Ratio estimates also have advantages from a statistical standpoint. The ratio 

 estimates had the smallest error terms of any of the estimation methods tested. A ratio 

 estimate is based on an assumption of linearity through the origin--in other words, when 

 there are no registrations, there would be no estimated use (Cochran 1963, section 6.9). 

 This assumption fits well. We observed use only for 12 hours on each of the 2 days in a 

 sample unit, while registered use was measured over the whole 48-hour period. This 

 means registered use could be either larger or smaller than observed use. If use and 

 registration were measured over identical time periods, actual use could not be less 

 than registered use. This difference could introduce a bias, probably small. 



Ratio estimation is also best if the variance of Y at a given value of X is 

 proportional to the value of X--in other words, if the variance of Y increases as X 

 increases. This also seems reasonable for trail registration data. 



In practical terms, ratio estimation is easy for land managers to understand and 

 apply. The procedure is intuitively obvious and the calculations are very simple. 



Stratified Random -Sampling Estimation 



Unbiased estimates of use with their associated standard errors were generated 

 using stratified random -samp ling estimation procedures (table 6) . Two sets of estimates 

 were produced: one based on data from persons interviewed when entering, the other 

 based on persons interviewed when leaving. These data were multiplied by the inverse 

 of the sampling fraction. For example, 12 of 14 possible 2-day units were sampled 

 in stratum 1, so the interview totals were multiplied by 14/12 or 1.1667. 



The estimates of the number of visits and number of groups entering and leaving 

 were about the same in the summer, but were markedly different in the fall. This was 

 attributed to the fact that visitors who entered the area prior to the arrival of the 

 interviewer at 8 a.m. (or at 12 noon the last few weeks) were more common in the fall 

 than in the summer. 



Expected and actual hours of use were quite similar in the summer, but expected 

 use (12,996 hours) far exceeded actual use (3,681 hours) in the fall. This was partly 

 attributed to the fact that unplanned factors reduced actual length of stay in the fall 

 about 10 percent below visitors' expectations. However, most of the difference between 

 expected and actual hours of use in the fall was attributed to sampling variability in 

 stratum 7 (one group that planned to stay 8 days--an unusually long time--was 

 interviewed only upon entering) . The precision of total estimated summer visitor-hours 

 was high for both entering and exiting visitors, but was unacceptably low for total 

 estimated fall visitor-hours. 'More precise estimates for the three key variables were 

 obtained by combining summer and fall strata. 



Sampling to obtain estimates of use was far less efficient in the fall than in the 

 summer. This probably reflected the light and variable use in the fall. It is also 

 more difficult to select hours in the fall for interviewing that would assure contact- 

 ing nearly all visitors at least once. Some hunters enter early in the day, a few 

 leave late. 



This type of estimation did not give adequate precision at reasonable cost. Sam- 

 pling intensities during summer, fall, and summer+fall were high (13, 15, and 14 percent, 

 respectively) as were costs; yet precision levels for several variables were considerably 

 less than desired. One advantage of this method is that unbiased estimates and preci- 

 sion levels are obtained for all variables of interest. 



Where highly reliable estimates are obtained for several variables, as was the 

 case for some strata in this study, they can be used as a standard for comparison with 

 estimates from other estimation methods. These other methods might be more efficient. 



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