{"text_format":"2","workbook":"xls","n_sheets":18,"sheets":["Instructions","Kragten summary","IPD0","Data0","IPD1","Data1","IPD2","Data2","IPD3","Data3","IPD4","Data4","IPD5","Data5","IPD6","Data6","IPD7","Data7"],"not_rendered":{"charts":8,"images":24,"macros":1,"external_links":1,"defined_names":152,"comments":11,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"run_cost":"one","rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900","formulas":"cached_only"}

{"sheet":"Instructions","index":0,"n_rows":28,"n_cols":4,"rows_kept":28,"cut":false,"hidden":false,"merged":[],"flags":["formulas_cached_only"]}
["Data presented in this file are based on the measurement of an urine sample spiked with 77Se"]
["Five replicate measurements were performed on each spiked sample"]
["As can be seen from the data, the levels of bromine were quite high in the urine sample (and the same for serum)"]
[]
[null,"Parameter","Value","Standard deviation"]
[null,"76Se",408.478,1.4816106101104218]
[null,"77Se",7480.058,43.6369759493402]
[null,"78Se",1419.0120000000002,8.114201747527517]
[null,"79Br",125761.71199999998,857.5662561716224]
[null,"80Se",7576.77,56.73072712390324]
[null,"81Br",131179.368,882.1692808761026]
[null,"82Se",5907.056,36.6116529264616]
[]
["The sheet IPD0 calculates the molar fraction of natural selenium and enriched selenium using multiple least squares"]
["The sheet Data0 performs the corrections for mass bias and isobaric interferences (SeH and BrH) on the measured intensities"]
["The scroll bars in sheet IPD0 can be moved to change the value of the mass bias, fSe and fBr used for correction (macros should be allowed)"]
[]
["Suggestion: set the values to 0 with the scroll bars and then use the Solver application to minimise the regression variance"]
["Solver tip: Set the convergence criterium to 0.0001 or lower for best results"]
[]
["For the multiple linear regression we have used matrix equations so it can be better understood. Similar results could have been obtained using the excel function \"LINEST\""]
[]
["Uncertainty calculations were based on Kragten's method. "]
["Each sheet IPD1, IPD2..., contains the same information as IPD0 except that the standard deviation has been added to one of the measured intensities."]
["For example in sheets Data1 and IPD1 the molar fractions are calculated after adding the standard deviation to the average intensity at mass 76"]
[]
["Sheet \"kragten summary\" collects all molar fractions from sheets IPD1, IPD2..., and calculated the total combined uncertainty for the whole procedure"]
["Finally, the concentrations are calculated in sheet \"Kragten summary\" taking into account other sources of uncertainty such as sample and spike  weights and atomic weights"]

{"sheet":"Kragten summary","index":1,"n_rows":39,"n_cols":9,"rows_kept":39,"cut":false,"hidden":false,"merged":[],"flags":["formulas_cached_only"]}
["Summary of Kragten procedure for uncertainty propagation"]
[]
[null,"Parameter","76Se","77Se","78Se","79Br","80Se","81Br","82Se"]
[null,"Mean value",408.478,7480.058,1419.0120000000002,125761.71199999998,7576.77,131179.368,5907.056]
[null,"Standard deviation",1.4816106101104218,43.6369759493402,8.114201747527517,857.5662561716224,56.73072712390324,882.1692808761026,36.6116529264616]
