> :LAnalysis of nearest-neighbor distances for the Redwood Seedling data in B&G. NotesZd=   ####%&(+-.00003577779:<========= = = == = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = !!= ""= ##= $$= %%= &&= ''= ((= ))= **= ++= ,,= --= ..= //= 00= 11= 22= 33= 44= 55= 66= 77= 88= 99= ::= ;;= <<= ==F BC<2\ZCC??>QpS8 9a"jL!$x'U*-nn-dist  c*Distance to nearest neighbor for each tree;3Notes("Distance to nearest neighbor for each tree")  @2Q@$zG@ =p @$zG@ =p @ =p @ =p @ =p @+@$zG@ffffff@ffffff@"ffffff@"ffffff@ffffff@ffffff@ =p @ffffff@ffffff@ =p @*Q@$zG@$zG@ =p @ =p @ffffff@ffffff@"ffffff@ffffff@ffffff@ffffff@ffffff@ffffff@ =p @ =p @ =p @ =p @+@ =p @ =p @"ffffff@"ffffff@8Q@$zG@ =p @ =p @ffffff@ffffff@$zG@$zG@$zG@:Gz@"ffffff@"ffffff@"ffffff@ =p @ffffff@ =p @ffffff@;@:R@:Rlog-dist cLog of nn-distBFormula(Log( :Name("nn-dist")))Notes("Log of nn-dist")  @c @=7^?2,_@=7^?2,_?2,_?2,_?2,_@R?1n@=7^?jڬ?jڬ@{@{?jڬ?jڬ?2,_?jڬ?jڬ?2,_@O!l@=7^@=7^?2,_?2,_?jڬ?jڬ@{?jڬ?jڬ?jڬ?jڬ?jڬ?2,_?2,_?2,_?2,_@R?1n?2,_?2,_@{@{@ T1V@=7^?2,_?2,_?jڬ?jڬ@=7^@=7^@=7^@ AY;@{@{@{?2,_?jڬ?2,_?jڬ@ X@ P,8@ P,8sample cvJBFormula(IfMZ(Random Uniform() <= 0.5, :Name("nn-dist"), Empty()))  @2Q@$zG@$zG@ =p @+@$zG@ffffff@ffffff@ffffff@ffffff@ =p @*Q@ =p @ffffff@"ffffff@ffffff@ =p @+@ =p @"ffffff@"ffffff@8Q@$zG@ =p @ffffff@$zG@:Gz@"ffffff@"ffffff@ =p @ =p @ffffff@:R@:Rarea c*Area of Redwood Plot (computed in INFOMAP)MFormula(44108)3Notes("Area of Redwood Plot (computed in INFOMAP)")  @剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀@剀lam cIntensity parameter@Formula(NRow() / :area)Notes("Intensity parameter")  ?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>?W5>mu cEstimated mean under HoJFormula(1 / (2 * Sqrt( :lam))) Notes("Estimated mean under Ho")  @*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^@*%e@^sig c&Standard Deviation of nn-dist under Hor7Formula(Sqrt((4 - Pi()) / (4 * :lam * Pi() * NRow())))/Notes("Standard Deviation of nn-dist under Ho")  ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘ?TaӘs-mean cSample Mean of nn-distO$Formula(Col Mean( :Name("nn-dist")))Notes("Sample Mean of nn-dist")  @"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2@"(2Z c,Standardized Sample Mean of nn-dist under Hok*Formula(( :Name("s-mean") - :mu) / :sig)5Notes("Standardized Sample Mean of nn-dist under Ho")  llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3llI3P-value cP-value for HoD!Formula(Normal Distribution( :Z))Notes("P-value for Ho")  >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ >$ S cSkellam Statistic\Formula(2 * ( :lam * Pi() * Local({j}, Summation(j = 1, NRow(), :Name("nn-dist")[j] ^ 2))))Notes("Skellam Statistic")  @OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG>@OCG> chi-square c>bProbability of a value as small as S under the chi-square distribution with 2n degrees of freedom.3Formula(ChiSquare Distribution( :S, 2 * NRow(), 0))kNotes("Probability of a value as small as S under the chi-square distribution with 2n degrees of freedom.")  >2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2>2 .05-quantile c5_.05-quantile for chi-square (point below which there is only a .05 chance under the chi-square)0Formula(ChiSquare Quantile(0.05, 2 * NRow(), 0))hNotes(".05-quantile for chi-square (point below which there is only a .05 chance under the chi-square)")  @X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X#@X# Column 14 cZ.&Formula(Normal Distribution(-3.38507))  ?7QW