CE3502 Environmental Monitoring, Measurements, and Data Analysis (EMMA) Spring 2008 Final Review

Transcription

1 CE35 Evirometal Moitorig, Meauremet, ad Data Aalyi (EMMA) Sprig 8 Fial Review I. Topic:. Decriptive tatitic: a. Mea, Stadard Deviatio, COV b. Bia (accuracy), preciio, Radom v. ytematic error c. Populatio v. ample d. Ditributio decriptio of populatio i. Normal, logormal ii. Tet for ormality: COV, mea/media/mode, kew, kurtoi, hitogram, probability plot e. Percetile, tolerace limit, outlier. Smoothig Techique for viualizatio a. Ruig average b. Weighted ruig average 3. Correlatio ad Regreio aalyi 4. Compario of umber: a. Cofidece iterval b. Detectio limit c. t-tet i. F tet for equal variace ii. Depedet v. idepedet data d. ANOVA 5. Sigificat Digit 6. Propagatio of error II. Vocabularly: Mea Media Mode Stadard Deviatio Error Ucertaity Stadard error Variace Coefficiet of variatio Radom error Sytematic error Accuracy Bia Preciio Populatio Ditributio Normal Logormal Gauia Smoothig Ruig average Epoetially-weighted ruig average Correlatio Coefficiet Itercept Slope Leat quare Percetile Cofidece Iterval Upper Tolerace Limit Outlier Idepedet Degree of Freedom Hitogram Error propagatio Null Hypothei Reidual ANOVA Factorial deig Balaced deig

2 III. Calculatio, equatio X i i = = CI = t να, j t = ( φφ ) t j j= MDL = t να, σ = ( ) i ε = ε + ε total radom ytematic S DL = mi σ SE = t mi t k j = t k + = Bl m S = Bl+ K Bl j = a + b + c ε ε ε ε a b c m f( ) = e σ π ( μ ) σ P = + zi UTL = + ki k = tνα, i + t* = y y ( ) + ( ) pool = + y y y δ di d = y = ( i i) ( d ) i d d = F = larg er maller F = b w

3 IV. Graph, graphical decriptio Error bar, bo ad whiker 5 MLSS (mg/l) 5 Cla average +/- S.D. Group mea, Cla mea, S.D. 5 Ditributio (pdf), Hitogram Frequecy lognormal Normal Meaured value 3

4 Liear Regreio 7 Iteity (i/hr) y = R = Duratio (mi.) Probability Plot Q(i) y = R = X(i) Smoothig 4

5 V. Computer output SUMMARY OUTPUT Regreio Statitic Multiple R.68 R Square.383 Adjuted R Square.346 Stadard Error.67 Obervatio 9 ANOVA df SS MS F Sigificace F Regreio Reidual Total 8.4 CoefficietStadard Error t Stat P-value Lower 95% Upper 95% Itercept X Variable Hitogram Bi Frequecy More 5

6 ANOVA Aova: Sigle Factor SUMMARY Group Cout Sum Average Variace Room A Room B Room C ANOVA Source of Variatio SS df MS F P-value F crit Betwee Group Withi Group Total 58 t-tet t-tet: Two-Sample Aumig Equal Variace Variable Variable Mea Variace Obervatio 7 7 Pooled Variace.43 Hypotheized Mea Differece df t Stat -.75 P(T<=t) oe-tail.34 t Critical oe-tail.78 P(T<=t) two-tail.468 t Critical two-tail.79 VI. Statitic Table. z table: Cumulative ormal ditributio (A..). t-table: Studet -t ditributio 3. Critical value of correlatio coefficiet 4. F-table 6

7 VII. Type of Eam Quetio True/Fale The graph below how the hitorical relatiohip betwee chlorophyll ad total phophoru i Lake Superior. The r value i o low that thi correlatio would ot be tatitically igificat uder ay circumtace. Chlorophyll (mg/m 3 ) y = R = Total P (mg/m 3 ) Short awer What i the value (approimate) of the mode i the graph below? Multiple choice Circle all that are true or correct: a. The Stadard Error i a meaure of the ucertaity of the ample mea; b. The Stadard Error i cotat for a give type of aalyi; c. The Stadard Error i the bia iheret i a aalytical method; d. The Stadard Error i defied mathematically a e. The Stadard Error i defied mathematically a You wih to predict the aual precipitatio that i likely to fall i 5 baed o the hitorical record of precipitatio that fell i Houghto. To bet awer thi quetio, you hould: a) Do a correlatio aalyi betwee year ad precipitatio amout; b) Perform a regreio aalyi o mothly precipitatio amout (i.e., date v. precipitatio amout); c) Perform a regreio aalyi o the aual precipitatio total (i.e., year v. precipitatio total); 7

8 d) Perform a multiple liear regreio aalyi where the depedet variable i precipitatio amout ad the idepedet variable are moth ad year; e) Perform a ANOVA to determie if ay of the year i the hitorical record were igificatly differet from oe aother. 8