II. Methods

Tribal Reservation Selection
There were three major complicating factors in selecting tribal reservations to observe. Together they required a somewhat more structured selection scheme than is used in most State safety belt use observation plans. As noted above, tribal reservations differ markedly in population. Reservations are not contiguous, as are the counties making up a State, but are scattered throughout much of the country. Finally, the same safety belt laws do not apply to all tribal reservations. Reservations are free to set their own safety belt laws. Some tribal reservations have no safety belt laws, some have a primary law, in which motorists can be stopped solely for safety belt violations, and other reservations have a secondary law that allows a law enforcement officer to ticket people for a safety belt violation only if they are already stopped for another infraction. Also, tribal reservations, particularly smaller ones, exist within the “context” of the safety belt laws governing the States within which they are located.

The tribal reservation selection plan was a systematic selection plan based on selecting from within Areas, as defined above. General criteria for making up the sample were that it should:

• include enough tribal reservations to be representative of the varying conditions that exist;
  
  
• sample from all areas of the country, again to be representative; and
  
  
• include enough sites per tribal reservation so that the final combined safety belt use rate will meet the reliability requirements of NHTSA’s Section 157 guidelines.²

In addition, the sample should be realistic within the scope of resources available for this effort – and, by extension, if this effort is successful, make it possible for future replications to track changes in belt use over time and with changing legal and countermeasure conditions.

The final recommendation asked for a total of about 150 sites to be sampled across 18 tribal reservations. These numbers represented our best estimate of a sampling plan meeting the criteria above while remaining within the project’s practical constraints. Two of the tribal reservations did not permit safety belt observations to be made in their territory, resulting in final data collection for 120 sites in 16 reservations.

Table 1 shows, by Area, the numbers and populations of tribal reservations, totals and “available for sampling.” The table also shows the recommended distribution of sampled tribal reservations across areas. The objective of the sampling procedure was to select tribal reservations according to probabilities generally proportional to their populations, based on two steps:

1. Include the Navajo reservation (Southwest Area), which has 22 percent of the total Indian Country population and 35 percent of the Native American population in Indian Country.
   
   
2. Sample, from each Area, at a rate of approximately one in four tribal reservations or one tribal reservation per 30,000 population.

Table 1. Native American Sites Area Distribution of Tribal Reservations and Population.

Area Total Reservations Reservations over 2,000 Pop Number to Sample2 Number Population Number Population Southwest1 71 322,023 21 293,301 6-1 South Central 11 52,850 2 48,856 1 South & East 33 33,496 6 26,369 2-1 Northwest 29 101,425 11 94,513 3 Northern Plains 20 162,659 17 159,293 5 Great Lakes 13 39,797 4 37,738 1 TOTAL 177 712,250 61 660,070 18-2 1 Includes Navajo Reservation in all cells. 2 Reflects inability to collect data on Navajo (Southwest) and Seneca Nation’s Cattaraugus (South & East) reservations.

Sampling procedures were repeated within each Area and involved seven steps:

1. Randomly reorder the list of tribal reservations so that every reservation had equal probability of being first, second, etc. in the list.
   
   
2. Set each tribal reservation’s initial weight for being selected on a single selection equal to the proportion of the reservation’s population to the total population of all eligible reservations within the Area, , where wij = initial weight for selection on a single selection for reservation j within Area i, Pop_ij = population of reservation j within Area i, and = sum of the population of all reservations eligible for selection within Area i. (Within each Area, these initial weights add to exactly 1.0.)
   
   
3. For Areas sampling a single tribal reservation, set the selection cutoff level s_ij = w_ij.
   
   
4. For Areas sampling more than one tribal reservation, adjust the cutoff levels to select all of the tribal reservations in a single sampling according to the formula:

(1)

where s_ij = selection cutoff level for reservation j in Area i and n_i = number of reservations to be selected within Area i. (Within Area i, the sum of the adjusted weights = n_i.) In all cases, the s_ij cutoff levels correspond roughly to the probability of the reservation being included in the final sample.

5. Generate a random number (from a rectangular distribution between 0 and 1) for each tribal reservation.
   
   
6. Starting at the top of the list, select for inclusion each tribal reservation whose random number is less than (or equal to) its adjusted selection cutoff, up to the number required to be sampled.
   
   
7. If the number of tribal reservations selected is less than the number required, select additional tribal reservations from the pool, selecting first the one whose random number exceeds its cutoff level by the least amount, etc., until the number of required tribal reservations has been identified.

The resulting target sample of 18 tribal reservations, together with the proposed number of observation sites as described below, is shown in Table 2. Note that the Navajo and Seneca are shaded; they did not participate.

Table 2. Final Sample of 18 Tribal Reservations.