["Parameter / Sheet","IPD0","IPD1","IPD2","IPD3","IPD4","IPD5","IPD6","IPD7"]
["76Se",408.478,409.9596106101104,408.478,408.478,408.478,408.478,408.478,408.478]
["77Se",7480.058,7480.058,7523.69497594934,7480.058,7480.058,7480.058,7480.058,7480.058]
["78Se",1419.0120000000002,1419.0120000000002,1419.0120000000002,1427.1262017475276,1419.0120000000002,1419.0120000000002,1419.0120000000002,1419.0120000000002]
["79Br",125761.71199999998,125761.71199999998,125761.71199999998,125761.71199999998,126619.2782561716,125761.71199999998,125761.71199999998,125761.71199999998]
["80Se",7576.77,7576.77,7576.77,7576.77,7576.77,7633.500727123904,7576.77,7576.77]
["81Br",131179.368,131179.368,131179.368,131179.368,131179.368,131179.368,132061.5372808761,131179.368]
["82Se",5907.056,5907.056,5907.056,5907.056,5907.056,5907.056,5907.056,5943.667652926461]
[]
["Molar fraction enriched",0.6853621430930292,0.6846507031781627,0.6869591043055,0.6853468212415774,0.6867918544828228,0.6831450484545344,0.6839888873522548,0.6867583272711559]
["Molar fraction natural",0.31767054319787214,0.3183879340467136,0.31605975118542684,0.31768596213496847,0.3162285642400756,0.3199069666002367,0.3190557078859319,0.3162634581320777]
[]
["Deviation enriched",null,-0.0007114399148665518,0.001596961212470771,-1.532185145181053e-05,0.001429711389793531,-0.002217094638494843,-0.001373255740774404,0.0013961841781267026]
["Deviation natural",null,0.0007173908488414815,-0.0016107920124452946,1.541893709633424e-05,-0.0014419789577965192,0.0022364234023645735,0.0013851646880597701,-0.0014070850657944556]
[]
["Sum of squares enriched",1.3851411508702475e-05,5.061467524653264e-07,2.550285114136115e-06,2.347591319113485e-10,2.04407465810535e-06,4.915508636042579e-06,1.885831329569857e-06,1.949330259251336e-06]
["Sum of squares natural",1.4089000825781623e-05,5.146496300015014e-07,2.594650907357562e-06,2.3774362118071217e-10,2.0793033147279356e-06,5.001589634643935e-06,1.9186812130477204e-06,1.9798883823817873e-06]
[]
[]
["Uncertainty enriched",0.003721748447800103]
["Uncertainty natural",0.0037535317803079307]
[]
[]
["Concentration of Selenium in the sample and propagated uncertainty"]
[]
[]
[null,"Value","Uncertainty",null,"Spike values",null,"Value",null,"Uncertainty"]
["nanomols 77Se added",0.246266392027799,0.0007202532497555076,null,"Mass 77Se",null,0.5429945041244003,"g",0.0001]
["total Se nanomols",0.3593230155905642,0.00221625115628417,null,"Concentration",null,34.9918941438586,"ng/g",0.10213639789389106]
["nanomols Se sample",0.114146337546152,0.0015214278408632912,null,"Atomic weight",null,77.1538741139847,"ng/nmol",0.001]
[]
["Se sample concentration ",29.6828565602152,"ng/g ",null,"Sample values",null,"Value",null,"Uncertainty"]
["Se sample uncertainty",0.3957560130636156,"ng/g ",null,"Mass sample",null,0.30395882581764866,"g",0.0001]
[{"$nulls":4},"Atomic weight",null,79.0421,"ng/nmol",0.001]

{"sheet":"IPD0","index":2,"n_rows":36,"n_cols":13,"rows_kept":36,"cut":false,"hidden":false,"merged":[[41,0,41,1]],"flags":["formulas_cached_only"]}
["Isotope Pattern Deconvolution for Selenium determinatin in SRM-2670 Freeze Dried Urine"]
["Internal correction of the mass bias and spectral interferences factors."]
