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{"sheet":"Data","index":0,"n_rows":122,"n_cols":27,"rows_kept":122,"cut":false,"hidden":false,"merged":[[6,12,6,13],[7,12,7,13],[1,2,1,7],[2,2,2,7],[3,2,3,7],[4,2,4,7],[6,19,6,22],[6,2,6,4],[6,6,6,8],[5,2,5,6],[6,15,6,16]]}
["mean(Time)",{"$f":"SUMPRODUCT(B10:B122,C10:C122)/g","v":84.901098901098905},"Initial values of the parameters"]
["s.d. (Time)",{"$f":"SQRT((SUMPRODUCT(B10:B122^2,C10:C122)-g*B1^2)/(g-1))","v":20.097017437672392},"g: the probability of a seed germinating",null,null,null,null,null,{"$f":"IF(N=\"\",\"\",g/N)","v":0.91}]
["last time",{"$f":"MAX($B$10:$B$122)","v":168},"l: an index of the duration of germination",null,null,null,null,null,{"$f":"1/(SUMPRODUCT(N10:N122,C10:C122)/g-1/$I$4)","v":44.302310107488175}]
["# seeds germinated",{"$f":"SUM(C$10:C122)","v":91},"m: the mean time to germination after the lag",null,null,null,null,null,{"$f":"mean-$I$5","v":32.201098901098902},null,null,null,null,null,null,null,null,null,{"$f":"SUM(T9,S10:S122)","v":100}]
[null,null,"t: the lag (delay in germination)",null,null,null,null,null,{"$f":"0.9*OFFSET($B$10,MATCH(0.5,$G$10:$G$122,1),0)+0.1*OFFSET($B$10,MATCH(0.5,$G$10:$G$122,1)-1,0)","v":52.7}]
["G(tk)",{"$f":"VLOOKUP(Tmax,$B$10:$I$122,8)","v":0.90999999999999992}]
[null,null,"individual proportions",null,null,null,"cumulative proportions",null,null,null,null,null,"Initial value ",null,null,"data for plot",null,null,null,"Deviance calculations - for seeds which have germinated",null,null,null,"based on all seeds",null,{"$f":"SUM(Z10:Z122)","v":0.98057147953418222},"sum"]
[null,"Time","ni","observed","expected",null,"Ni","observed","expected",null,"Log-Likelihood",null,"calculations",null,null,"x","y",null,"E(ni)","contracting E(ni)","ni","ni Log(ni/(Nk pi) )",null,"ni Log(ni/(Nk pi) )",null,"Unconditional probabilites"]
[null,"# seeds ungerminated",{"$f":"IF(N=\"\",\"unknown\",N-g)","v":9},{"$f":"IF(g_not=\"unknown\",\"\",g_not/N)","v":0.09},{"$f":"IF(g_not=\"unknown\",\"\",1-SUM(E10:E122))","v":9.000000000000008E-2},null,null,null,null,null,{"$f":"IF($C9=\"unknown\",\"\",IF(C9=0,0,LN(E9)*C9))","v":-21.671510477866839},null,null,null,null,"incr.",{"$f":"(Tmax-lag)/100","v":1.153},null,null,{"$f":"IF(N=\"\",\"\",N*E9)","v":9.0000000000000071},{"$f":"IF(N=\"\",\"\",g_not)","v":9},{"$f":"IF(N=\"\",\"\",IF(p<1,0,U9*LN(U9/T9)))","v":0},null,{"$f":"IF($C9=\"unknown\",\"\",IF($C9=0,0,$C9*LN(C9/E9/N)))","v":-7.9936057773011302E-15}]
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[null,103,3,0.03,4.9096414592511163E-2,null,81,0.81,0.76836327426586515,null,-9.0419078082111586,null,99.5,2.1367521367521368E-2,null,6.1360424224098864,60.770999999999994,null,4.9096414592511159,{"$f":"IF(B17=\"\",\"\",IF(SUM($S$10:$S17)<1,\"\",IF(SUM($S$10:$S16)<1,SUM($S$10:$S17),IF(SUM(T$10:T16)=g,\"\",IF(S18<1,g-SUM($S$10:$S16),S17)))))","v":4.9096414592511159},{"$f":"IF(T17=\"\",\"\",IF(T16=\"\",SUM(C$10:C17),IF(T18=\"\",g-SUM(C$10:C16),C17)))","v":3},-1.4777658837487859,null,-1.4777658837487866,null,{"$f":"IF(B17=\"\",\"\",IG(Data!$B16,Data!$B17,Mu,lag,scale))","v":5.2903894392090429E-2}]
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{"sheet":"Statistical analysis","index":1,"n_rows":18,"n_cols":10,"rows_kept":18,"cut":false,"hidden":false,"merged":[[2,0,2,2],[5,0,5,2],[6,0,6,2],[3,0,3,2],[4,0,4,2],[4,5,4,9],[12,0,12,3],[11,0,11,3],[7,0,7,2],[8,0,8,2],[9,0,9,2]]}
[null,100,"The number of seeds used (if known)",null,null,null,null,{"$f":"IF(g_not<0,\"impossible number:\",\"\")","v":""}]
