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{"sheet":"Calculation of LOD (expt data)","index":0,"n_rows":28,"n_cols":16,"rows_kept":28,"cut":false,"hidden":false,"merged":[[24,0,26,1],[27,0,30,1]]}
[null,null,"Concentration (x)","Signal (y)","x_fit","y_fit","x^2","sigma_x","sigma_y","mean_x+conf_x","Signal(Y)","mean_x-conf_x","Signal(y)","d_i^2","mean_x+sigma_x","mean_x+sigma_x"]
["t =",3,{"$f":"'[1]Calculation of LOD (simul data)'!F2","v":0},null,null,{"$f":"m*C2+b","v":10.074782634923068}]
["n=",{"$f":"COUNT(D2:D1048576)","v":10},1,10.967044169999999,{"$f":"(D3-b)/m","v":0.8745933390771452},{"$f":"m*C3+b","v":11.094984247730261},{"$f":"C3^2","v":1},{"$f":"sigma_y/ABS(m)*SQRT(1/k+E3^2*n/D+SUM($G$2:$G$107)/D-2*E3*SUM($C$2:$C$107)/D)","v":10.792014256117071},{"$f":"sigma_y","v":9.9085327754196726},{"$f":"E3+t*H3","v":33.250636107428356},{"$f":"D3","v":10.967044169999999},{"$f":"E3-t*H3","v":-31.501449429274068},{"$f":"D3","v":10.967044169999999},{"$f":"(D3-m*C3-b)^2","v":1.6368663489625471E-2},{"$f":"E3+H3","v":11.666607595194217},{"$f":"E3-H3","v":-9.9174209170399248}]
["k=",1,4,13.726656200000001,{"$f":"(D4-b)/m","v":3.5795606664729882},{"$f":"m*C4+b","v":14.155589086151839},{"$f":"C4^2","v":16},{"$f":"sigma_y/ABS(m)*SQRT(1/k+E4^2*n/D+SUM($G$2:$G$107)/D-2*E4*SUM($C$2:$C$107)/D)","v":10.710108097699317},9.9085327754196726,{"$f":"E4+t*H4","v":35.709884959570935},{"$f":"D4","v":13.726656200000001},{"$f":"E4-t*H4","v":-28.55076362662496},{"$f":"D4","v":13.726656200000001},{"$f":"(D4-m*C4-b)^2","v":0.18398342082254543},{"$f":"E4+H4","v":14.289668764172305},{"$f":"E4-H4","v":-7.1305474312263293}]
["intercept= ",{"$f":"INTERCEPT(D2:D107,C2:C107)","v":10.074782634923068},9,21.677432580000001,11.372899042132477,19.256597150187805,81,10.505550841261895,9.9085327754196726,42.889551565918168,21.677432580000001,-20.14375348165321,21.677432580000001,5.8604441782340038,21.878449883394374,0.86734820087058218]
["slope =",{"$f":"SLOPE(D2:D107,C2:C107)","v":1.0202016128071929},16,28.05018029,17.619456222594788,26.398008439838154,256,10.376667197405805,9.9085327754196726,48.749457814812203,28.05018029,-13.510545369622626,28.05018029,2.7296718224672167,27.996123420000593,7.2427890251889835]
["Sigma_slope =",{"$f":"SQRT(B10^2*n/D)","v":9.6649066125483629E-2},25,36.03149269,25.442725956543327,35.579822955102891,625,10.261207461362387,9.9085327754196726,56.226348340630487,36.03149269,-5.3408964275438322,36.03149269,0.20400554942202495,35.703933417905716,15.18151849518094]
["R^2 =",{"$f":"RSQ(D2:D107,C2:C107)","v":0.93301149381029902},36,51.96673578,41.06242591580186,46.802040695982015,1296,10.189267739581004,9.9085327754196726,71.630229134544862,51.96673578,10.494622697058851,51.96673578,26.674075310879545,51.251693655382866,30.873158176220855]
["D =",{"$f":"SUM(G2:G107)*B3-SUM(C2:C107)^2","v":105105},49,55.153226310000001,44.185818870682645,60.064661662475523,2401,10.200607318176198,9.9085327754196726,74.787640825211241,55.153226310000001,13.583996916154049,55.153226310000001,24.122197221546351,54.386426188858842,33.985211552506449]
["sigma_y =",{"$f":"SQRT(SUM(N2:N107)/(n-2))","v":9.9085327754196726},64,74.657328759999999,63.303709104488874,75.367685854583414,4096,10.453886457576054,9.9085327754196726,94.665368477217044,74.657328759999999,31.942049731760711,74.657328759999999,0.50460720182499086,73.757595562064921,52.84982264691282]