[]
["DATA","ISOTOPIC COMPOSITION"]
["Isotope","Se 77","Se nat","Blend","Calculated","residuals","To be adjusted using the Solver application",{"$nulls":5},"COMMENT"]
["76Se",1.03,9.37,3.6825112107943183,3.682495997149882,1.5213644436240514e-05]
["77Se",91.1,7.63,64.8603178417773,64.86031748037472,3.6140258430350514e-07,"Mass bias factor (x -10000)",null,374.7781600083251]
["78Se",3.9,23.77,10.223924624081393,10.223941169876234,-1.6545794840894246e-05,"fBr (x 10000)",null,417.2165951212458]
["80Se",3.4,49.61,18.089868731939468,18.089866934562735,1.7973767327816859e-06,"fSe (x 10000)",null,263.2956311902298]
["82Se",0.54,8.73,3.143377591407516,3.1433593993876596,1.8192019856311248e-05]
[{"$nulls":6},"Regression variance",null,2.7984302178307456e-10]
["Sum",99.97000000000001,99.11,99.99999999999999]
[{"$nulls":6},"Degrees of freedom",null,3]
[]
["Matrix X"]
[1.03,9.37,null,"Matrix X'"]
[91.1,7.63,null,1.03,91.1,3.9,3.4,0.54]
[3.9,23.77,null,9.37,7.63,23.77,49.61,8.73]
[3.4,49.61]
[0.54,8.73]
[{"$nulls":4},"Matrix X' * X",null,null,"Matrix X' * y"]
[{"$nulls":4},8327.332499999999,970.8353,null,6015.644225554901]
[{"$nulls":4},970.8353,3248.3916999999997,null,1697.292117656823]
["Molar fractions (results)"]
[null,"Value","Uncertainty",null,"Matrix (X' * X)-1",null,null,"Variance-Covariance matrix"]
["Se 77",0.6853621430930292,1.865972885100894e-07,null,0.0001244217127783439,-3.718547576995636e-05,null,3.481854807931754e-14,-1.0406095905905888e-14]
["Se nat",0.31767054319787214,2.987611245445304e-07,null,-3.718547576995636e-05,0.0003189581393539358,null,-1.0406095905905888e-14,8.925820953911239e-14]
[]
["Uncertainty calculations"]
["X","Yexp","Ycal","Residuals","Residuals^2"]
[76,3.6825112107943183,3.682495997149882,1.5213644436240514e-05,2.3145497703235195e-10]
[77,64.8603178417773,64.86031748037472,3.6140258430350514e-07,1.3061182794125214e-13]
[78,10.223924624081393,10.223941169876234,-1.6545794840894246e-05,2.7376332691696265e-10]
[80,18.089868731939468,18.089866934562735,1.7973767327816859e-06,3.2305631195449677e-12]
[82,3.143377591407516,3.1433593993876596,1.8192019856311248e-05,3.309495864524227e-10]
[null,null,"sum of squares of residuals",null,8.395290653492236e-10]

{"sheet":"Data0","index":3,"n_rows":36,"n_cols":4,"rows_kept":36,"cut":false,"hidden":false,"merged":[],"flags":["formulas_cached_only"]}
["Signals"]
[]
["Mass","I experimental","I SeH and BrH corrected"]
["76Se",408.478,408.478]
["77Se",7480.058,7469.302952716268]
["78Se",1419.0120000000002,1222.3485164513525]
["79Br",125761.71199999998,125729.52809758263]
["80Se",7576.77,2331.1254380925575]
["81Br",131179.368,131117.99048563937]
["82Se",5907.056,436.595845044164]
[]
["fBr",0.04172165951212458]
[]
["fSe",0.026329563119022983]
[]
["Isotope ratios corrected for spectral interferences"]
[]
["Se Isotope Ratio","Experimental","Mass difference","Corrected"]
["76/80",0.17522780770400626,4,0.20356760269312943]
["77/80",3.2041617455077933,3,3.585449889266468]
["78/80",0.5243598205729927,2,0.565174063758132]
["82/80",0.18728972620255407,-2,0.17376453295415956]
["Sum",5.091039099987347,null,5.527956088671889]
[]
[]
["Mass bias factor",-0.037477816000832505]
[]
["Isotope abundances corrected for mass bias"]
[]
["Isotope","Abundance"]
["76Se",3.6825112107943183]
["77Se",64.8603178417773]
["78Se",10.223924624081393]
["80Se",18.089868731939468]
["82Se",3.143377591407516]
["Sum",99.99999999999999]

{"sheet":"IPD1","index":4,"n_rows":38,"n_cols":9,"rows_kept":38,"cut":false,"hidden":false,"merged":[[40,0,40,1]],"flags":["formulas_cached_only"]}
["Isotope Pattern Deconvolution for Selenium determinatin in SRM-2670 Freeze Dried Urine"]
["Internal correction of the mass bias and spectral interferences factors."]