Tribe	Location	Area	State Primary Law?	Total Pop.	% Native Amer. 1	# Sites
Navajo Nation (AZ-NM-UT)	Window Rock, AZ	SW	No/Yes	155,214	96%	27
Ute Indian Tribe (Uintah and Ouray Reservation)	Ft Duchesne, UT	SW	No	19,182	14%	9
Gila River Pima-Maricopa	Sacaton, AZ	SW	No	11,257	92%	7
Pueblo of Zuni	Zuni, NM	SW	Yes	7,758	96%	6
Taos Pueblo	Taos, NM	SW	Yes	4,484	30%	5
Pueblo of Acoma	Avomita, NM	SW	Yes	2,802	97%	4
Osage Tribe	Pawhuska, OK	So-Cent	Yes	44,437	14%	14
Eastern Band of Cherokee	Cherokee, NC	So+East	Yes	8,092	82%	6
Seneca Nation of Indians [Cattaraugus Reservation]	Erie, Chautaqua, Cattaraugus Counties, NY	So+East	Yes	2,412	88%	4
Yakama Nation	Toppenish, WA	NW	Yes	31,646	23%	12
The Tulalip Tribes	Marysville, WA	NW	Yes	9,246	22%	7
Confederated Tribes of the Colville Reservation	Nespelem, WA	NW	Yes	7,582	60%	6
Eastern Shoshone & Arapaho Tribes [Wind River Reservation]	Ft Washakie, WY	NoPlns	No	23,245	28%	10
Rosebud Sioux	Rosebud, SD	NoPlns	No	9,050	86%	6
Cheyenne River Sioux	Eagle Butte, SD	NoPlns	No	8,466	74%	6
Crow	Crow Agency, MT	NoPlns	No	6,894	75%	6
Three Affiliated Tribes [Ft. Berthold]	New Town, ND	NoPlns	No	5,915	67%	5
Saginaw Chippewa [Isabella Reservation]	Mt. Pleasant, MI	GrLks	Yes	25,822	5%	11
1 Percent of reservation’s total population that are Native American; source, 2000 U.S. Census Data.

Site Selection
The site selection procedure was applied independently for each tribal reservation.

Roads in and immediately around the population centers were treated as one stratum (“collectors”), and the major connecting roads were treated as a second stratum (“arterials”). For each tribal reservation with an even number of sites, half of the final observation sites were from each stratum; for each tribal reservation with an odd number of sites, one stratum provided one more site than the other.

In order to avoid roads with very little traffic, a structured selection of observation sites was made based on the use of the roads and their likely volume. Roads eligible for sampling were: paved or gravel (excluded dirt and unimproved); under BIA or tribal control (excludes State and county highways patrolled by State and county police); and collectors or arterials (excluded local streets). Eligible roads were divided into segments, i.e., stretches of roads between intersections large enough for significant changes in the road’s traffic volume or makeup.

For each tribal reservation, lists of possible road segments were assembled from qualified road segments that were likely to have adequate traffic volume. Lists were based on road maps and input from local authorities. Population centers were identified, and the main roads within the centers and providing access in and out of the centers were identified. Each access road was included from the center out into more rural areas for a few miles. In addition, major connecting roads with adequate traffic but not near population centers were included.

From the eligible roads, segments for safety belt observation were selected randomly, with the probability of selection proportional to the length of the segment. Specific observation points were selected on the segment by the observers in the field, based on ease of observing belt use and safety. Observation points were documented so that they could be used in future belt use studies.

Traffic counts were determined for each location at the time of belt use observations. These counts served as our estimate of traffic density. At locations where every passing vehicle could be observed, the count was equal to the number of vehicles observed. Where traffic volumes were too heavy to permit observation of every vehicle, we conducted a ten-minute traffic count before belt use observations, conducted a second ten-minute count after observations, and weighted the number of observations as a function of the number of vehicles counted (i.e., the estimate of the number of vehicles that would have been observed had we been able to observe every vehicle). At most sites, where traffic volumes permitted, observations and traffic counts included traffic in both directions.

We proposed 150 total sites. This is similar to the numbers of sites used for State belt use determinations, and thus was judged likely to provide a suitably stable overall estimate of belt use. The number of sites per tribal reservation was proportional to the square root of the population. The numbers are shown in Table 2 above. For example, if there are a total of 151 observation sites (varied from the target of 150 due to rounding), there would be 27 sites on the Navajo Nation and 4 sites on a small reservations with just over 2,000 population. No reservation had fewer than 4 sites.

We were unable to obtain permission to collect safety belt observations on the Navajo and Cattaraugus reservations. That left a total of 120 observation sites (the defections were confirmed too late to adjust the numbers of sites on other tribal reservations). Even with the smaller number of sites, and the large variability of belt use rates between sites and tribal reservations, the final overall safety belt use rate estimate met the Section 157 target for reliability.

