Forest Service National Visitor Use Monitoring Process: Research Method Documentation

Transcription

1 Forest Service National Visitor Use Monitoring Process: Researc Metod Documentation Donald B. K. Englis Researc Social Scientist Soutern Researc Station 320 Green Street Atens, GA Susan M. Kocis NVUM Project Coordinator 1645 Hwy 20 East Bend, OR Stanley J. Zarnoc Matematical Statistician Soutern Researc Station 200 Weaver Blvd. Aseville, NC J. Ross Arnold Resource Economist Strategic Planning and Resource Assessment Wasington, D.C May 2001

2 We would like to tank tose wo provided review comments on earlier versions of tis paper. In alpabetical order, tese include: Debora Cavez (USDA-FS), Tim Green (USDA-FS), Troy Hall (Virginia Tec), Scott Jackson (USA-COE), Dennis Propst (Micigan State), Cris Siderelis (Nort Carolina State), and Jo Tynon (Oregon State). In addition, tere were a number of Forest Service personnel wo provided significant contributions to our metod, including (also alpabetically) Jim Bedwell, Ric Calnan, Ken Cordell, Dave Hackett, Margaret Lincoln, Mike Noland, Stan Spect, Jerry Stokes, Greg Super, Francisco Valenzuela, and Larry Warren. Please Address all Comments to: Dr. Donald B. K. Englis Soutern Researc Station 320 Green Street Atens, GA 30602

3 Abstract In response to need for improved information on te recreational use of National Forest System lands, a nationwide, systematic monitoring process as been developed. Tis paper documents te metods used in estimating annual recreational use of National Forest System lands. Te basic unit of measure is te exiting volume of visitors from a recreation site on a given day. Sites are stratified according to te type of site. Days are stratified according to te expected volume of exiting recreation visitors. A double-sampling strategy is te primary means used to obtain measures of exiting recreation traffic. Were possible, observable counts of oter measures tat are igly correlated wit visitation, suc as fee envelopes, ski lift tickets, or concessionaire reports are used, in order to reduce variation in te visitation estimates. In addition to sowing ow te sampling units are defined, tis paper also provides te calculations used in developing estimators for te mean and variance of visitation. Key words: Recreation use, Sampling, Monitoring, Wilderness, Researc metods 1

4 Forest Service National Visitor Use Monitoring Process: Researc Metod Documentation INTRODUCTION Overview Te credibility of recreational visitation estimates reported by te Forest Service as been questioned bot by Congress and te General Accounting Office. Accurate information about te amount of recreation tat occurs on National Forest System (NFS) lands is necessary for a variety of reasons, including forest planning and budget allocation. Te metods tat ave been used to estimate recreation use are inconsistent across reporting units and often yield results of questionable validity. In response to te need for improved information, te Forest Service as initiated an ongoing process of measuring recreation visitation on te national forests and grasslands, and will incorporate tat process into its standard inventory and monitoring efforts. As a first step in tis process, te agency completed a pilot study in Tat study s purpose was to test a statistically valid metod for estimating visitor use. Building on tat effort, a team of researc scientists and NFS personnel ave developed a standard metod to be used across te country. Te ongoing effort to implement and refine tis metod is a partnersip of te agency Recreation Staff, Researc and Development, Ecosystem Management, Inventory and Monitoring, te Missoula Tecnology and Development Center, and Strategic Planning and Resource Assessment staff. Te process we describe ere is called National Visitor Use Monitoring (NVUM). It is designed to provide statistically reliable estimates of recreation visitation to te national forests and grasslands and designated Wilderness witin tem. 2

5 Wat tis process provides: Te NVUM process is designed to provide an estimate of national forest recreation visits. Moreover, it will elp to ensure Forest Service-wide consistency in data collection and establis a minimum standard of statistical accuracy. A national forest recreation visit is defined as one person entering and exiting a national forest for te purpose of recreation. In a single visit, an individual may participate in any number of recreation activities. Also, a single visit can last 15 minutes, and it can last 15 or more days; it migt be one individual visiting only one recreation site, or te same individual visiting every recreation site on a national forest. Counts or estimates of recreation users exiting individual sites on a national forest are referred to as recreation site visits. NVUM samples and develops estimates of recreation site visits as an intermediate step in estimating national forest recreation visits. In implementing te NVUM, visitation estimates will be generated for individual national forests, Forest Service regions, and for te National Forest System as a wole. Te primary reporting unit will be te national forest or national grassland. Recreation visitation estimates will be developed annually for about one-fourt of te reporting units in eac region; once te cycle is establised, eac unit will be re-surveyed every 5 years. Regional and national visitation estimates will be developed by summing estimates from forests and grasslands. In te first 3 years, regional and national estimates will be made by extrapolating data from reporting units tat ave been surveyed. In te fourt and subsequent years, regional and national figures will be calculated as te sum of te most recent estimate for eac reporting unit in te region. Statistically, visitation 3

