National Survey of Fishing, Hunting, and Wildlife ... - All About Birds
National Survey of Fishing, Hunting, and Wildlife ... - All About Birds
National Survey of Fishing, Hunting, and Wildlife ... - All About Birds
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tables indicated by the numerator.The approximate The approximate st<strong>and</strong>ard error, st<strong>and</strong>ard s x,p, can error, be sobtained x,p,can be by obtained use <strong>of</strong> the by formula use <strong>of</strong> the formulasx,p,pbp( 100 p)x(3)(3)Here, x is the Here, total x is number the total <strong>of</strong> number sportspersons, <strong>of</strong> sportspersons, hunters, etc., hunters, which etc., is the which base is <strong>of</strong> the the base percentage; <strong>of</strong> the percentage; p is the percentage p is the percentage ; <strong>and</strong> b is (0 ≤ p ≤the parameter 100); in <strong>and</strong> the tables b is the associated parameter with in the the tables characteristic associated in with the numerator the characteristic <strong>of</strong> the percentage. in the numerator <strong>of</strong> the percentage.Illustration Illustration <strong>of</strong> the Computation <strong>of</strong> the Computation <strong>of</strong> the St<strong>and</strong>ard <strong>of</strong> the St<strong>and</strong>ard Error <strong>of</strong> an Error Estimated <strong>of</strong> an Estimated Percentage PercentageSuppose there Table were 1 shows an estimated that <strong>of</strong> the 13,674,000 12,510,000 hunters hunters age 16 16 years years old old <strong>and</strong> <strong>and</strong> older, 18.3 <strong>of</strong> whom percent 18.9 hunted percent migratory hunted migratory birds. From table D-7,birds. From the table appropriate D-5, the b appropriate parameter b is parameter 5,756. Using is 15,798. formula Using (3), the formula approximate (3), the approximate st<strong>and</strong>ard error st<strong>and</strong>ard on the estimate error on <strong>of</strong> the 18.3 esti-percenmate <strong>of</strong> 18.9 percent isis5, 756 18. 3 100 18.3s xp , 5, 756 083 .5, 75618. 312 18 , 510 100. 3 ,000100 18.3 18.3,s xp , 083 .12, 510,000 083 .150 2006 <strong>National</strong> <strong>Survey</strong> <strong>of</strong> <strong>Fishing</strong>, <strong>Hunting</strong>, <strong>and</strong> <strong>Wildlife</strong>-Associated Recreation U.S. Fish & <strong>Wildlife</strong> Servics xpConsequently, the 95-percent confidence interval for the estimate percentage <strong>of</strong> migratory bird hunters 16 years old <strong>and</strong> olderis from 16.3 Consequently, percent to 21.5 the 95-percent percent, i.e., confidence 18.9 ± 1.96 interval x 1.33. for the 12, estimate 510,000percentage <strong>of</strong> migratory bird hunters 16 years old <strong>and</strong> olderConsequently, is from 16.7 the 95-percent to 19.9 confidence percent, interval ie. 18.3 for ± 1.96 the estimate x 0.83. percentage <strong>of</strong> migratory bird hunters 16 years old <strong>and</strong> olderConsequently, the 95-percent confidence interval for the estimate percentage <strong>of</strong> migratory bird hunters 16 years old <strong>and</strong> olderSt<strong>and</strong>ard is from Error 16.7 <strong>of</strong> percent a Difference. to 19.9 The percent, st<strong>and</strong>ard ie. 18.3 error ± 1.96 <strong>of</strong> the x difference 0.83. between two sample estimates is approximately equal toSt<strong>and</strong>ard is from 16.7 Error percent <strong>of</strong> a Difference. to 19.9 percent, The st<strong>and</strong>ard ie. 18.3 ± error 1.96 <strong>of</strong> x the 0.83. difference between two sample estimates is approximately equal toSt<strong>and</strong>ard Error <strong>of</strong> a Difference. The st<strong>and</strong>ard error <strong>of</strong> the difference 2 2 between two sample estimates is approximately equal toSt<strong>and</strong>ard Error <strong>of</strong> a Difference. The st<strong>and</strong>ard s errorx y <strong>of</strong> s thexdifference s between two sample estimates is approximately (4) equal toy2 2(4)s 2 2x y where s