 01617633 Large 25707.88 0.09083 11.010

4U 060373 00111436 Large 3714.67 0.01371 72.940

4U 060373 00141835 Large 18691.52 0.06899 14.496

4U 060373 00144643 Large 15860.41 0.05854 17.083

4U 060374 00103979 Large 6157.12 0.02245 44.548

4U 060374 00139305 Large 8604.77 0.03137 31.876

4U 060374 00167718 Large 3330.21 0.01214 82.363

4U 060375 00111425 Large 8106.42 0.02944 33.965

4U 060375 00139666 Large 26016.40 0.09449 10.583

4U 060375 00141675 Large 30214.99 0.10974 9.112

4U 060591 00099246 Large 10484.13 0.05189 19.271

4U 060591 00123565 Large 5154.44 0.02551 39.198

4U 060591 00160483 Large 8312.88 0.04114 24.305

4U 060730 00175398 Large 19373.77 0.05198 19.236

4U 060730 00175456 Large 30242.23 0.08115 12.323

4U 060730 00180783 Large 7395.23 0.01984 50.395

4U 060810 00105207 Large 3719.18 0.03871 25.835

4U 060810 00130051 Large 19473.43 0.20267 4.934

4U 060810 00181095 Large 9812.63 0.10212 9.792

4U 060850 00120961 Large 7934.66 0.03008 33.240

4U 060850 00153374 Large 6578.03 0.02494 40.096

4U 060850 05957381 Large 1861.99 0.00706 141.650

4U 080010 00210878 Large 6495.45 0.17031 5.872

4U 080010 00227815 Large 2345.70 0.06150 16.259

4U 080010 00228546 Large 7057.09 0.18504 5.404

29