6 estimates for every level of reporting are to be witin 15 percent of actual visitation, at te 80 percent confidence level. Collaborative efforts among brances of te agency ensures quality control in data collection, sampling design, and statistical accuracy. In addition, ongoing researc efforts will be incorporated into te process to improve te estimates= accuracy and reduce costs. Consistency among reporting units is te key element in tis process; all will follow te same national protocol. In addition to total visitation estimates, annual reports will provide, to some extent, a profile of visitors. Descriptions will be averages for te sampled population or percentage distributions across several categories. For example, sample averages for lengt of stay, number of annual visits to te forest, and party size will be available. Percentage distributions will include proportion of visitors tat engaged in different recreation activities, proportion of visitors from various distance zones, and proportion of visitors wo used designated Wilderness Areas. Eac reporting unit will obtain an estimate of te number of recreation visits to Wilderness, te percentage tat are overnigt visits, and te percentage of visitors wo use outfitter or guide services. Wat tis process does NOT provide: Te data collection and reporting processes will not estimate recreation visits to particular sites or ranger districts, nor will any description of visitors to any particular site or district be made. Results will describe te size and composition of te overall recreation visitor population for a 4

7 national forest or grassland. Descriptive information for particular subgroups of recreation users, e.g., campers, dispersed users, local users, generally will not be available. Witin te NVUM process framework, opportunities for more detailed sampling of particular users groups or for special data collection for a national forest are limited. A major goal of NVUM is to ensure te consistency of metods used to estimate recreation visits across reporting units. More intensive sampling of particular user types could compromise metodological consistency and increase te difficulty of calculating statistical accuracy of visitation estimates. Opportunities for special studies: Special studies tat gater in-dept information from or about selected subgroups of recreation visitors (including tose engaged in particular activities or using individual recreation sites) are pursued in separate survey efforts, not as a part of te NVUM process. Impact on field personnel is reduced by focusing on te sampling required for NVUM. Special surveys must be fully funded by te requesting unit. Federal law requires tat suc surveys be administered witin te guidelines of information collections approved by te Office of Management and Budget (OMB). Tecnical assistance in developing survey instruments and sampling plans tat conform to OMB guidelines is available from te NVUM researc team. 5

8 RESEARCH DESIGN Te researc design for NVUM uses te double sampling tecnique developed over 35 years ago to measure recreation use on national forests (James and Ripley 1963; James 1967; James and Henley 1968). Te first stage involves selecting a stratified random sample of te times and locations were recreational visitors can be counted. For eac, traffic counts are taken for a 24-our period. Concurrently, interviews are conducted wit a random sample of visitors to calibrate traffic counts to te number of unique visits. Eac reporting unit must do some pre-sampling work to identify its population of recreation sites and te days eac is open for public use. A summary of te pre-work steps and data collection processes is presented as a flow cart in Appendix A. Defining recreation sites It is elpful to categorize a recreation visit wit reference to bot were and wen it occurs. Recreation sites and te days tey are open form te population of sampling units. Categorizing te types of locations is done wit five strata: 1. Day-use developed sites (DUDS) include sites wit facilities tat meet te Infra 1 definition development scale for moderate, eavy, or ig degrees of modification. Generally suc facilities provide for visitor comfort, convenience, and education opportunities. For tis project, 1 Infra (sort for INFRAstructure) is te Forest Service=s corporate database tat tracks te resources and infrastructure on agency lands as well as te outputs tat come from tem. Additional information about Infra data and definitions is available on te Web at ttp:// 6

9 sites wit facilities tat only provide for ealt and safety only are not sufficiently developed to include in tis category. DUDS includes picnic sites, fis viewing sites, fising sites, interpretive sites, observation sites, playground-park sport sites, ski areas (bot alpine and nordic), some wildlife viewing sites, caves, visitor centers, museums, and swimming areas. DUDS does not include overnigt sites. Generally, boat launces, traileads, and ranger stations tat only provide minimal information services are not included. 2. Overnigt-use developed sites (OUDS) meet te Infra definition for development scales of moderate, eavy, or ig degrees of modification. Tese sites include campgrounds (family and group), fire lookouts and cabins, otels, lodges, and resorts (bot publicly and privately owned), orse camps, organization sites (bot publicly and private owned), and any oter overnigt developed sites witin Forest Service jurisdiction, weter managed by te agency or by concessionaire. Organizational camps are not included in tis category. Recreational residences also are not included; typically tey are sampled as part of te general forest area. 3. Wilderness (WILD) includes lands and waters tat are part of te National Wilderness Preservation System. Wilderness Study Areas, Researc Natural Areas, or oter roadless areas are not included in tis category. Interviews wit Wilderness visitors may be conducted at traileads and oter access points. 4. General forest area (GFA) includes all of te residual part of a national forest not included in DUDS, OUDS, or WILD categories. Generally, sample points are at traileads or on NFS roads were users exit te national forest. Tese are te portals toug wic visitors engaging in dispersed activities suc as iking, unting, and dispersed camping can access undeveloped areas. In some cases, a GFA entry point will be a river, lake, boat arbor, or airport. 7

