National Survey of Fishing, Hunting, and Wildlife ... - All About Birds

tables indicated by the numerator.The approximate The approximate standard error, standard s x,p, can error, be sobtained x,p,can be by obtained use of the by formula use of the formulasx,p,pbp( 100 p)x(3)(3)Here, x is the Here, total x is number the total of number sportspersons, of sportspersons, hunters, etc., hunters, which etc., is the which base is of the the base percentage; of the percentage; p is the percentage p is the percentage ; and b is (0 ≤ p ≤the parameter 100); in and the tables b is the associated parameter with in the the tables characteristic associated in with the numerator the characteristic of the percentage. in the numerator of the percentage.Illustration Illustration of the Computation of the Computation of the Standard of the Standard Error of an Error Estimated of an Estimated Percentage PercentageSuppose there Table were 1 shows an estimated that of the 13,674,000 12,510,000 hunters hunters age 16 16 years years old old and and older, 18.3 of 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 standard error standard on the estimate error on of the 18.3 esti-percenmate of 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 National Survey of Fishing, Hunting, and Wildlife-Associated Recreation U.S. Fish & Wildlife Servics xpConsequently, the 95-percent confidence interval for the estimate percentage of migratory bird hunters 16 years old and 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 of migratory bird hunters 16 years old and 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 of migratory bird hunters 16 years old and olderConsequently, the 95-percent confidence interval for the estimate percentage of migratory bird hunters 16 years old and olderStandard is from Error 16.7 of percent a Difference. to 19.9 The percent, standard ie. 18.3 error ± 1.96 of the x difference 0.83. between two sample estimates is approximately equal toStandard is from 16.7 Error percent of a Difference. to 19.9 percent, The standard ie. 18.3 ± error 1.96 of x the 0.83. difference between two sample estimates is approximately equal toStandard Error of a Difference. The standard error of the difference 2 2 between two sample estimates is approximately equal toStandard Error of a Difference. The standard s errorx y of s thexdifference s between two sample estimates is approximately (4) equal toy2 2(4)s 2 2x y where s xand where s yare sxand the sy standard are the standard errors of errors the estimates of the ssx estimates x and y sy. The x yxand 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 standard quite error accurately quite accurately for the difference for the difference between estimates between estimates of the same of the characteristic same characteristic in two in twodifferent areas, different where sxand syare the standard errors of the estimates x and y. The estimates can numbers, percentages, ratios, etc. Thisor sxfor areas, andthe sy or aredifference for the the standard difference errorsbetween separate between of theand separate estimatesuncorrelated and x and 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 standard error quite accurately for the difference between estimates of the same characteristic in twoa high positive a will high represent(negative) positive (negative) the actual standardcorrelation correlation error the between quite accuratelytwo characteristics, the two characteristics, for the differencethe formula the will formula betweenoverestimate will estimates overestimate of the same(underestimate) (underestimate) characteristicthe true the in true twodifferent areas, or for the difference between separate and uncorrelated characteristics in the same area. However, if there isstandard error. standard different error. areas, or for the difference between separate and 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 truestandard error.Illustration Illustration standard error.of the Computation of the Computation of the Standard of the Standard Error of Error a Difference of a DifferenceIllustration of the Computation of the Standard Error of a DifferenceSuppose there In Illustration Table were 8, an of ofestimated the the 11,655,000 Computation13,608,000 females of thefemales in the Standard age in the range Errorage of range 18-24, of a Differenceof 18-24 726,000 of whom or 6.2 percent 726,000 are or 5.3 sportspersons. percent were Similarly, of thesportspersons. In Table 11,638,000 Similarly, of 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 of 18-24, or 16.6726,000 percent males in or are the 6.2 sportspersons. same percent age are range sportspersons. The of apparent whom 2,160,000 difference Similarly, or between of the16.7 percent the Inwere percent Table 8,sportspersons. of of female the 11,655,000 and The male femalesapparent