Goal of the Lecture. Lecture Structure. FWF 410: Analysis of Habitat Data I: Definitions and Descriptive Statistics

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1 FWF : Aalyss f Habtat Data I: Defts ad Descrptve tatstcs Number f Cveys A A B Bur Dsk Bur/Dsk Habtat Treatmet Matthew J. Gray, Ph.D. Cllege f Agrcultural ceces ad Natural Resurces Uversty f Teessee-Kvlle Readg Assgmets: Gal f the Lecture T famlarze studets wth statstcal ccepts, defts, ad measures ecessary t aalyze wldlfe habtat data. Chap : - Blgcal, pltcal ad research (statstcal) ppulats Factrs that fluece the Pwer f a Test Type I ad II Errr Chap : 7-77 Ctuus, dchtmus, ad categrcal varables amplg errr ad types f bas Lecture tructure I. Defts & Ccepts II. tatstcal Measures

2 What s tatstcs? The subdscple f mathematcs that uses mathematcal therems, prcples, ad techques t aalyze data. Fudametal Ccept: Is statstcs ecessary fr a cesus? Cllect f all dvduals r pssble measuremets ample Ppulat µ,n σ ample vs. Cesus Feld f tatstcs ample ubset f all dvduals r pssble measuremets p N Pt Estmates Respse Varable: Epermetal Ut: Ppulat: ample: Parameter: tatstc: Prbablty: tatstcal Defts The characterstc f terest measured. e.g., ar temperature, g f seed, tree desty The atural r artfcal etty that s measured. e.g., amal, plt (area), water clum The etre cllect f epermetal uts. e.g., all amals, all ptetal plts (-m ) The subset f epermetal uts whch are actually measured. e.g., amals measured, plts measured The ukw true measure f cetral tedecy, varablty, r relat. e.g., true mea weght (all amals) µ A estmate f a ppulat parameter calculated frm data. e.g., mea weght f measured amals The chace f ccurrg. Prvdes the feretal framewrk (cfdece!) fr determg f dffereces est a respse varable betwee > ppulats % Cfdet A Dfferece Ests! (r % cfdet that 7 < N < qual) tatstcal Ntat Fr a respse varable,, we dete a sample frm the ppulat as:,,,,, where: = measuremet EU #, = measuremet EU #,, = measuremet the last EU ad, = sample sze Fr mre geeral tat, we let = EU #, thus t dete the sum f all measuremets a sample: = L+ uppse, we have the fllwg data set: = Plt % Capy = = =

3 Dchtmus: Categrcal: Ctuus: Types f Data Data that ca ly take values (.e., bary). e.g., speces ccurrece (abset =, preset =) Data that ca take > values. e.g., habtat qualty (lw =, mderate =, hgh = ) If data have terpretatve rder f magtude Ordal Prprts Nparametrc Aalyses Data that ca ay umercal value wth a subset r the etre set f U. e.g., turkey mass, tree heght abudace? Parametrc Aalyses The type f data yu cllected wll dctate the type f aalyss yu wll perfrm. ample Meda: Temp Data ample Mea: = ( ) = = Measures f Cetral Tedecy Where s the ceter f ur data? The umber where eactly % f the data le abve ad belw t. Odd : Eve : 6, 66,,, 7 6, 66,,, 7, 7 M = (+)/ = M = (take average) The umber such that the sum f devats frm each measuremet t t =. Deted as: ad estmates µ X_ X_Bar (X_-Xbar) um = D e v a t s The ample Meda s LE affected by Outlers (cmpared t the sample mea) Cmputatally: = = = 6 = Measures f Prprt What prprt f the ppulat s? The true ppulat prprt, P, s estmated by calculatg relatve frequecy. Relatve Frequecy Frequecy f X = = Ttal Number f Idvduals p ample Value f JUV UBADULT ADULT_F ADULT_M Frequecy P_Hat /7=. =p /7=. =p /7=.8 =p /7=. =p Prprt Juv ubadult Adult_F Adult_M Demgraphc Categry Bar Chart

4 Measures f Varablty Ppulat Mea Hw shuld we measure varat? Hw abut usg devats? ( ) Nw, a reasable estmate f varat mght be Average Devats frm the Mea: But, f we square ur devats (all wll be pstve), the umeratr wll t equal zer. ample Varace, : Average quared Devats If devats are small, ur measuremets are clustered (precse)! ( ) = = = Whch s t helpful. ( ) ( ) = = Based Average quared Devats frm the ample Mea Ubased s squared uts (e.g., g ) whch s t very useful = ample tadard Devat, : ample Rage, R: Measures f Varablty Ppulat Mea = MAX MIN Calculatg Varace & tadard Devat: um f quares s umeratr Ppulat tadard Devat, σ: = ( ) = [ ] X_ X_Bar Average Devats frm the ample Mea Therefre s a measure f varat measuremet uts (e.g., g, m) I measuremet uts, but ly uses data pts. (X_-Xbar) (X_-Xbar)^ um = = =. F [ 6 ] = = F = Degrees f Freedm s dematr MOT UEFUL True Natural Varat f Idvduals a Ppulat Use t estmate σ.. 76 F O average, temps vary.76 F frm the Mea Measures f Varablty Ppulat Prprt Calculatg the sample stadard devat fr relatve frequeces (.e., prprts) s much easer. pq $ $ = where, q$ = p$ Demgraphc Data: Juv ubadult Freq P_Hat..7 Q_Hat (.*.667) = Adult_F Adult_M =

5 Determg Requred ample ze Plag Epermets Z α/ =.6 (% cfdece) = 6. = stadard devat frm a prevus study d d= errr estmat Errr Estmat s the amut f errr yu are wllg t tlerate yur estmate ( data uts) f µ Hardwd Percet Capy = 76%, = 7.8% We set tlerable errr = % Overstry Hardwd Desty = 8. trees, =. trees We set tlerable errr = trees = (. 6)( 78%). % plts trees = plts (. 6 )(. ) trees