10 Sample points may include bot FS and non-fs managed roads, as well as bot ig-speed and low-speed roads. 5. On-forest viewing corridors: It is widely accepted tat viewing scenery on FS lands from public roads, ferries, scenic trains, cruise sips, airplanes, trams or oter travel corridors is a popular recreation activity. In many rural communities, money spent by tis sort of tourist is a vital economic force. Managing te viewsed of tese travel corridors is an ongoing element in FS stewardsip. People doing tis activity ave represented a significant proportion of recreation visitation reported by te FS in te past. However, almost none of tis activity meets a strict definition for national forest recreation visits. For example, people traveling on roads not under Forest Service jurisdiction do not officially >enter= a national forest, so tey can not be officially counted as recreation visitors. Still, tere is enoug significance attaced to tis type of activity tat te NVUM process incorporates sampling in tis stratum to rougly estimate its magnitude. Te estimate of te number of people wo travel tese corridors to view te forest is not included wit national forest recreation visitation, but is reported separately. No effort is made to reac a preassigned level of statistical accuracy. Tis stratum allows reporting units to identify important travel corridors beyond tose listed in GFA, tat pass troug or close to NFS lands but were te speed, layout, jurisdiction, and/or location of te travel corridor do not provide pysical access to te forest. Individuals wo stay witin tese travel corridors would not be counted by sampling at te oter four types of sites. Tis stratum of sites includes places from wic visitors view scenery, wildlife, and objects wile traveling troug or proximate to NFS lands. Most sites of tis type are travel corridors (most often a road) owned or maintained by some oter public agency. 8

11 We identified two classes of travel corridors tat could provide opportunities for viewing forest scenery. For eac, we developed criteria to define caracteristics of te travel route and of te people on tem wo migt be viewing te forest landscape. Tese criteria ensure consistency across reporting units in categorizing travelways and travelers. Class 1: Tis is recreation activity tat occurs on igways, roads, or oter travelways designed for viewing scenery, were tose travelways are witin NFS lands but not under NFS jurisdiction. Travelways can include interstate, state, or local igways, as well as rivers or oter water passages. All types of air travel are excluded. Travelways tat qualify witin tis class must be: (a) displayed on secondary series-base maps (forest visitor maps) as directly traversing FS ownersip witout intervening non-fs lands; and (b) of sufficient lengt to require at least 15 continuous minutes of travel at normal speed troug agency lands. Visitors must: (a) be on a recreational trip, or (b) be on a trip for anoter purpose, and specifically state tat viewing forest scenery was te main reason for coosing tat particular travel route. It is difficult to get an unbiased estimate of te proportion of people traveling on te viewing scenery corridors wo are tere to view te forest landscape. Surveying at optional pull-offs like rest areas and scenic views are suitable and safe locations to interview. However, tese locations would provide a self-selected set of individuals/veicles, and probably a biased 9

12 sample. Stopping people at random on ig speed or busy roads can be unsafe for bot te interviewers and travelers. We decided safety was paramount, and cose interview locations accordingly. Class 2: Included ere are commercial trips or tours werein te purpose is to view national forest scenery, but were individuals do not enter into travelways as defined in Class 1. Te distinguising caracteristic for tis type of viewing activity is tat te visitor as made a conscious decision to pay for commercial services specifically to view scenery on FS lands. Reporting units must document te number of passengers, but surveys are not needed. Trips or tours tat qualify ere include scenic boat trips on waters adjacent to FS lands, scenic overfligts, and bus, train, or tram tours wose purpose is viewing national forest scenery. Site-days Some developed sites, traileads, Wilderness, forest roads, or oter access points are open and available for public recreation use every day of te year; oters are open only seasonally. Recreation use can be measured any day tat suc a site is open. A site-day describes te spatial-temporal combination of a location open for one calendar day. Any recreation visit to any site necessarily involves te individual entering te site, engaging in one or more recreation activities, and exiting te site. It is important to count eac visitor only once per site-visit. Te risk of double counting is minimized if counts are made eiter wen visitors first enter te site, or at teir final exit. If te goal is simply a count of visitors, ten it makes no difference weter te count is at te entry or exit time. However, by surveying visitors as tey leave, better information is collected about teir visit (James 1967). Exiting 10

13 visitors can provide information about lengt of stay, facilities used, and activities. In addition, entering visitors may be less willing to be interviewed. For tese reasons, we count and interview visitors as tey exit recreation sites and areas. Basic data sampling process On eac randomly selected sample day, we collect two types of data. First, we get a 24-our count of exiting visitor traffic. Second, during te 24-our sample period, we conduct 6 ours of on-site interviews. Te 24-our count is usually obtained via a mecanical counter. However, were available we use oter types of data tat are routinely collected, suc as ski lift tickets, mandatory permits, or fee envelopes. On-site interviews occur during one of two randomly selected 6-our interview periods during te sample day. We interview a sample of visitors as tey exit te site. Full interviews are administered only to visitors wo recreated at te site and are leaving for te last time tat day. By identifying te proportion of last-exiting recreation visitors to total exit traffic, we can calibrate te 24-our traffic count to estimate te number of unique recreation visits in te 24-our period. Interviewing protocol for on-forest viewing corridors is sligtly different. Installing 24-our traffic counters on some travelways, especially on major federal and state igways, may be unsafe. As a substitute, interviewers count traffic manually using a and tally recorder. Tese traffic counts occur on te roadway. Interview locations are moved back from te roadway to a rest area or similar pull-off, also for safety reasons. Generally, it is very difficult to simultaneously interview and conduct a and tally. Interviewers alternate between te two activities, according to a specified scedule. During te and tally time, interviewers count all traffic crossing te counter 11