The calculated safety belt use percentage for each tribal reservation was the combination of belt use percentages at each site weighted directly by the number of vehicles passing during the observation period and inversely by the likelihood of selection of the segment (i.e., the segment length). (For sites where vehicle volume was estimated from pre- and post-observation counts, those estimated values were used.) For each site, the belt use percentage was the number of belted persons observed divided by the total number of persons for whom belt use/nonuse was observed. The same arithmetic was used to calculate safety belt usage for subsets, e.g., males, drivers, pickup drivers, or passenger-car occupants. Weights for combining sites for subsets were the total vehicle counts, based on the assumption that distributions of subsets are balanced across sites and that the total vehicle count is the most stable estimate.

Data Collection
Observers
Observers were hired by Preusser Research Group. Most observers had done safety belt observations prior to this project. The other observers received extensive training over several days, first watching an expert observer, then observing in parallel, then observing with supervision.

Scheduling
Observations were conducted Monday-Sunday during daylight hours, between 7 a.m. and 6 p.m. Scheduling was done to balance observations for time of day and day of week, with weekdays being considered roughly equivalent for the purposes of efficient use of observer field and travel time. Observations were balanced by type and time of day within Areas and, as much as practicable, within tribal reservations.

Observations
Data collection was done according to the instructions in Appendix A. Each observation period lasted a full hour. Survey information was recorded on an observation data collection form (Appendix B). The form was designed so that pertinent site information could be documented, including tribal reservation name, city/town/area identifier, exact roadway location, date, day of week, time, weather condition, and direction(s) of traffic flow and lane(s) observed. Each one-page form included space to record information for 70 vehicles, the driver of that vehicle, and the outboard, front seat passenger, if any.

Calculation of Overall Safety Belt Usage Rate and Variability

Overall Rates
Safety belt usage rates were calculated in two stages. Within each reservation, usage was

(2)

where p_ij = safety belt usage for reservation j in Area i, k = site within the reservation, V_ijk = weight for each road segment (site), π_ijk = = the proportion of the length L that
road segment ijk is of the chosen road segments in reservation j in Area i, B_ijk = number of belted occupants (drivers and outboard, front seat passengers) observed at the site, and O_ijk = total number of occupants observed at the site. For sites where all vehicles were observed, V_ijk = the number of observed vehicles. For sites where the number of vehicles were estimated from 10-minute counts before and after the observation period, V_ijk = (number counted 10 minutes before + number counted 10 minutes after) * 60/20, for a standard 60-minute observation period. Where raw counts were based on travel in both directions, they were divided in half to be comparable to counts based on travel in only one direction.
Values for π_ijk = were calculated separately within each stratum for each tribal reservation. The actual calculations are represented as π_ijkl = , where l is the
stratum and n_ij1 + n_ij2 = n_ij. The result of this was that collectors and arterials contributed equally to each reservation’s belt use rate estimate, regardless of differences in the total length of the selected collector segments versus the total length of the selected arterial segments.

Next, the overall rate across all tribal reservations was calculated according to the formula

(3)

where W_ij = Pop_ij / s_ij , i.e., the population of tribal reservation i in Area j times the inverse of the
selection cutoff level, where the cutoff level was approximately equal to the probability of including tribal reservation j of Area i in the sample. This is the directly analogous to the Section 157 guidelines allowing population weighting in the absence of traffic volume data.

At an informational level, calculations of belt use could also be done for subsets of the entire sample and population. For example, BIA and PRG were interested in belt use rates for the different Areas. It was also interesting to compare tribal reservations with primary safety belt laws versus those with secondary or no safety belt laws, and tribal reservations within States with primary laws versus those in States with secondary laws.

Additionally, a large percentage of tribal reservation vehicles were pickup trucks, and in State belt use observations it is routinely found that belt use in pickup trucks is much less than that in all other passenger vehicle types. Thus it was of interest to calculate safety belt use rates for subsets of vehicle types, as well as male/female and driver/passenger subsets.

All of these “subset” calculations use formulas (2) and (3) as defined above, with adjustments in formula (2) to B_ijk and O_ijk (but not V_ijk) to reflect different subsets of vehicles or occupants and adjustments to the specific tribal reservations included in the formula (3) computations (but no changes to the W_ij values) for different Area or other tribal reservation subsets.

The Standard Error of the Overall Safety Belt Use Rate
Standard error of estimate values were estimated through a jackknife approach, based on the general formula:

   (4)

where σˆ_p = standard deviation (standard error) of the estimated Indian Country safety belt use proportion p, n = the number of sites, i.e., 120, and p_i = the estimated Indian Country belt use proportion with site i excluded from the calculation.

The relative error rate, i.e., σˆ _p / p , also was calculated, as was the 95 percent confidence interval, i.e.,
p ± 1.96σˆ _p . These values are reported for the overall Indian Country safety belt use rate.

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² Though this project was not conducted under Section 157, the observation plan was designed and implemented consistent with Section 157 guidelines so that the results would be readily interpretable.