x<strong>and</strong> where s yare sx<strong>and</strong> the sy st<strong>and</strong>ard are the st<strong>and</strong>ard errors <strong>of</strong> errors the estimates <strong>of</strong> the ssx estimates x <strong>and</strong> y sy. The x yx<strong>and</strong> estimates y. s(4)yThe estimates can be numbers, can numbers, percentages, percentages, ratios, etc. ratios, This etc. (4) Thiswill where represent will represent the actual the actual st<strong>and</strong>ard quite error accurately quite accurately for the difference for the difference between estimates between estimates <strong>of</strong> the same <strong>of</strong> the characteristic same characteristic in two in twodifferent areas, different where sx<strong>and</strong> syare the st<strong>and</strong>ard errors <strong>of</strong> the estimates x <strong>and</strong> y. The estimates can numbers, percentages, ratios, etc. Thisor sxfor areas, <strong>and</strong>the sy or aredifference for the the st<strong>and</strong>ard difference errorsbetween separate between <strong>of</strong> the<strong>and</strong> separate estimatesuncorrelated <strong>and</strong> x <strong>and</strong> uncorrelated y. The estimatescharacteristics characteristics can be numbers,in the same in the area. same percentages,However, area. However, ratios,if there is if etc. there Thiswill represent the actual st<strong>and</strong>ard error quite accurately for the difference between estimates <strong>of</strong> the same characteristic in twoa high positive a will high represent(negative) positive (negative) the actual st<strong>and</strong>ardcorrelation correlation error the between quite accuratelytwo characteristics, the two characteristics, for the differencethe formula the will formula betweenoverestimate will estimates overestimate <strong>of</strong> the same(underestimate) (underestimate) characteristicthe true the in true twodifferent areas, or for the difference between separate <strong>and</strong> uncorrelated characteristics in the same area. However, if there isst<strong>and</strong>ard error. st<strong>and</strong>ard different error. areas, or for the difference between separate <strong>and</strong> uncorrelated characteristics in the same area. However, if there isa high positive (negative) correlation between the two characteristics, the formula will overestimate (underestimate) the truea high positive (negative) correlation between the two characteristics, the formula will overestimate (underestimate) the truest<strong>and</strong>ard error.Illustration Illustration st<strong>and</strong>ard error.<strong>of</strong> the Computation <strong>of</strong> the Computation <strong>of</strong> the St<strong>and</strong>ard <strong>of</strong> the St<strong>and</strong>ard Error <strong>of</strong> Error a Difference <strong>of</strong> a DifferenceIllustration <strong>of</strong> the Computation <strong>of</strong> the St<strong>and</strong>ard Error <strong>of</strong> a DifferenceSuppose there In Illustration Table were 8, an <strong>of</strong> <strong>of</strong>estimated the the 11,655,000 Computation13,608,000 females <strong>of</strong> thefemales in the St<strong>and</strong>ard age in the range Errorage <strong>of</strong> range 18-24, <strong>of</strong> a Difference<strong>of</strong> 18-24 726,000 <strong>of</strong> whom or 6.2 percent 726,000 are or 5.3 sportspersons. percent were Similarly, <strong>of</strong> thesportspersons. In Table 11,638,000 Similarly, <strong>of</strong> the males 11,655,000 suppose in the females there same were age in range, the estimated age 1,929,000 range 12,909,000 <strong>of</strong> 18-24, or 16.6726,000 percent males in or are the 6.2 sportspersons. same percent age are range sportspersons. The <strong>of</strong> apparent whom 2,160,000 difference Similarly, or between <strong>of</strong> the16.7 percent the Inwere percent Table 8,sportspersons. <strong>of</strong> <strong>of</strong> female the 11,655,000 <strong>and</strong> The male femalesapparent participants in thedifference is age 10.4 rangebetween percent. <strong>of</strong> 18-24,the Using 