14 location on te same side of te roadway as te rest area, and record te proportion of commercial and private traffic for a sample of veicles. Proxy (external) Information Operating some recreation sites involves collecting information tat is closely related to te amount of recreation visitation. Altoug suc information is often collected for an entire use season or year, it is possible to ave it for only one or a few days. If tis external information meets certain criteria, it can serve as a proxy for te amount of visitation on te site (Yuan and oters 1995). Site-days for wic suc information exists are called `proxy site-days.= Incorporating proxy information sould improve te accuracy of site visitation estimates and reduce te error of total visitation estimates at te national forest level. Ultimately, tere is a reduction in te amount of sampling necessary to reac targeted accuracy levels. Some visitor sampling is needed to estimate conversion rates from te observed proxy measure to te desired visitation units. However, proxy site-days can be sampled at a lower rate, because conversion coefficients are more easily estimated. Several criteria are used to determine te feasibility of visitation proxy information. First, te proxy information must represent all users of te site. Proxy data tat pertains to only a particular segment of users, e.g., number of visitors using outfitters but not individuals wo do not use outfitters, is not acceptable. Second, te proxy count must be an exact tally; it cannot be an estimate. Tird, only a few types of proxy information are acceptable: fee receipts, fee envelopes, mandatory permits, permanent traffic counters, and ticket sales. Fee sites or sites employing a fee-envelope system primarily include campgrounds, ski areas, fee demo sites, and some oter 12

15 day-use recreation sites. Some Wilderness, backcountry areas, and rivers require permits for all users. Tese are acceptable proxy measures. Voluntary permit and trail register systems are not. Using tese criteria, eac reporting unit can determine wic proxy information can be used. Use-level strata For eiter proxy or standard sites, it is possible to enumerate all te site-days werein recreation could occur. Days on wic te site is closed or recreation use is expected to be zero are classified as Closed/Zero days. Tese days are not sampled, as use for tose days is assumed to be a known zero. Te remaining site-days can ten be stratified to reduce te variance of estimated annual visitation. Previous Forest Service researc stratified sites by expected annual use and by weekday versus weekend or oliday day types (James and Ric 1966; James and Henley 1968; Lucas, Screuder, and James 1971; Yuan and oters, 1995; Gregoire and Buyoff 1999). However, analysis of a pilot study for NVUM indicated tat exit volume for many overnigt sites and traileads was near zero on a number of Saturdays, but quite ig on Sundays and Monday olidays. Tis resulted in ig variance in exiting recreation volume for weekend strata. We felt tat more omogeneous strata could be developed by asking reporting units to stratify site-days by te expected level of exiting visitor traffic, relative to all site-days in tat site type. Stratification of day-use sites results from identifying site-days tat ave te igest and lowest level of last-exiting recreation traffic. We stratify site-days in eac site-type stratum into four classes: Hig, Medium, Low and Zero/Closed exit volume, in order to most efficiently use te limited number of available sampling days. Tis divides site-days into classes tat minimize exit volume differences witin a class, and maximize differences across classes. 13

16 Sample allocation Units involved in te first year of sampling ad an average of 64,000 site-days. Based on results from a 1998 pilot study for tis project, an average of about 200 sampling days per reporting unit (more on tose wit larger populations of site-days, less on tose wit smaller populations) are needed to obtain te targeted level visitation-estimate accuracy. Eac Forest Service region is allotted 200 sampling days per surveyed reporting unit. Witin regions, sampling days are allocated to reporting units in a series of stages. Te process for allocating days to a reporting unit is: Step 1. Assign to eac reporting unit 8 sample days 2 in on-forest viewing corridors, 3 eac for ig- and medium-use days and 2 for low-use days. Step 2. Eac reporting unit is allotted no more tan 50 sample days for proxy site-days. Allocations witin a reporting unit are made as follows: a. Initial allocation of 4 sample days for eac proxy sample cell (defined by a combination of site-type and proxy-type); b. If any of te 50 remain, allocate a fift sample day to eac sample cell wit more tan tree different sites; c. If any of te 50 days still remain, assign a sixt sample day to cells wit more tan five different sites; 2 In NVUM=s first year, eac reporting unit was allocated 5 sample days for tis site type. 14

17 d. If any of te 50 days still remain, assign a sevent sample day to cells wit eigt or more sites; e. If any of te 50 days still remain, assign an eigt sample day to cells wit ten or more different sites; f. Return any unallocated proxy sample days to te unobligated regional total. Step 3. Eac reporting unit will ave up to 12 sample cells (combinations of site-type and use level) for site-days witout proxy information. Sample days are allocated among tese cells witin te region according to te following rules: a. Initial minimum allocation of 8 sample days per non-proxy sample cell for eac reporting unit. Tis ensures tat visitation variance for eac cell is computed on at least eigt observations (unless te cell as fewer tan 8 site-days). b. Any sample days for te region tat are still available are allocated across all nonproxy cells in all survey units. Allocation proportions are determined by te number of site-days in eac cell (provided in te pre-work spreadseet), weigted by te product of: (1) te cell=s estimated standard error from te previous year s survey, and (2) a factor tat reflects te relative importance of eac use-level stratum in visitation estimates. Te importance weigt factors are: Hig: 20 Medium: 10 Low: 1 15