[]
["DATA","ISOTOPIC COMPOSITION"]
["Isotope","Se 77","Se nat","Blend","Calculated","residuals","To be adjusted using the Solver application"]
["76Se",1.03,9.37,3.6885213698763195,3.6884851662912137,3.6203585105809566e-05]
["77Se",91.1,7.63,64.80097947850058,64.80097899630704,4.821935419840884e-07,"Mass bias factor (x -10000)",null,364.09260699167066]
["78Se",3.9,23.77,10.238194271261786,10.238218934685216,-2.466342342977157e-05,"fBr (x 10000)",null,417.2997774282363]
["80Se",3.4,49.61,18.123037550453198,18.123037798863216,-2.484100178890003e-07,"fSe (x 10000)",null,261.25132180918484]
["82Se",0.54,8.73,3.1492673299081217,3.1492380439440177,2.9285964104008855e-05]
[{"$nulls":6},"Regression variance",null,9.256486471466718e-10]
["Sum",99.97000000000001,99.11,100.00000000000003]
[{"$nulls":6},"Degrees of freedom",null,3]
[]
["Matrix X"]
[1.03,9.37,null,"Matrix X'"]
[91.1,7.63,null,1.03,91.1,3.9,3.4,0.54]
[3.9,23.77,null,9.37,7.63,23.77,49.61,8.73]
[3.4,49.61]
[0.54,8.73]
[{"$nulls":4},"Matrix X' * X",null,null,"Matrix X' * y"]
[{"$nulls":4},8327.332499999999,970.8353,null,6010.416297189988]
[{"$nulls":4},970.8353,3248.3916999999997,null,1698.9317931526741]
["Molar fractions (results)"]
[null,"Value","Uncertainty",null,"Matrix (X' * X)-1",null,null,"Variance-Covariance matrix"]
["Se 77",0.6846507031781627,3.3936822200811e-07,null,0.0001244217127783439,-3.718547576995636e-05,null,1.151707901089458e-13,-3.442068533996545e-14]
["Se nat",0.3183879340467136,5.433628347516881e-07,null,-3.718547576995636e-05,0.0003189581393539358,null,-3.442068533996545e-14,2.952431701893903e-13]
[]
["Uncertainty calculations"]
["X","Yexp","Ycal","Residuals","Residuals^2"]
[76,3.6885213698763195,3.6884851662912137,3.6203585105809566e-05,1.3106995745135962e-09]
[77,64.80097947850058,64.80097899630704,4.821935419840884e-07,2.325106119311608e-13]
[78,10.238194271261786,10.238218934685216,-2.466342342977157e-05,6.082844552762052e-10]
[80,18.123037550453198,18.123037798863216,-2.484100178890003e-07,6.170753698761345e-14]
[82,3.1492673299081217,3.1492380439440177,2.9285964104008855e-05,8.576676935012952e-10]
[]
[]
[null,null,"sum of squares of residuals",null,2.7769459414400153e-09]

{"sheet":"Data1","index":5,"n_rows":36,"n_cols":4,"rows_kept":36,"cut":false,"hidden":false,"merged":[],"flags":["formulas_cached_only"]}
["Signals"]
[]
["Mass","I experimental","I SeH and BrH corrected"]
["76Se",409.9596106101104,409.9596106101104]
["77Se",7480.058,7469.347750983973]
["78Se",1419.0120000000002,1223.8743027002977]
["79Br",125761.71199999998,125729.73812206912]
["80Se",7576.77,2330.070826555013]
["81Br",131179.368,131118.49459166534]
["82Se",5907.056,435.48413901726417]
[]
["fBr",0.04172997774282363]
[]
["fSe",0.026125132180918484]
[]
["Isotope ratios corrected for spectral interferences"]
[]
["Se Isotope Ratio","Experimental","Mass difference","Corrected"]
["76/80",0.17594298247844753,4,0.20352666376195208]
["77/80",3.2056312047936033,3,3.5756135966776785]
["78/80",0.5252519746405236,2,0.5649270572198182]
["82/80",0.18689738271223422,-2,0.17377149504550737]
["Sum",5.093723544624809,null,5.517838812704956]
[]
[]
["Mass bias factor",-0.03640926069916706]
[]
["Isotope abundances corrected for mass bias"]
[]
["Isotope","Abundance"]
["76Se",3.6885213698763195]
["77Se",64.80097947850058]
["78Se",10.238194271261786]
["80Se",18.123037550453198]
["82Se",3.1492673299081217]
["Sum",100.00000000000003]

{"sheet":"IPD2","index":6,"n_rows":38,"n_cols":9,"rows_kept":38,"cut":false,"hidden":false,"merged":[[40,0,40,1]],"flags":["formulas_cached_only"]}
["Isotope Pattern Deconvolution for Selenium determinatin in SRM-2670 Freeze Dried Urine"]
["Internal correction of the mass bias and spectral interferences factors."]