726,000percentage formula or<strong>of</strong> female (3) 6.2 <strong>and</strong> percent<strong>and</strong> the male appropriate are sportspersons.sportspersons b parameter Similarly,is 11.4 from table <strong>of</strong> the11,638,000 males in the same age range, 1,929,000 or 16.6 percent are sportspersons. The apparent difference betweenpercent. Using D-7, 11,638,000 the formula approximate males in(3) <strong>and</strong> st<strong>and</strong>ard the samethe appropriate errors age range, <strong>of</strong> b parameter 6.21,929,000 percent from <strong>and</strong> or 16.6table percent areD-5, the sportspersons.approximate 0.55 <strong>and</strong> 0.85, st<strong>and</strong>ard respectively. The apparenterrors <strong>of</strong> Using difference5.3 percent formula betweenthe percent <strong>of</strong> female <strong>and</strong> male participants is 10.4 percent. Using formula (3) <strong>and</strong> the appropriate b parameter from table (4), the<strong>and</strong> 16.7 percent approximate the percent <strong>of</strong>are 0.79 st<strong>and</strong>ard female 1.35, error <strong>and</strong> malerespectively. <strong>of</strong> the participants estimated Using difference is 10.4 percent.formula (4), <strong>of</strong> 10.4 Usingthe approximate percent formula is (3) <strong>and</strong> the appropriate b parameter from tableD-7, the approximate st<strong>and</strong>ard errors <strong>of</strong> 6.2 percent <strong>and</strong> 16.6 percent are 0.55 <strong>and</strong>D-7, the approximate st<strong>and</strong>ard errors <strong>of</strong> 6.2 percent <strong>and</strong> 16.6 percent are 0.55st<strong>and</strong>ard 0.85, respectively.<strong>and</strong> 0.85,errorrespectively.<strong>of</strong> the Using estimated formulaUsingdifferenceapproximate <strong>of</strong> 11.4 percent st<strong>and</strong>ard is error <strong>of</strong> the estimated difference <strong>of</strong> 10.4 2 percent 2 is(4), theformula (4), theapproximate st<strong>and</strong>ard error <strong>of</strong> the estimated difference <strong>of</strong> 10.4 percent iss xs xy 055 . 0. 85 102 .2 2 ys055 . 2 2x 055.0. 85 0. 85102 . 102 .The 95-percent confidence interval on the difference y between 18-24 year old female <strong>and</strong> male sportspersons is from 8.4 to15.8 to 17.6, i.e., 16.7 ± 1.96 x 0.45.The The 95-percent 95-percent 12.4, i.e., 10.4 confidence ± 1.96 interval interval x 1.02. on the on Since difference the the difference interval between between does 18- not 18-24 to contain 24-year-old zero, we female can conclude <strong>and</strong> male with sportspersons 95 percent is confidence from 8.3 8.4 to that theto 14.5, i.e., percentage The 95-percent11.4 ± <strong>of</strong> 18-24 confidencex 1.56. year Since old intervalthe female on sportspersons the differencedoes not is less betweenzero, than the 18-24we percentage year oldcan <strong>of</strong> female 18-24 <strong>and</strong>with 95 year male old sportspersons male sportspersons. is from 8.4 to12.4, i.e., 10.4 ± 1.96 x 1.02. Since the interval does not contain zero, we can conclude with 95 percent confidence that that the the12.4, i.e., 10.4 ± 1.96 x 1.02. Since the interval does not contain zero, we can conclude with 95 percent confidence that thepercentage <strong>of</strong> 18- <strong>of</strong> 18-24 to 24-year-old female sportspersons is less than the percentage <strong>of</strong> 18-24 to 24-year-old male male sportspersons.St<strong>and</strong>ard percentage Errors <strong>of</strong> 18-24 <strong>of</strong> Estimated year old Averages. female sportspersons Certain mean is less values than for the sportspersons, percentage <strong>of</strong> anglers, 18-24 year etc., old shown male in sportspersons.the report were calculatedErrors Errors as <strong>of</strong> the Estimated <strong>of</strong> ratio Estimated <strong>of</strong> two Averages. numbers. Averages. Certain For Certain example, mean mean values average values for for days sportspersons, per angler anglers, is calculated anglers, etc., etc., shown as: shownSt<strong>and</strong>ard St<strong>and</strong>ardSt<strong>and</strong>ard Errors <strong>of</strong> Estimated Averages. Certain mean values for sportspersons, anglers, etc.,in the inshownreport the reportinwere werethe reportcalculatelatedas the ascalcu-were calculatedratio the ratioas<strong>of</strong>thetwo <strong>of</strong> tworationumbers. numbers.