18 Tat is, ig-use site-days (regardless of site type) ave a weigt 20 times tat of low-use site-days, and twice tat of medium-use site-days. [Note: In NVUM=s first 2 years, no standard errors estimates will be available, so weigts equal te importance factor alone.] Selection of interviewing days and times Te set of days for sampling visitors is drawn at random for eac stratum, but wit a small adjustment. We encountered a logistical problem wen te same calendar day was selected for more sites tan survey crews could cover. To avoid tat problem, we take te following steps in developing a sampling calendar: 1. Group te site-days selected for sampling by calendar day. 2. Identify any calendar days tat ave more tan 3 site-days sceduled; select two at random and retain tem in te sample. 3. Determine te number of site-days in eac proxy and non-proxy stratum tat need to be replaced. 4. Draw replacements at random from te set of unused site-days on calendar days tat ave fewer tan 2 site-days already selected for sampling. Previous researc (Yuan and oters 1995) indicated tat te percent of visitors exiting a site for te last time varies by time of day. To ensure unbiased estimates of te volume of last-exiting recreation traffic, we sample over as muc of te day as is practical. For non-proxy sample days, one of two interview periods is selected at random wit equal probability. Te AM survey period begins at 8AM and concludes at 2PM; te PM period runs from 2PM to 8PM. From 16

19 late fall to early spring, scedules sould be adjusted to ensure tat interviews are completed before dark. For example, if te sun sets between 5 and 5:30PM, an appropriate afternoon interview period may be 11AM to 5PM. For proxy site-days, a particular time period is not identified. Te purpose of surveying is to obtain information to convert proxy counts to site visit estimates. Interviews are conducted during te 6-our dayligt period wit greatest level of exiting recreation traffic. Closed Sites Unpredictable weater, precipitation patterns, fires, or oter natural penomena may cange te dates a site is open or closed. Some canges may be for an extended period. Unfortunately, no ex post adjustment for suc canges really is possible. Reporting units must try to determine a priori a site s most likely opening and closing dates. Te set of open site-days is defined before te survey year begins, and it is to tat set tat te visitation estimate applies. For all days tat a site will be closed due to reconstruction, restoration, or for some oter reason, tat site sould be listed as closed. Sites may be administratively closed, in wole or part, on days tey were expected to be open for unforseen reasons suc as visitor safety (fire, flood, too muc snow), construction (including unforseen repairs), or resource protection (too little snow, wildlife protection). In suc cases, a site will be sown as open but wit below-normal visitation. If a site is partially closed, interviewing sould continue as sceduled, but below-normal visitation sould be noted in te daily summary form. If a site as been unexpectedly and completely closed, te interviewer 17

20 records zero traffic counts on te daily summary form. Conversely, sites tat are open wen tey are expected to be closed are treated as closed. Selecting interviewees Interviewers are to conduct as many surveys as possible, altoug more tan 60 interviews a day is unnecessary. It is important, owever, to spread out interviews over an entire sampling day. For instance, at a busy developed site were many interviews could be conducted quickly, interviewers sould time tem to cover te wole sampling period. To determine te individual in a veicle or group to survey, use a random selection process (te person over age 15 wit te most recent birtday). Survey forms Eac interviewee is asked basic survey form questions. One or two additional questions are asked at proxy sites to convert proxy counts to site visit estimates. One-fourt of te sample are asked a set of questions about economic benefits and trip-related spending. Anoter one-fourt are asked questions about teir satisfaction wit recreation services and facilities. DATA ANALYSIS PART I. Daily site visits at Non-proxy site-days: Altoug traffic counters tally eiter exiting veicles or exiting persons, te metod for estimating daily site visits is essentially te same for bot. Most of te site-visit estimators follow 18

21 standard formulae for stratified random samples (Cocran 1977). For a given stratum (=1, 2, 3,..., H) and sampled site-day i (i=1, 2, 3,..., n ) witin stratum let: C i = te total car (or person) count (obtained from traffic counter) during te 24-our sampling period for day i in stratum ; V ij = te number of persons in te jt (j = 1, 2, 3,... J) sampled veicle on site-day i (obtained from te on-site questionnaire; note tat wen traffic counts are of exiting visitors, V ij = 1 is a constant); LR ij = indicator variable in te on-site questionnaire, coded as: = 1 if te jt veicle sampled on site-day i is a last-exiting recreation veicle, = 0 oterwise ; P i = J j=1 LR J ij Te proportion of veicles on site-day i tat were last-exiting (P i ) is V i = J LR j=1 J j=1 ij LR V ij ij Te mean persons per recreation veicle for last exiting recreation veicles (V i ) is Terefore, te estimate for total exiting site visits (SV i ) on site-day i is 19

22 SV i = C i P i V i An estimate of mean daily site visits for stratum is simply: SV = n i=1 SV n i V( SV )= n i=1 2 ( SV i- SV ) n ( n -1) wit estimated variance Tis formula implies a simplifying assumption. Te sampling frame for non-proxy days is actually a two-stage design. Te first stage is a random sample of site days, and te second is a random sample of visitors witin eac first-stage sampling unit. However, te first-stage sampling rates are relatively small. Preliminary information from te pre-sampling work for reporting units surveyed in te first year indicates tat across all sampled forests, te average first-stage sampling rate was about 0.25 percent. Hence, te second term in te sample variance equation for a two-stage sample (see Cocran 1977 p.278) will be negligible and could be eliminated, yielding te above formula. Expansion to te stratum total (SV ) is 20

