Reasons for Sampling. Forest Sampling. Scales of Measurement. Scales of Measurement. Sampling Error. Sampling - General Approach

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1 Foret amplig Aver & Burkhart, Chpt. & Reao for amplig Do NOT have the time or moe to do a complete eumeratio Remember that the etimate of the populatio parameter baed o a ample are ot accurate, therefore the iclude a certai amout of error Need to be able to quatif the amout of error cale of Meauremet Differet decriptive tatitic are permiible depedig o the cale ued to meaure to characteritic of a populatio cale of Meauremet cale Baic Operatio Example Nomial Determiatio of equalit Aigig code umber to tree pecie Ordial Iterval Determiatio of greater or le (rakig) Determiatio of the equalit of iterval (arbitrar origi) Lumber or log gradig ite cla etimatio Temperature Caledar time Ratio Determiatio of the equalit of ratio (abolute origi) Legth, volume, weight Frequec of item amplig - Geeral Approach Whe dealig with the variou approache to amplig, we will be cocered with everal parameter: combied with N > combied with N > ^ CI of both ad T > required to achieve a pecified ^ level of accurac i both ad T amplig Error Accurac f (Preciio, Bia)

2 amplig Error Accurac f (Preciio, Bia) Bia - ca cotrol bia b applig proper probabilit amplig deig Preciio - ca icreae preciio (i.e., reduce error) b icreaig ample ize imple Radom amplig R i the mot baic probabilit amplig method R form the bai of all probabilit baed amplig deig imple Radom amplig The baic idea i R: i chooig a ample of uit, ever poible combiatio of uit hould have a equal chace of beig elected thi i ot the ame a requirig that ever uit i the populatio ha a equal chace of beig elected the electio of a give uit hould be completel idepedet of the electio of all other uit imple Radom amplig electio of a R from a populatio require the developmet of a amplig Frame (i.e., a lit of all the amplig uit i a populatio) ample uit are the radoml elected from the frame 0 imple Radom amplig How doe R cotrol bia? Doe icreaed ample ize icreae preciio (reduce tad error of etimate)?

3 0 Developig a amplig frame ACRE FORET amplig uit / acre plot Mea: R - Cotiuou variable i i Variace: i i i i tadard Error of the Mea: N N Cofidece Iterval of the Mea: ± t Example Example (cotiued). Determie average ft volume per plot ad total ft volume i etire acre foret tad. Radoml elect te plot from the populatio of plot withi the tad ample i Plot # i Σ i Σ i Example (cotiued) Mea Σ i / ft /plot Variace [Σ ( i ) - (Σ i ) / ] / ( - ) [ - ( ) / ] / ( - ) (ft /plot) td.dev. ( ) ft /plot Example (cotiued) tadard Error of the Mea N N. 0 0.

4 Example (cotiued) 0% Cofidece Iterval t CI(factor) t * Lower boud 0. - Upper boud 0. + R - Cotiuou variable Determiig the required ample ize to achieve a etimate of the mea withi a give level of accurac Defie our pecified error (E) a / width of the CI, ad olve for E t t N N 0 R - Cotiuou variable ize of ample to achieve a pecified error (E) about the mea: N t N E ize of ample to achieve a allowable error (E%) about the mea: + t N t CV N E + % t CV Example (cotiued) Determie the umber of ample plot to meaure to attai a deired error of the etimatio of mea volume of ft /plot at % cofidece E t N Example (cotiued) E t N N olvig for :.0 *. +.0 *.. R - Cotiuou variable Populatio Total: T ˆ N * tadard Error of the Populatio Total : * N Cofidece Iterval of the Populatio Total : ± t * T ˆ

5 Example (cotiued) Total Volume i foret tad N * * 0.. tad Error of Total Volume ˆ N * T *.. % Cofidece Iterval for Total t * ±. ±.*. (0.,.) R - Cotiuou variable ize of ample to achieve a pecified error (E T ) about the Populatio Total: N ET + t N R - Dicrete variable Retrictio o the value for the i R - Dicrete variable Mea Populatio Proportio: implet cae, i a biomial variable e. g., i 0 if ucce if failure i i umber of uccee total umber oberved R - Dicrete variable Variace: ( ) i i ( i ) i i i R - Dicrete variable tadard error of mea: N i i N i i N [ ] N 0