["from eq(11) using s[y]: LOD[2] =",{"$f":"2/D/((n/D-ABS(m)^2/t^2/sigma_y^2))*(SUM(C2:C107)-SQRT(SUM(C2:C107)^2-D^2*(n/D-ABS(m)^2/t^2/sigma_y^2)*(SUM(G2:G107)/D+1/k)))","v":61.281303128338671},81,71.995613700000007,60.694700231550513,92.711113272305695,6561,10.401118323884345,9.9085327754196726,91.89805520320354,71.995613700000007,29.491345259897479,71.995613700000007,429.13192253019719,71.09581855543486,50.293581907666166]
["from eq(15) Currie and Svehla: LOD[3] =",{"$f":"2*t*sigma_y/(n*t^2*sigma_y^2-D*m^2)*(t*sigma_y*SUM(C2:C107)-SQRT(D*m^2*SUM(G2:G73)+m^2*D^2))","v":63.85632290520369},100,129.29973680000001,116.86411065065545,112.09494391564236,10000,12.604591043022761,9.9085327754196726,154.67788377972374,129.29973680000001,79.050337521587167,129.29973680000001,296.00489819364344,129.46870169367821,104.25951960763268]
["assuming error free calibration: Xc = LOD[1] =",{"$f":"t*(sigma_y)/m","v":29.136984252030224}]
[]
[null,{"$f":"t*SQRT(sigma_y^2+B5^2)+b","v":52.467263125248465}]
[0,{"$f":"b+m*B11/2","v":41.334424778151863}]
[{"$f":"B11","v":61.281303128338671},{"$f":"B16","v":41.334424778151863}]
[{"$f":"A17","v":61.281303128338671},0]
[]
[]
[]
["sigma_intercept",{"$f":"B7*(SQRT(SUM(G2:G107)/n))","v":4.8645309799971237}]
["t x s_0",{"$f":"SQRT(B22^2+sigma_y^2)*t","v":33.114711998630739}]
[]
["Please change only values in red. All other values are calculated. "]
[]
[]
["Please cite \"Detection limits of chemical sensors: applications and misapplications\", Hans-Peter Loock* and Peter D Wentzell, Sens. Act. B: Chem, (2012)"]

{"sheet":"Calculation of LOD (simul data)","index":1,"n_rows":21,"n_cols":16,"rows_kept":21,"cut":false,"hidden":false,"merged":[[0,3,0,4],[1,3,1,4],[20,0,24,2]]}
["t =",3,null,"Random Numbers",null,"x","y","x_fit","y_fit","x^2","sigma_x","d_i^2","mean_x+sigma_x","mean_x+sigma_x","mean_x+conf_x","mean_x-conf_x"]
["n=",{"$f":"COUNT(F3:F101)","v":10},null,null,null,0,null,null,{"$f":"m*F2+b","v":0.33171983660520254}]
["k=",1,null,{"$f":"SQRT(-2*LN(RAND()))* COS(2*PI()*RAND())","v":-1.9693227102562563},{"$f":"SQRT(-2*LN(RAND()))* SIN(2*PI()*RAND())","v":1.8091162933417513},1,{"$f":"F3*(1+$B$18*PI()*D3)+$B$19*(E3)","v":0.78111532671265782},{"$f":"(G3-b)/m","v":0.46481100768650963},{"$f":"m*F3+b","v":1.2985547064251288},{"$f":"F3^2","v":1},{"$f":"sigma_y/ABS(m)*SQRT(1/k+F3^2*n/D+SUM($J$3:$J$101)/D-2*F3*SUM($F$3:$F$101)/D)","v":4.851113171067051},{"$f":"(G3-m*F3-b)^2","v":0.26774351167722676},{"$f":"H3+K3","v":5.3159241787535603},{"$f":"H3-K3","v":-4.3863021633805417},{"$f":"H3+t*K3","v":15.018150520887662},{"$f":"H3-t*K3","v":-14.088528505514642}]
["intercept=",{"$f":"INTERCEPT(G3:G101,F3:F101)","v":0.33171983660520254},null,0.70975058130602053,0.25762607832507661,{"$f":"2^$B$17","v":4},{"$f":"F4*(1+$B$18*PI()*D4)+$B$19*(E4)","v":4.4588307463386698},4.2686823143875072,4.1990593158849077,16,4.8105418890042211,6.7481196079993797E-2,9.0792242033917283,-0.54185957461671386,18.700307981400172,-10.162943352625156]
["Sigma_intercept=",{"$f":"Sigma_slope*(SQRT(SUM(J3:J101)/n))","v":2.0730218098798727},null,0.24922745323741546,-0.52123443236576672,{"$f":"3^$B$17","v":9},9.3262752896553121,9.3030937689756179,9.0332336649845395,81,4.7497993285989706,8.5873393789685934E-2,14.052893097574589,4.5532944403766473,23.552491754772529,-4.946304216821293]