23 SV = N SV 2 V( SV )= N V( SV ) wit estimated variance were N = total number of site-days in stratum. PART II. Proxy site-visit estimates Estimation of recreation site visits for te proxy component differs from tat of te non-proxy in several ways. First, strata are defined differently. For a given site-type tere may be several different types of proxy information. Eac unique combination of site type and proxy type constitutes a stratum. Second, a component of te proxy site visit estimation equation is not based on a sampling survey but is obtained by a direct census (a count known witout error) of te proxy count, wic yields a reduction in estimator variance. Here, te purpose of sampling is to obtain te information needed to convert proxy counts to site visits. Let P k be te annual total proxy count for site k in stratum, and let CR k be te known compliance rate of visitors wit respect to te proxy count at tat site. For example, not all campground users may pay te required fee, or not all wilderness users may obtain te mandatory permits. Ten, te compliance-adjusted proxy count for site k (PC k ) is te proxy count tat would ave been observed wit 100 percent compliance, and PC k is: P PC k = 21 CR k k

24 PC = K k=1 K k=1 PC N k k For a given stratum te mean daily proxy count is were N k is te number of site-days wose use is represented by proxy count for site k in stratum. Conversion coefficients are needed to obtain site visit estimates from proxy counts. Coefficients for eac sitetype - proxy type stratum are obtained by sampling individuals on randomly selected site-days witin te stratum. Two different variables are needed to make te conversion. Consider a campground tat collects fee envelopes from campers. Payment is required for eac nigt a campsite is occupied. However, a person, group, or family camping for a week can pay in one envelope for te wole week (one proxy), or as many as one envelope eac day (seven proxies). Te first conversion variable (R) measures te proxy count per group recreation visit. Te second conversion variable (G) measures te number of people per group recreation visit. For example, up to 5 people are allowed to use te same campsite. Let R ij = te number of proxies per group recreation site visit for te j t group surveyed in sample day i in stratum, (R ij $ 1.0), G ij = group size for te j t surveyed group on te i t sample day in stratum. Because individual surveys are clustered witin sample days, te conversion coefficient for eac stratum is calculated using a ratio of means approac. Let te sum of R ij and G ij over all surveys 22

25 on te i t day be SR i and SG i respectively. Ten te estimate of te proxy conversion coefficient A = n i=1 n i=1 SG SR i i (A ) for stratum is were n is te number of days sampled in stratum, and wic as a variance of A )= [ SG + A SR -2 2 A ( n )(n -1)( SR n ) i i i/ i i ( SG V( isri i i )] Ten te estimator for mean daily site visits in stratum is SV = A PC wit a variance of V( SV )=V( A ) PC 2 An exception is if te proxy count is a permanent traffic counter tat may count non-recreation use as well as recreation users, suc as along a scenic roadway or at a day use site 23

26 were people may enter just to use te batroom. In tese cases, te mean daily proxy count is adjusted by te proportion of all of te individuals surveyed on site-days in tat stratum wo were = A recreating at te site (RP ). Here, te mean daily site visit estimate is given by SV PC RP V( SV )= RP PC V( A )+ A PC V( RP )- PC V( A )V( RP ) and its variance by SV = N Expansion to total site visits for stratum is were N is te total number of site-days in stratum. Te estimated variance for total site visits SV 2 V( SV )= N V( SV ) is PART III. Expansion to forest population mean and total To estimate mean daily site visits for te entire population of site-days over all strata, combining bot proxy and non-proxy, let strata weigts be defined as 24

27 W = N H N =1 SV = H =1 W SV H 2 V( SV )= W V( SV =1 ) SV = N SV ten te mean daily site visit estimator is wit estimated variance Site-visit estimate for te total population is were N is te total number of site-days in te reporting unit=s population, and te estimated 2 V(SV) = N V( SV ) variance is 25

28 PART IV. Estimating national forest visits. Te original NVUM survey for a given National Forest was based on a stratified random sampling design of site-days wit strata defined by site-type and daily exit volume (i.e., DUDS LOW). Te objective was to estimate mean daily site visits and total annual site visits from a sample of site days randomly selected in eac strata. Site visit estimates were obtained for eac sample day, averaged by strata and ten expanded according to classical stratified random sampling metodology. However, a primary reporting goal of NVUM is te number of national forest visits (NFV). Because eac national forest visit is comprised of a variable number of site-visits, we realized tat complications existed for suc estimates because of te possibility of recreationists moving out of teir sampling unit by visiting multiple sites. A person wo visits two sites on a national forest visit could be contacted and correctly included in te sample on te last exit for eiter or bot site visits, even if te sites are of different site-types and/or exit volume levels. Conversely, a person visiting only one site could only be interviewed wen last exiting tat site. Tus, visitors wit more site visits per national forest visit will be over represented in te sample, leading to an upward bias in te estimator for mean number of site visits per national forest visit, and a downward bias in number of national forest visits. Tis type of problem is uncommon in most classical sampling situations, but a related issue as been identified in some on-site visitor samples (Saw). Tese problems associated wit estimating NFV were alleviated by using te following approac. Consider eac national forest visitor wit a coupon tat is distributed proportionately to eac site visited on tat trip. For instance, if tree sites are visited on an NFV trip, ten eac site 26

29 gets 1/3 of te coupon. Te true NFV number is te total number of coupons on all site-days in te forest. For a given site-day te estimator of NFV is defined matematically as Nˆ FV i= P i*cars i*cbar i were P i = proportion of veicles tat were last exiting recreationists on site-day i, CARS i = number of veicles obtained from te car counter adjusted for axles and one-two-way traffic on site-day i and CBAR i = average number of coupons per last exiting recreating veicle on site-day i (remembering to use proportions of a coupon if multiple sites were visited). To furter clarify te meaning of CBAR, let n = number of last exiting recreating veicles interviewed, PEOPLE j = number of people in last exiting recreating veicle j and SVPNFV j = te number of sites visited on tis national forest visit for te people in veicle j ten CBAR is defined as 1 CBAR = n n j=1 PEOPLE SVPNFV j j 27