participants in thedifference is age 10.4 rangebetween percent. of 18-24,the Using 726,000percentage formula orof female (3) 6.2 and percentand the male appropriate are sportspersons.sportspersons b parameter Similarly,is 11.4 from table of 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) and standard the samethe appropriate errors age range, of b parameter 6.21,929,000 percent from and or 16.6table percent areD-5, the sportspersons.approximate 0.55 and 0.85, standard respectively. The apparenterrors of Using difference5.3 percent formula betweenthe percent of female and male participants is 10.4 percent. Using formula (3) and the appropriate b parameter from table (4), theand 16.7 percent approximate the percent ofare 0.79 standard female 1.35, error and malerespectively. of the participants estimated Using difference is 10.4 percent.formula (4), of 10.4 Usingthe approximate percent formula is (3) and the appropriate b parameter from tableD-7, the approximate standard errors of 6.2 percent and 16.6 percent are 0.55 andD-7, the approximate standard errors of 6.2 percent and 16.6 percent are 0.55standard 0.85, respectively.and 0.85,errorrespectively.of the Using estimated formulaUsingdifferenceapproximate of 11.4 percent standard is error of the estimated difference of 10.4 2 percent 2 is(4), theformula (4), theapproximate standard error of the estimated difference of 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 and 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 and male with sportspersons 95 percent is confidence from 8.3 8.4 to that theto 14.5, i.e., percentage The 95-percent11.4 ± of 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 of female 18-24 andwith 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 of 18- of 18-24 to 24-year-old female sportspersons is less than the percentage of 18-24 to 24-year-old male male sportspersons.Standard percentage Errors of 18-24 of Estimated year old Averages. female sportspersons Certain mean is less values than for the sportspersons, percentage of anglers, 18-24 year etc., old shown male in sportspersons.the report were calculatedErrors Errors as of the Estimated of ratio Estimated of 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: shownStandard StandardStandard Errors of Estimated Averages. Certain mean values for sportspersons, anglers, etc.,in the inshownreport the reportinwere werethe reportcalculatelatedas the ascalcu-were calculatedratio the ratioasofthetwo of tworationumbers. numbers.of 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 totalanglersanglersStandard errors for these averages may be approximated by the use of formula (5) below.Standard Standard errors errors for these for these averages averages may may be be approximated by the by use the use of formula of formula (5) below. (5) below.Standard errors for these averages may be approximated by the use of 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 and the denominator of the estimate. (5) In theIn formulaabove(5), rformula,representsusethe0.7correlationas an estimate 15.8 tocoefficientof 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 and and the denominator the denominator of the ofIn formula (5), r represents the correlation coefficient between the numerator and the denominator estimate. the estimate.of the In estimate. the In theIn theabove above formula, formula, use use 0.7 as 0.7 an as estimate an estimate of r. of r.Illustration above formula, of the use Computation 0.7 as an estimate of the of Standard r. Error of an Estimated AverageIllustration of the Computation of the Standard Error of an Estimated AverageTable Illustration 2 shows of that the the Computation average days of per the angler Standard 16 years Error old of and an older Estimated for all fishing Average was 17.3 days. Using formulas (1) andU.S. Fish Table and (2) 2 Wildlife shows above, Service that we the compute and average U.S. Census the days standard Bureau per angler error 16 on years total 2011 days, old National and 516,781,000, older Survey for of Fishing, all and fishing total Hunting, was anglers, and 17.3 Wildlife-Associated 29,952,000, days. Using to formulas Recreation be 15,828,079 (1) 125 and and399,342, Table 2 shows respectively. that the The average approximate days per standard angler 16 error years on old the and estimated older for average all fishing of 17.3 was days 17.3 isdays. Using formulas (1) and(2) above, we compute the standard error on total days, 516,781,000, and total anglers, 29,952,000, to be 15,828,079 and(2) above, we compute the standard error on total days, 516,781,000, and total anglers, 29,952,000, to be 15,828,079 and399,342, respectively. The approximate standard error on the estimated average of 17.3 days is399,342, respectively. The approximate standard error on the estimated average of 17.3 days is