[]
["DATA","ISOTOPIC COMPOSITION"]
["Isotope","Se 77","Se nat","Blend","Calculated","residuals","To be adjusted using the Solver application"]
["76Se",1.03,9.37,3.6690513269395018,3.6690477460421143,3.58089738750067e-06]
["77Se",91.1,7.63,64.99351045544083,64.99351030377585,1.516649774657708e-07,"Mass bias factor (x -10000)",null,376.0499516102607]
["78Se",3.9,23.77,10.191874647999189,10.191880792469046,-6.144469857360946e-06,"fBr (x 10000)",null,417.2072904623599]
["80Se",3.4,49.61,18.015383916751535,18.015385210947727,-1.2941961919921141e-06,"fSe (x 10000)",null,260.4986792730461]
["82Se",0.54,8.73,3.130179652868928,3.1301595441737464,2.0108695181431102e-05]
[{"$nulls":6},"Regression variance",null,1.5221163462543112e-10]
["Sum",99.97000000000001,99.11,99.99999999999997]
[{"$nulls":6},"Degrees of freedom",null,3]
[]
["Matrix X"]
[1.03,9.37,null,"Matrix X'"]
[91.1,7.63,null,1.03,91.1,3.9,3.4,0.54]
[3.9,23.77,null,9.37,7.63,23.77,49.61,8.73]
[3.4,49.61]
[0.54,8.73]
[{"$nulls":4},"Matrix X' * X",null,null,"Matrix X' * y"]
[{"$nulls":4},8327.332499999999,970.8353,null,6027.378838814107]
[{"$nulls":4},970.8353,3248.3916999999997,null,1693.6100205709668]
["Molar fractions (results)"]
[null,"Value","Uncertainty",null,"Matrix (X' * X)-1",null,null,"Variance-Covariance matrix"]
["Se 77",0.6869591043055,1.3761697673211548e-07,null,0.0001244217127783439,-3.718547576995636e-05,null,1.8938432284887616e-14,-5.6600620512694195e-15]
["Se nat",0.31605975118542684,2.2033869330680123e-07,null,-3.718547576995636e-05,0.0003189581393539358,null,-5.6600620512694195e-15,4.854913976814862e-14]
[]
["Uncertainty calculations"]
["X","Yexp","Ycal","Residuals","Residuals^2"]
[76,3.6690513269395018,3.6690477460421143,3.58089738750067e-06,1.2822826099809124e-11]
[77,64.99351045544083,64.99351030377585,1.516649774657708e-07,2.300226538969276e-14]
[78,10.191874647999189,10.191880792469046,-6.144469857360946e-06,3.775450982801724e-11]
[80,18.015383916751535,18.015385210947727,-1.2941961919921141e-06,1.6749437833668892e-12]
[82,3.130179652868928,3.1301595441737464,2.0108695181431102e-05,4.0435962189971044e-10]
[]
[]
[null,null,"sum of squares of residuals",null,4.5663490387629337e-10]

{"sheet":"Data2","index":7,"n_rows":36,"n_cols":4,"rows_kept":36,"cut":false,"hidden":false,"merged":[],"flags":["formulas_cached_only"]}
["Signals"]
[]
["Mass","I experimental","I SeH and BrH corrected"]
["76Se",408.478,408.478]
["77Se",7523.69497594934,7513.05417799813]
["78Se",1419.0120000000002,1223.2979309324649]
["79Br",125761.71199999998,125729.84525046345]
["80Se",7576.77,2331.2291932802345]
["81Br",131179.368,131118.63978740675]
["82Se",5907.056,436.69075651858566]
[]
["fBr",0.041720729046235985]
[]
["fSe",0.02604986792730461]
[]
["Isotope ratios corrected for spectral interferences"]
[]
["Se Isotope Ratio","Experimental","Mass difference","Corrected"]