30 Note tat te NFV estimator is identical to te SV estimator except tat CBAR is used instead of average people per veicle. Justification for tis approac for estimating NFV is verified by a couple of examples. If all visitors only go to one site on teir national forest visit, ten SVPNFV = 1 and CBAR reduces to te average people per car and NFV = SV as is expected. Alternately, if all people go to two sites on teir national forest visit, ten SVPNFV = 2 and CBAR equals one alf te average people per car and NFV = 0.5 SV as expected. Logical extensions to oter scenarios were te number of sites visited per visitor varies are more complicated but sould be obvious. Since te NFV estimator is identical to te SV estimator except for CBAR, all te statistical metodology previously explained for te SV estimator is appropriate for te NFV estimator. In particular, te NFV i =s are used to calculate strata means and variances tat are ten expanded to forest level estimates. Tis approac can be extended to te proxy portion of te NFV estimator by a simple A = n i=1 n i=1 SG SR i i modification of te proxy conversion coefficient A- for stratum defined previously as SC i = m j=1 GRPSIZE ( SVPNFV ij ij ) For te NFV estimator SG i must be replaced wit SC i wic is defined as All oter statistical metodologies follow as outlined previously for te proxy situation. 28

31 PART V. Expansion to regional and national estimates All estimates at te reporting unit level, weter totals or means, ave been based on a stratified random sampling design. To calculate regional-level estimates, tese estimates are folded into a two-stage sampling design from wic te appropriate estimators and teir variances are obtained. National totals and teir variances are simply te sum of all of te regional totals and teir variances. An unbiased estimator for regional totals of a variable of interest, suc as total number of site days, is based on Cocran (1977, equation 11.21) and is defined as Yˆ u= N n n i=1 M i y i were N = total number of reporting units in te region, n = number of reporting units sampled in te region, M i = total number of site-days in reporting unit i and y- i = mean estimate per site-day for reporting unit i based on stratified random sampling. An estimate of te variance is obtained as a sligt modification of Cocran (1977 equation 11.24) due to stratified random sampling and is defined as 29

32 n i=1 2i were Ŷ i = estimate of te total for reporting unit i, Y- u = average total estimate for a reporting unit, f = (1-n/N) = te finite population correction for reporting units and 2 s 2i = variance of te mean estimate based on stratified random sampling. Note tat te finite population correction at te second stage level is ignored for simplicity because te number of site-days sampled witin a reporting unit is negligible compared to te total number of site-days in te unit. Te unbiased ratio to size estimator from Cocran (1977, equation 11.25) is used to estimate regional means after sligt modification and is defined as Y R = n i=1 n i=1 M i M y i i wit estimated variance after modification from Cocran (1977, equation 11.30) as 2 (Yˆ - ) 2 i Y u n N (1- f ) i=1 N 2 2 V( Yˆ u )= + M i s n n -1 n 2 n 2 ( - n 1 N (1- f ) y Y ) 2 i R N 2 2 V( Y R )= ( M + M i s2i) 2 i M 0 n i=1 n -1 n i=1 30

33 were M 0 = N n i=1 M n i Again, te finite population correction at te second stage level is ignored for simplicity. PART VI. Estimators for Visitor Caracteristics Te NVUM survey and reporting process also provides tree types of estimates for various visitor caracteristics tat are important to managers. Tese consists of: (1) total estimates suc as total number of NFV visits by cildren under sixteen, (2) mean estimates suc as mean trip or site visit duration time, and (3) proportion estimates suc as proportion of visitors tat camp. In addition, eac of tese could be defined on one of tree scales: (a) site visit, (b) national forest visit, or (c) annual basis. For instance, an estimator may be developed for te proportion of visitors tat camp some time during teir national forest visit, or for ow often te average visitor visits te forest per year. Tus, wit 3 estimator types and 3 scale levels, tere are 9 different estimators for a specific visitor caracteristic. Te most meaningful estimator will depend on te question asked and estimator desired. All total estimates follow te previously defined metodology for SV and NFV estimates except wit appropriate minor canges to include te variable of interest. All mean and proportion 31

34 estimates are developed as ratios of two total estimates. Te total estimates are defined on a site-day basis as Tˆ OTAL=P i i*cars*x i i were P i =proportion of veicles tat were last exiting recreationists on site-day i, CARS i = number of veicles obtained from te car counter adjusted for axles and one-twoway traffic on site-day i, X ij = a variable dependent on te scale and level of te estimator for group j in site-day i = Z 1 / (Z 2 * Z 3 ) and X- i = te average of te X ij over all groups. Te X ij is straigtforwardly defined. Te Z 1 is te variable of interest. Te Z 2 and Z 3 variables are defined so as to adjust Z 1 to te appropriate scale. Te following table gives some examples of common estimators wic clarify ow te estimators are computed for different scales and types. Given tat: SVPNFV = te number of site visits per national forest visit for veicle j and NFVPY = te number of national forest visits per year for veicle j, ten for SV scale estimators Z 2 = 1 Z 3 = 1 32

35 NFV scale estimators Z 2 = SVPNFV Z 3 = 1 Annual scale estimators Z 2 = SVPNFV Z 3 = NFVPY Defining a total estimator in tis manner on a site-day basis allows application of te same statistical metodology as previously described for te SV and NFV estimators. 33