["slope=",{"$f":"SLOPE(G3:G101,F3:F101)","v":0.96683486981992628},null,0.82386982960354305,1.1826188577977794,{"$f":"4^$B$17","v":16},18.129741666247302,18.408543573689055,15.801077753724023,256,4.679746265826517,5.4226756174882249,23.088289839515571,13.728797307862539,32.447782371168607,4.3693047762095034]
["Sigma_slope=",{"$f":"SQRT(B10^2*n/D)","v":4.1187037929557607E-2},null,-0.6027013247334353,7.5317955465457664E-2,{"$f":"5^$B$17","v":25},22.636963330159027,23.070375500325298,24.50259158210336,625,4.6164972125588193,3.4805687744528675,27.686872712884117,18.453878287766479,36.919867138001756,9.2208838626488401]
["R^2=",{"$f":"RSQ(G3:G101,F3:F101)","v":0.98568976574163147},null,0.46809674273146334,0.90267912666412886,{"$f":"6^$B$17","v":36},38.692158674975268,39.676308784265018,35.13777515012255,1296,4.5817737538441987,12.633642241744427,44.258082538109214,35.094535030420822,53.421630045797613,25.930987522732423]
["D =",{"$f":"SUM(J3:J101)*B2-SUM(F3:F101)^2","v":105105},null,-3.2521516207810993E-3,1.5998938228015802,{"$f":"7^$B$17","v":49},49.054963198821575,50.394586379875925,47.706628457781591,2401,4.6023238263604078,1.8180065738953619,54.996910206236336,45.792262553515513,64.201557858957145,36.587614900794705]
["sigma_y=",{"$f":"SQRT(SUM(L3:L101)/(n-2))","v":4.222525179059847},null,-1.177461728446304,-0.60773937925584143,{"$f":"8^$B$17","v":64},52.132476659933047,53.5776671283854,62.209151505080484,4096,4.7075841930096702,101.53937593482712,58.285251321395073,48.870082935375727,67.700419707414412,39.454914549356388]
["estimated x[LOD] from eq (11) =",{"$f":"2/D/((n/D-ABS(m)^2/t^2/sigma_y^2))*(SUM(F3:F101)-SQRT(SUM(F3:F101)^2-D^2*(n/D-ABS(m)^2/t^2/sigma_y^2)*(SUM(J3:J101)/D+1/k)))","v":28.182450664939271},null,-0.14379390616249119,0.49869459336315231,{"$f":"9^$B$17","v":81},79.195380118782353,81.568903588330002,{"$f":"m*F11+b","v":78.645344292019232},{"$f":"F11^2","v":6561},4.9253627788602072,0.30253941072299045,86.494266367190207,76.643540809469798,96.34499192491063,66.792815251749374]
["estimated x(LOD) from Currie&Svehla=",{"$f":"'Eqns from Currie and Svehla'!B15","v":28.398043687482396},null,6.9920230129539351E-2,0.84827657074301865,{"$f":"10^$B$17","v":100},101.14071823509849,{"$f":"(G12-b)/m","v":104.26702795407972},{"$f":"m*F12+b","v":97.015206818597832},{"$f":"F12^2","v":10000},{"$f":"sigma_y/ABS(m)*SQRT(1/k+F12^2*n/D+SUM($J$3:$J$101)/D-2*F12*SUM($F$3:$F$101)/D)","v":5.2768496337772692},{"$f":"(G12-m*F12-b)^2","v":17.019844447677261},{"$f":"H12+K12","v":109.543877587857},{"$f":"H12-K12","v":98.990178320302448},120.09757685541153,88.436479052747913]
["estimated x(LOD) from eq (15) =",{"$f":"2*t*sigma_y/(n*t^2*sigma_y^2-D*m^2)*(t*sigma_y*SUM(F3:F101)-SQRT(D*m^2*SUM(J3:J67)+m^2*D^2))","v":28.398043687482399}]
[0,{"$f":"b+m*B11/2","v":13.95560784652673}]
[{"$f":"B11","v":28.182450664939271},{"$f":"B14","v":13.95560784652673}]
[{"$f":"A15","v":28.182450664939271},0]
["Concentration range power(1-5) =",2]
["Average slope variance (0-1) =",0.05]
["Average intercept variance (0-1) =",0.05]
[]
["The LOD is caluclated using equation (11) in the manuscript. --- Please change only values in red/bold face. All other values are calculated. To generate new random numbers, select an empty cell and press <delete>."]