["76/80",0.1752200089023582,4,0.20366212254449087]
["77/80",3.2227865881460733,3,3.6076672446045883]
["78/80",0.5247437422534943,2,0.5657317487706889]
["82/80",0.1873221036255664,-2,0.1737503717563489]
["Sum",5.110072442927493,null,5.550811487676118]
[]
[]
["Mass bias factor",-0.03760499516102607]
[]
["Isotope abundances corrected for mass bias"]
[]
["Isotope","Abundance"]
["76Se",3.6690513269395018]
["77Se",64.99351045544083]
["78Se",10.191874647999189]
["80Se",18.015383916751535]
["82Se",3.130179652868928]
["Sum",99.99999999999997]

{"sheet":"IPD3","index":8,"n_rows":38,"n_cols":9,"rows_kept":38,"cut":false,"hidden":false,"merged":[[42,0,42,1]],"flags":["formulas_cached_only"]}
["Isotope Pattern Deconvolution for Selenium determinatin in SRM-2670 Freeze Dried Urine"]
["Internal correction of the mass bias and spectral interferences factors."]
[]
["DATA","ISOTOPIC COMPOSITION"]
["Isotope","Se 77","Se nat","Blend","Calculated","residuals","To be adjusted using the Solver application"]
["76Se",1.03,9.37,3.682625860414798,3.682624691083479,1.1693313188843035e-06]
["77Se",91.1,7.63,64.85903907718993,64.8590393061975,-2.290075684641124e-07,"Mass bias factor (x -10000)",null,374.69019625054807]
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[78,10.195892509971284,10.195939876156995,-4.736618571143936e-05,2.243555548850562e-09]
[80,18.02484871027298,18.024808470654303,4.0239618677162525e-05,1.6192269112834471e-09]
[82,3.1318064963138403,3.1318294862194627,-2.2989905622328166e-05,5.285357605235563e-10]
[]
[]
[null,null,"sum of squares of residuals",null,9.675939622835966e-09]

{"sheet":"Data7","index":17,"n_rows":36,"n_cols":4,"rows_kept":36,"cut":false,"hidden":false,"merged":[],"flags":["formulas_cached_only"]}
["Signals"]
[]
["Mass","I experimental","I SeH and BrH corrected"]
["76Se",408.478,408.478]
["77Se",7480.058,7468.654978673779]
["78Se",1419.0120000000002,1210.5179513608855]
["79Br",125761.71199999998,125727.91933059027]
["80Se",7576.77,2283.184983845833]
["81Br",131179.368,131115.63089038208]
["82Se",5943.667652926461,423.24114177162664]
[]
["fBr",0.042103496537114884]
[]
["fSe",0.02791587631701488]
[]
["Isotope ratios corrected for spectral interferences"]
[]
["Se Isotope Ratio","Experimental","Mass difference","Corrected"]
["76/80",0.1789070981502135,4,0.20364537081751896]
["77/80",3.2711563151985428,3,3.604844419408424]
["78/80",0.5301882939514914,2,0.5656575915758058]
["82/80",0.18537312778691833,-2,0.1737493915568299]
["Sum",5.165624835087166,null,5.547896773358578]
[]
[]
["Mass bias factor",-0.032378359100483575]
[]
["Isotope abundances corrected for mass bias"]
[]
["Isotope","Abundance"]
["76Se",3.6706769995332196]
["77Se",64.97677528390868]
["78Se",10.195892509971284]
["80Se",18.02484871027298]
["82Se",3.1318064963138403]
["Sum",100]