[null,null,null,"estimate","s.e.",null,null,{"$f":"IF(g_not<0,\"check individual counts\",\"\")","v":""}]
["mean time to germination from sowing",null,null,{"$f":"Mu+lag","v":84.901098901098905},{"$f":"s.e.!R6","v":5.6908576617709388}]
["standard deviation of time to germination",null,null,{"$f":"SQRT(Mu^3/scale)","v":27.453192339191801},{"$f":"SQRT(9/4*Mu/scale*$E$9^2+(Mu/scale)^3/4*E8^2-3/2*(Mu/scale)^2*$E$9*$E$8*H8)","v":9.8786042376807313}]
[" time to 50% germination",null,null,{"$f":"VLOOKUP(0.001,s.e.!$W$12:$Y$23,3)","v":76.534668039439623},{"$f":"s.e.!Y8","v":1.9157117565936799},"Correlations between estimates"]
[" number of viable seeds",null,null,{"$f":"IF(N=\"\",g/Data!$Z$7,N*p)","v":92.803025479824569},{"$f":"IF(N=\"\",\"\",$E$7*N)","v":4.0123267598497829},{"$f":"IF(N=\"\",\"\",\"g\")","v":"g"},"l","m","t"]
["g: the probability of a seed germinating",null,null,{"$f":"IF(N=\"\",\"\",MIN(1,g/(N*Data!$Z$7)))","v":0.92803025479824575},{"$f":"IF(N=\"\",\"\",s.e.!R$5)","v":4.0123267598497825E-2},{"$f":"IF(N=\"\",\"\",1)","v":1},{"$f":"s.e.!T5","v":-0.50549506757519103},{"$f":"s.e.!U5","v":0.58983618844301433},{"$f":"s.e.!S5","v":0.35461825062942243},{"$f":"IF(N=\"\",\"\",\"g\")","v":"g"}]
["l: an inverse measure of variance",null,null,{"$f":"Data!I3","v":44.302310107488175},{"$f":"s.e.!R3","v":13.05468597403628},null,{"$f":"s.e.!T3","v":1},{"$f":"s.e.!T4","v":-0.59155561155319614},{"$f":"s.e.!T2","v":-0.79351716545960937},"l"]
["m:  mean time from sowing - lag",null,null,{"$f":"Data!I4","v":32.201098901098902},{"$f":"s.e.!R4","v":5.4205795081570542},null,null,{"$f":"s.e.!U4","v":1},{"$f":"s.e.!U2","v":0.35697066861125071},"m"]
["t: the lag, or delay in germination",null,null,{"$f":"Data!I5","v":52.7},{"$f":"s.e.!R2","v":0.66257959805986444},null,null,null,1,"t"]
[null,null,"likelihood",{"$f":"SUM(Data!K9:K122)","v":-214.91184424117887}]
["Maximise the likelihood in cell D10 by running Tools/Solver"]
["(You will vary l, m and t in cells B7, B8 and B9)"]
[]
[null,null,null,"A guide to whether the Inverse Gaussian model fits"]
[null,"c2","d.f.","p-value"]
["Deviance (original table)",{"$f":"2*SUM(Data!X9:X122)","v":17.616029799188112},{"$f":"COUNT(Data!C10:C122)-4","v":9},{"$f":"CHIDIST(B17,C17)","v":3.9898818589414339E-2}]
["Deviance (collapsed table)",{"$f":"2*SUM(Data!$V$9:$V$122)","v":7.2506543510286301},{"$f":"COUNT(Data!$V$11:$V$122)-4","v":5},{"$f":"CHIDIST($B$18,$C$18)","v":0.20265624963217699}]

{"sheet":"s.e.","index":2,"n_rows":123,"n_cols":29,"rows_kept":123,"cut":false,"hidden":false,"merged":[[7,13,7,15]]}
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[null,null,null,null,null,null,null,null,null,null,null,null,"# viable seeds",null,null,null,null,{"$f":"SQRT(MMULT(MMULT(D8:F8,N2:P4),TRANSPOSE(D8:F8)))*g/Gtk","v":2.2674629319189954},null,null,null,null,null,"g''(t(1))",{"$f":"Y6*(-1.5/(Y12-lag)-scale/(2*Mu^2)+scale/2/(Y12-lag)^2)+Y2*(1.5/(Y12-lag)^2-scale/(Y12-lag)^3)","v":1.9635364020235214E-5},null,null,"transformed (-2f)",{"$f":"1/(1+0.2316419*2*f)","v":0.64791738178606462}]
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[null,null,null,"First derivatives of G(ti)",null,null,6,7,8,9,10,11,null,{"$f":"SUMPRODUCT($C12:$C123,N12:N123)+N11","v":-3.9413373789010508},{"$f":"SUMPRODUCT($C12:$C123,O12:O123)+O11","v":-7.5777098593799927E-2},{"$f":"SUMPRODUCT($C12:$C123,P12:P123)+P11","v":-0.30830298477089313},"should be 0"]
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