<strong>of</strong> twoFornumbers.example, For example,Foraverage x averageexample, total days daysaverageper days angler per anglerdaysispercalculated is calculatedangler isas: as:calculated as:x yxtotal total totaldays anglers daysy total y totalanglersanglersSt<strong>and</strong>ard errors for these averages may be approximated by the use <strong>of</strong> formula (5) below.St<strong>and</strong>ard St<strong>and</strong>ard errors errors for these for these averages averages may may be be approximated by the by use the use <strong>of</strong> formula <strong>of</strong> formula (5) below. (5) below.St<strong>and</strong>ard errors for these averages may be approximated by the use <strong>of</strong> formula (5) below.2x sssr ssx y x yy(5)y x 2 2y 2x2 ss xysr ssx y x yx y(5)In formula (5), r represents the correlation coefficient y x 2sssbetween rssx y xy yx y2(5)y x 2 y 2 xythe numerator xy <strong>and</strong> the denominator <strong>of</strong> the estimate. (5) In theIn formulaabove(5), rformula,representsusethe0.7correlationas an estimate 15.8 tocoefficient<strong>of</strong> 17.6, r. i.e., 16.7 ± 1.96 x 0.45.In formula (5), r represents the correlation coefficient between between the numerator the numerator <strong>and</strong> <strong>and</strong> the denominator the denominator <strong>of</strong> the <strong>of</strong>In formula (5), r represents the correlation coefficient between the numerator <strong>and</strong> the denominator estimate. the estimate.<strong>of</strong> the In estimate. the In theIn theabove above formula, formula, use use 0.7 as 0.7 an as estimate an estimate <strong>of</strong> r. <strong>of</strong> r.Illustration above formula, <strong>of</strong> the use Computation 0.7 as an estimate <strong>of</strong> the <strong>of</strong> St<strong>and</strong>ard r. Error <strong>of</strong> an Estimated AverageIllustration <strong>of</strong> the Computation <strong>of</strong> the St<strong>and</strong>ard Error <strong>of</strong> an Estimated AverageTable Illustration 2 shows <strong>of</strong> that the the Computation average days <strong>of</strong> per the angler St<strong>and</strong>ard 16 years Error old <strong>of</strong> <strong>and</strong> an older Estimated for all fishing Average was 17.3 days. Using formulas (1) <strong>and</strong>U.S. Fish Table <strong>and</strong> (2) 2 <strong>Wildlife</strong> shows above, Service that we the compute <strong>and</strong> average U.S. Census the days st<strong>and</strong>ard Bureau per angler error 16 on years total 2011 days, old <strong>National</strong> <strong>and</strong> 516,781,000, older <strong>Survey</strong> for <strong>of</strong> <strong>Fishing</strong>, all <strong>and</strong> fishing total <strong>Hunting</strong>, was anglers, <strong>and</strong> 17.3 <strong>Wildlife</strong>-Associated 29,952,000, days. Using to formulas Recreation be 15,828,079 (1) 125 <strong>and</strong> <strong>and</strong>399,342, Table 2 shows respectively. that the The average approximate days per st<strong>and</strong>ard angler 16 error years on old the <strong>and</strong> estimated older for average all fishing <strong>of</strong> 17.3 was days 17.3 isdays. Using formulas (1) <strong>and</strong>(2) above, we compute the st<strong>and</strong>ard error on total days, 516,781,000, <strong>and</strong> total anglers, 29,952,000, to be 15,828,079 <strong>and</strong>(2) above, we compute the st<strong>and</strong>ard error on total days, 516,781,000, <strong>and</strong> total anglers, 29,952,000, to be 15,828,079 <strong>and</strong>399,342, respectively. The approximate st<strong>and</strong>ard error on the estimated average <strong>of</strong> 17.3 days is399,342, respectively. The approximate st<strong>and</strong>ard error on the estimated average <strong>of</strong> 17.3 days is