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["t =",3,null,"Random Numbers",null,"x","y","x_fit","y_fit","(y-yfit)^2","x^2","s_x","mean_x+sigma_x","mean_x+sigma_x","mean_x+conf_x","mean_x-conf_x"]
["m =",{"$f":"COUNT(F3:F101)","v":10},null,null,null,{"$f":"'Calculation of LOD (simul data)'!F2","v":0},null,null,{"$f":"b*F2+a","v":0.33171983660520254}]
["n =",1,null,{"$f":"'Calculation of LOD (simul data)'!D3","v":-1.9693227102562563},{"$f":"'Calculation of LOD (simul data)'!E3","v":1.8091162933417513},{"$f":"'Calculation of LOD (simul data)'!F3","v":1},{"$f":"'Calculation of LOD (simul data)'!G3","v":0.78111532671265782},{"$f":"(G3-a)/b","v":0.46481100768650963},{"$f":"b*F3+a","v":1.2985547064251288},{"$f":"(G3-I3)^2","v":0.26774351167722676},{"$f":"F3^2","v":1},{"$f":"s_y/ABS(b)*SQRT(1/n+1/m+m*(I3-SUM($I$3:$I$102)/m)^2/((m*SUM($K$3:$K$102)-SUM($F$3:$F$102)^2)*b^2))","v":4.851113171067051},{"$f":"H3+L3","v":5.3159241787535603},{"$f":"H3-L3","v":-4.3863021633805417},{"$f":"H3+t*L3","v":15.018150520887662},{"$f":"H3-t*L3","v":-14.088528505514642}]
["intercept, a=",{"$f":"INTERCEPT(G3:G101,F3:F101)","v":0.33171983660520254},null,{"$f":"'Calculation of LOD (simul data)'!D4","v":0.70975058130602053},{"$f":"'Calculation of LOD (simul data)'!E4","v":0.25762607832507661},{"$f":"'Calculation of LOD (simul data)'!F4","v":4},{"$f":"'Calculation of LOD (simul data)'!G4","v":4.4588307463386698},{"$f":"(G4-a)/b","v":4.2686823143875072},4.1990593158849077,{"$f":"(G4-I4)^2","v":6.7481196079993797E-2},16,4.8105418890042211,9.0792242033917283,-0.54185957461671386,{"$f":"H4+t*L4","v":18.700307981400172},-10.162943352625156]
["s_a=",{"$f":"s_b*(SQRT(SUM(K3:K101)/m))","v":2.0730218098798727},null,{"$f":"'Calculation of LOD (simul data)'!D5","v":0.24922745323741546},{"$f":"'Calculation of LOD (simul data)'!E5","v":-0.52123443236576672},{"$f":"'Calculation of LOD (simul data)'!F5","v":9},{"$f":"'Calculation of LOD (simul data)'!G5","v":9.3262752896553121},9.3030937689756179,9.0332336649845395,8.5873393789685934E-2,81,4.7497993285989715,14.052893097574589,4.5532944403766464,23.552491754772532,-4.9463042168212965]
["slope,b=",{"$f":"SLOPE(G3:G101,F3:F101)","v":0.96683486981992628},null,{"$f":"'Calculation of LOD (simul data)'!D6","v":0.82386982960354305},{"$f":"'Calculation of LOD (simul data)'!E6","v":1.1826188577977794},{"$f":"'Calculation of LOD (simul data)'!F6","v":16},{"$f":"'Calculation of LOD (simul data)'!G6","v":18.129741666247302},18.408543573689055,15.801077753724023,5.4226756174882249,256,4.679746265826517,23.088289839515571,13.728797307862539,{"$f":"H6+t*L6","v":32.447782371168607},4.3693047762095034]
["s_b=",{"$f":"SQRT(m*s_y^2/(m*SUM(K3:K101)-SUM(F3:F101)^2))","v":4.1187037929557607E-2},null,{"$f":"'Calculation of LOD (simul data)'!D7","v":-0.6027013247334353},{"$f":"'Calculation of LOD (simul data)'!E7","v":7.5317955465457664E-2},{"$f":"'Calculation of LOD (simul data)'!F7","v":25},{"$f":"'Calculation of LOD (simul data)'!G7","v":22.636963330159027},23.070375500325298,24.50259158210336,3.4805687744528675,625,4.6164972125588193,27.686872712884117,18.453878287766479,36.919867138001756,9.2208838626488401]