36 Table 1. Some interesting estimators. Y Estimator Description Equation Type Scale Y 1 Total number of annual X=PEOPLE Total SV site visits Y 2 Total number of annual X=PEOPLE/SVPNFV Total NFV national forest visits Y 3 Total number of different X=PEOPLE/(SVPNFV*NFVPY) Total Annual visitors to te national forest on an annual basis Y 4 Average number of national Y 2 / Y 3 Average Annual forest visits per visitor per year Y 5 Total number of annual X=NKIDS/SVPNFV Total NFV national forest visits by cildren under 16 Y 6 Proportion of national Y 5 / Y 2 Proportion NFV forest visits by cildren under 16 Y 7 Total number of national X=(PEOPLE*CAMP)/SVPNFV Total NFV forest visits were camping was an activity Y 8 Proportion of national Y 7 / Y 2 Proportion NFV forest visits were camping was an activity Y 9 Total number of group trips X=1/SVPNFV Total NFV to te national forest on an annual basis Y 10 Sum of te ages of one person X=(1*AGE)/SVPNFV Total NFV per group for eac group trip to te national forest Y 11 Average age of a national Y 11 / Y 9 Average NFV forest visitor 34

37 35

38 Literature Cited Cocran, W.G Sampling Tecniques. 3 rd Edition. New York: Wiley. Gregoire, T. G., and G. J. Buyoff Sampling and estimating recreation use. USDA- Forest Service. Pacific Nortwest Researc Station. General Tecnical Report pp. James, G.A Recreation use estimation on Forest Service lands in te United States. USDA-Forest Service, Souteastern Forest Experiment Station. Researc Note SE-79. July pp. James, G.A., and T.H. Ripley Instructions for using traffic counters to estimate recreaiton visits and use. USDA- Forest Service. Souteastern Forest Experiment Station, Researc Paper SE pp. James, G.A., and J.L. Ric Estimating recreation use on a complex of developed sites. USDA- Forest Service. Souteastern Forest Experiment Station, Researc Note SE pp. James, G.A., and Henley, R.K Sampling procedures for estimating mass and dispersed recreation use on large areas. USDA- Forest Service. Souteastern Forest Experiment Station, Researc paper SE pp. Lucas, R.C., H.T. Screuder, and G.A. James Wilderness use estimation: A pilot test of sampling procedures in te Mission Mountains Primitive Area. USDA-Forest Service. Intermountain Forest and Range Experiment Station. Researc Paper pp. Mood, A.M., F.A. Graybill, and D.C. Boes Introduction to te Teory of Statistics. 3 rd Edition. New York: McGraw-Hill. Saw, Daigee. On-site samples= regression: Problems of non-negative integers, truncation, and endogenous stratification. Journal of Econometrics 37(1988): Yuan. S., B Maiorano, M. Yuan, S. M. Kocis, and G.T. Hoside Tecniques and equipment for gatering visitor use data on recreation sites. USDA- Forest Service, Tecnology and Development Program. Publication MTDC. August pp. 36

39 APPENDIX A NVUM PROCESS FLOWCHART PHASE I: PRE-WORK Define Forest=s Rec sites, Classify into site types (OUDS, DUDS, Wilderness, GFA) [Forest, Regional Coordinator]* \/ ID dates eac site is expected to be OPEN CLOSED ========> Site Visits = 0 [Forest] \/ Determine if proxy information is available for eac open site-day [Forest] \/ \/ NO YES (Non-proxy site-days) (Proxy site-days) Stratify days in eac site type by expected exit volume: Hig Medium Low [Forest] Complete spreadseet: Site ID, Site type, Date, Use Class [Forest] Determine sampling scedule [National Team] Stratify days in eac site type by expected exit volume: Hig Medium Low [Forest] Complete spreadseet: Site ID, Site type, Date, Use Class, Proxy type, Proxy units, [Forest] Determine sampling scedule [National Team] Train, scedule, interview staff [Forest, Regional Coordinator] * Brackets indicate wo is primarily responsible for accomplising te task. 37

40 PHASE II: SURVEY PROCESS (for forest staff) NON-PROXY SITE-DAYS One day prior to sceduled sampling, determine if te site will be open on te sampling day, or closed due to unusual circumstances (eg, late snow) \/ \/ YES NO ===> Record 0 visits and Do not attempt interviews \/ Set up traffic counter To obtain daily count On sceduled sampling day, - Conduct as many EXIT interviews as is practical for te assigned time (1 interview per group) - Retrieve traffic counter at day=s end - Record traffic count on sampling spreadseet 1 Day after sceduled sampling: - Ceck interview forms for completeness - Mail completed forms to regional coordinator 38

41 PHASE II: SURVEY PROCESS (for forest staff) PROXY SITE-DAYS For eac day during te interview year, Record te proxy count for sites. One day prior to sceduled sampling, determine if te site will be open on te sampling day, or closed due to unusual circumstances (eg, late snow) YES NO ===> Record 0 visits and Do not attempt interviews On sceduled sampling days, - Obtain compliance ceck for te proxy count, to determine wat % of users are measured by te proxy - Conduct EXIT interviews for te assigned time frame One Day after sceduled sampling: - Ceck interview forms for completeness - Mail completed forms to regional coordinator 39