*LAnalysis of nearest-neighbor distances for the Redwood Seedling data in B&G. Notes5d)))))) ) ) ) ) )) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) !!) "") ##) $$) %%) &&) '') (() )) )F -"IC(CC44C9CQX8 N ] WxuQ!X  c&  @A@HY@Oٙ@S`@T@!fffffg@733333@D@L@Rl@@5333333@@@@F@P@@V@@ٙ@G@N@T@Ws33333@.@A@L@R @U@X@@1@@ٙ@G@J@@Rl@U@733333@Oٙ@S`@V@1@A@G@O@Y  c&  @X`@V33333@W@X`@U@TS33333@U@@T33333@S33333@S33333@Offffg@P33333@Q33333@Q33333@Offffg@Rs33333@Jffffg@L@J@@Nffffg@N@I@D@E@@Hfffffg@G@Hfffffg@9@A@9@9@A@?L@B&ffffg@5L@2@.@6@!@fffffg@$@nn-dist  c*Distance to nearest neighbor for each tree;3Notes("Distance to nearest neighbor for each tree")  @-(\)@&G{@, =p @&\(\@&\(\@.fffff@.fffff@&G{@-(\)@,zG{@.kQ@(Q@(Q@)@(Q@,Q@*zG@*zG@%ffffff@+Q@(p =q@.kQ@+Q@ Q@*zG@&ffffff@(p =q@..zG@.zG@%QR@' =p@ Q@*Q@&ffffff@%QR@+33333@,Q@,Q@+fffff@)@)@+33333log-dist cLog of nn-distBFormula(Log( :Name("nn-dist")))Notes("Log of nn-dist")  @oZq@%$;E@)@P!\@P!\@柌@柌@%$;E@oZq@?쥱@ƏYq@*@*@48.@*@I@NĬ>@NĬ>@BY9@4љK@KaX@ƏYq@4љK@Ŗ]E@NĬ>@Sʚ^@KaX@V_X@v@@"ֲX@Ŗ]E@;7ɇ@Sʚ^@@hu…@I@I@vGJ@eCM@eCM@hu…area c*Area of Redwood Plot (computed in INFOMAP)MFormula(10481)3Notes("Area of Redwood Plot (computed in INFOMAP)")  @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@xlam cIntensity parameter@Formula(NRow() / :area)Notes("Intensity parameter")  ?piN&?piN&?piN&?piN&?piN&?piN&?piN&?piN&?piN&?piN&?piN&?piN&?piN&?piN&?piN&?piN&?piN&?piN&?piN&?piN&?piN&?piN&?piN&?piN&?piN&?piN&?piN&?piN&?piN&?piN&?piN&?piN&?piN&?piN&?piN&?piN&?piN&?piN&?piN&?piN&?piN&?piN&mu cEstimated mean under HoJFormula(1 / (2 * Sqrt( :lam))) Notes("Estimated mean under Ho")  @a@a@a@a@a@a@a@a@a@a@a@a@a@a@a@a@a@a@a@a@a@a@a@a@a@a@a@a@a@a@a@a@a@a@a@a@a@a@a@a@a@asig c&Standard Deviation of nn-dist under Hov;Formula(Sqrt((4 - Pi()) / (((4 * :lam) * Pi()) * NRow())))/Notes("Standard Deviation of nn-dist under Ho")  ?b9,?b9,?b9,?b9,?b9,?b9,?b9,?b9,?b9,?b9,?b9,?b9,?b9,?b9,?b9,?b9,?b9,?b9,?b9,?b9,?b9,?b9,?b9,?b9,?b9,?b9,?b9,?b9,?b9,?b9,?b9,?b9,?b9,?b9,?b9,?b9,?b9,?b9,?b9,?b9,?b9,?b9,s-mean cSample Mean of nn-distO$Formula(Col Mean( :Name("nn-dist")))Notes("Sample Mean of nn-dist")  @)7@)7@)7@)7@)7@)7@)7@)7@)7@)7@)7@)7@)7@)7@)7@)7@)7@)7@)7@)7@)7@)7@)7@)7@)7@)7@)7@)7@)7@)7@)7@)7@)7@)7@)7@)7@)7@)7@)7@)7@)7@)7Z c,Standardized Sample Mean of nn-dist under Hok*Formula(( :Name("s-mean") - :mu) / :sig)5Notes("Standardized Sample Mean of nn-dist under Ho")  @b L"@b L"@b L"@b L"@b L"@b L"@b L"@b L"@b L"@b L"@b L"@b L"@b L"@b L"@b L"@b L"@b L"@b L"@b L"@b L"@b L"@b L"@b L"@b L"@b L"@b L"@b L"@b L"@b L"@b L"@b L"@b L"@b L"@b L"@b L"@b L"@b L"@b L"@b L"@b L"@b L"@b L"P-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")  @fc{k@fc{k@fc{k@fc{k@fc{k@fc{k@fc{k@fc{k@fc{k@fc{k@fc{k@fc{k@fc{k@fc{k@fc{k@fc{k@fc{k@fc{k@fc{k@fc{k@fc{k@fc{k@fc{k@fc{k@fc{k@fc{k@fc{k@fc{k@fc{k@fc{k@fc{k@fc{k@fc{k@fc{k@fc{k@fc{k@fc{k@fc{k@fc{k@fc{k@fc{k@fc{k 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.")  ?????????????????????????????????????????? .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)")  @O)UI@O)UI@O)UI@O)UI@O)UI@O)UI@O)UI@O)UI@O)UI@O)UI@O)UI@O)UI@O)UI@O)UI@O)UI@O)UI@O)UI@O)UI@O)UI@O)UI@O)UI@O)UI@O)UI@O)UI@O)UI@O)UI@O)UI@O)UI@O)UI@O)UI@O)UI@O)UI@O)UI@O)UI@O)UI@O)UI@O)UI@O)UI@O)UI@O)UI@O)UI@O)UI