["s_y=",{"$f":"SQRT(SUM(J3:J101)/(m-2))","v":4.222525179059847},null,{"$f":"'Calculation of LOD (simul data)'!D8","v":0.46809674273146334},{"$f":"'Calculation of LOD (simul data)'!E8","v":0.90267912666412886},{"$f":"'Calculation of LOD (simul data)'!F8","v":36},{"$f":"'Calculation of LOD (simul data)'!G8","v":38.692158674975268},39.676308784265018,35.13777515012255,12.633642241744427,1296,4.5817737538441987,44.258082538109214,35.094535030420822,53.421630045797613,25.930987522732423]
["r(a,b)=",{"$f":"-AVERAGE(F3:F101)/SQRT(SUM(K3:K101)/m)","v":-0.76492246860627866},null,{"$f":"'Calculation of LOD (simul data)'!D9","v":-3.2521516207810993E-3},{"$f":"'Calculation of LOD (simul data)'!E9","v":1.5998938228015802},{"$f":"'Calculation of LOD (simul data)'!F9","v":49},{"$f":"'Calculation of LOD (simul data)'!G9","v":49.054963198821575},50.394586379875925,47.706628457781591,1.8180065738953619,2401,4.6023238263604078,54.996910206236336,45.792262553515513,64.201557858957145,36.587614900794705]
["R^2=",{"$f":"r_a_b^2","v":0.58510638297872342},null,{"$f":"'Calculation of LOD (simul data)'!D10","v":-1.177461728446304},{"$f":"'Calculation of LOD (simul data)'!E10","v":-0.60773937925584143},{"$f":"'Calculation of LOD (simul data)'!F10","v":64},{"$f":"'Calculation of LOD (simul data)'!G10","v":52.132476659933047},53.5776671283854,62.209151505080484,101.53937593482712,4096,4.7075841930096702,58.285251321395073,48.870082935375727,67.700419707414412,39.454914549356388]
["s_0=",{"$f":"SQRT(s_a^2+s_y^2)","v":4.7039492250695067},null,{"$f":"'Calculation of LOD (simul data)'!D11","v":-0.14379390616249119},{"$f":"'Calculation of LOD (simul data)'!E11","v":0.49869459336315231},{"$f":"'Calculation of LOD (simul data)'!F11","v":81},{"$f":"'Calculation of LOD (simul data)'!G11","v":79.195380118782353},81.568903588330002,78.645344292019232,0.30253941072299045,6561,4.9253627788602072,86.494266367190207,76.643540809469798,96.34499192491063,66.792815251749374]
["K =",{"$f":"1+r_a_b*(s_a/s_0)*t*(s_b/b)","v":0.95691876217825911},null,{"$f":"'Calculation of LOD (simul data)'!D12","v":6.9920230129539351E-2},{"$f":"'Calculation of LOD (simul data)'!E12","v":0.84827657074301865},{"$f":"'Calculation of LOD (simul data)'!F12","v":100},{"$f":"'Calculation of LOD (simul data)'!G12","v":101.14071823509849},{"$f":"(G12-a)/b","v":104.26702795407972},{"$f":"b*F12+a","v":97.015206818597832},{"$f":"(G12-I12)^2","v":17.019844447677261},{"$f":"F12^2","v":10000},{"$f":"s_y/ABS(b)*SQRT(1/n+1/m+m*(I12-SUM($I$3:$I$102)/m)^2/((m*SUM($K$3:$K$102)-SUM($F$3:$F$102)^2)*b^2))","v":5.2768496337772701},{"$f":"H12+L12","v":109.543877587857},{"$f":"H12-L12","v":98.990178320302448},{"$f":"H12+t*L12","v":120.09757685541153},{"$f":"H12-t*L12","v":88.436479052747913}]
["I =",{"$f":"1-t^2*(s_b/b)^2","v":0.98366726114017011}]
["RSQ = ",{"$f":"RSQ(G3:G101,F3:F101)","v":0.98568976574163147}]
["estimated x(LOD) from Currie&Svehla=",{"$f":"2*t*s_0/b*(K/I)","v":28.398043687482396}]
["estimated LOD from eq (11) =",{"$f":"'Calculation of LOD (simul data)'!B11","v":28.182450664939271}]
[0,{"$f":"t*s_0+a","v":14.443567511813722}]
[{"$f":"B15","v":28.398043687482396},{"$f":"B17","v":14.443567511813722}]
[{"$f":"A18","v":28.398043687482396},0]
[]
["The LOD is calculated using equation (4.19) from Currie and Svehla, Pure& Appl. Chem, 66,3(1996) 595 --- Please change only values in red/bold face. All other values are calculated. To generate new random numbers, select an empty cell and press <delete>."]