TRNG I HC TY NGUYNKHOA NNG LM NGHIP
PGS.TS. BO HUY
TIN HC THNG K TRONG QUN L TI NGUYN THIN NHIN X l thng k bng phn mm Statgraphics Centurion XV v MS. Excel 2007
Thng 5 nm 2009
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Mc lc1. TNG QUT V CHC NNG X L THNG K CA MS.EXCEL 2007 V STATGRAPHICS CENTURION XV ............................................................................ 71.1. 1.2. Tng qut v phn x l thng k trong MS. Excel ................................................. 7 Tng qut v phn mm x l thng k Statgraphics Centurion ............................. 8
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THNG K M T ........................................................................................... 10
3. SP XP V V BIU PHN B TN S XUT HIN THEO CP, C, HNG ....................................................................................................................... 12 4. SO SNH 1 2 MU QUAN ST BNG TIU CHUN T ............................... 144.1. 4.2. So snh mt mu vi mt gi tr cho trc Kim tra T mt mu ........................ 14 So snh s sai khc gia trung bnh 2 mu Kim tra T 2 mu ........................... 16
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PHN TCH PHNG SAI ............................................................................... 195.1. 5.2. Phn tch phng sai 1 nhn t vi cc th nghim ngu nhin hon ton ........... 19 Phn tch phng sai 2 nhn t ............................................................................. 22
5.1.1. Phn tch phng sai 2 nhn t vi 1 ln lp li: (B tr th nghim theo khi ngu nhin y (Randomized Complete Blocks) (RCB): ..................................................................22 5.1.2. Phn tch phng sai 2 nhn t m ln lp ...................................................................28
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PHN TCH TNG QUAN - HI QUY ........................................................... 326.1. 6.2. 6.3. 6.4. 6.5. Hi quy tuyn tnh 1 lp ......................................................................................... 32 Dng phi tuyn a v tuyn tnh 1 lp ................................................................. 34Lp m hnh hm m trong Excel: ...............................................................................34 Lp m hnh hm m mt lp trong Statgraphics:.......................................................36
6.2.1. 6.2.2.
c lng cc dng hi quy mt lp tuyn tnh hoc phi tuyn tnh trn th ... 40 Hi quy tuyn tnh nhiu lp .................................................................................. 45 Hi quy phi tuyn tnh nhiu lp, t hp bin......................................................... 47
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M HNH HO QUY LUT PHN B .............................................................. 577.1. 7.2. 7.3. M hnh ho phn b gim theo hm Meyer .......................................................... 57 M phng phn b thc nghim theo phn b khong cch-hnh hc: ................. 60 M phng phn b thc nghim theo phn b Weibull: ......................................... 62
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LI NI UTrong qun l ti nguyn thin nhin, ng dng cng ngh tin hc ng vai tr quan trng trong phn tch, qun l c s d liu; trong ng dng tin hc trong x l thng k c p dng ngy cng rng ri. Thng qua x l thng k trn cc phn mm, gip chng ta h thng ha c s d liu, nh gi cc th nghim, phn tch cc mi quan h phc tp trong t nhin v vi cc nhn t x hi tm ra quy lut nhm qun l bn vng. X l thng k thng qua cng ngh tin hc ngy nay pht trin mt bc di, n gip cho con ngi rt ngn c thi gian tnh ton, x l c mt lng ln thng tin v c c nhng hiu bit mt cch khch quan cc quy lut t nhin v x hi. Do thnh tu ca cng ngh x l thng k tin hc cn c ng dng mt cch rng ri hn trong quan l ti nguyn thin nhin. C rt nhiu phn mm ng dng x l thng k nh SPSS, Statgraphics, Excel.... Microsoft Excel c mi ngi bit n khi ni n cng c bng tnh, tnh tan..., nhng nhng chc nng chuyn su v ng dng thng k trong sinh hc, qun l ti nguyn thin nhin, mi trng li t c cp n. Trong khi chc nng x l thng k ca phn mm Excel l ht sc phong ph v mnh ng dng trong cc th nghim, phn tch, nh gi cc kt qu nghin cu, iu tra kho st v lm nghip, qun l ti nguyn thin nhin. Trong bao gm cc x l thng k ph bin nh: Phn tch cc c trng mu, so snh cc mu th nghim, phn tch phng sai, tng quan hi quy, d bo.. do phn mm Excel c chn la gii thiu. Cc phn mm thng k chuyn dng v ph bin trn th gii l Statgrahics, SPSS, . y l cc phn mm thng k c ng dng rng trong hu ht cc lnh vc nghin cu, phn tch d liu ca nhiu ngnh khc nhau v x hi, t nhin. ng dng mnh ca cc phn mm ny l phn tch cc m hnh hi quy a bin dng tuyn tnh hay phi tuyn tnh vi cc cch phn tch a dng nh hi quy lc, hi quy tng bc, t hp bin, m ha t ng cc bin nh tnh, .. Do phn mm Statgraphics Centurion XV cng c gii thiu ngi c c th tip cn vi cng c phn tch thng k ny. Ti liu ny s khng i su vo l thuyt xc sut thng k, m thin v hng ng dng n gin, d hiu, km theo cc v d ngi c c th thc hnh cc chc nng x l, phn tch d liu bng Excel, Statgraphics Centurion XV mt cch nhanh chng, thun tin trong hot ng qun l v nghin cu lm nghip, qun l ti nguyn thin nhin, mi trng.
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1. TNG QUT V CHC NNG X L THNG K CA MS.EXCEL 2007 V STATGRAPHICS CENTURION XV1.1. Tng qut v phn x l thng k trong MS. Excel Excel thit k sn mt s chng trnh x l s liu v phn tch thng k c bn ng dng trong nhiu lnh vc: - Chc nng x l s liu, to bng tng hp d liu: Sp xp, tnh ton nhanh cc bng tng hp t s liu th,... - Chc nng ca cc hm: Cung cp hng lot cc hm v k thut, thng k, kinh t ti chnh, hm tra cc ch tiu thng k nh t, F, 2 - Chc nng Data Analysis: Dng phn tch thng k nh phn tch cc c trng mu, tiu chuNn t so snh s sai khc, phn tch phng sai, c lng cc tng quan hi quy - Phn tch m hnh tong quan hoc hi quy d bo cc thay i theo thi gian ngay trn th. Lu : V vic ci t chng trinh phn tch d liu (Data Analysis) trong Excel: - Khi ci t phn mm Excel phi thc hin trong ch chn la ci t, sau phi chn mc: Add-Ins v Analysis Toolpak. - Khi chy Excel ln u cn m ch phn tch d liu bng cch: Menu Tools/Add-Ins v chn Analysis Toolpak-OK. (i vi MS. Office 2003)
i vi MS. Office 2007, tin hnh m ch phn tch thng k nh sau: Kch vo Microsoft Office Button sau chn excel options, kch vo Add-ins, v chn Analysis ToolPak trong hp thoi - OK.
Nh vy trong thc t qun l d liu nng lm nghip ni ring, vic khai thc ht tim nng ng dng ca Excel cng mang li hiu qu tt m khng nht thit phi tm kim thm mt phn mm chuyn dng no khc. Vn t ra l xc nh chin lc ng dng v khai thc ng v su cc cng c chc nng sn c mt phn mm ph bin bt k mt vi tnh c nhn no.
8 Mt s hm thng dng trong thng k: o Tnh tng: =Sum(dy s). o Tng bnh phng: =Sumq(dy s). o Trung bnh: =Average(dy s). o Ly gi tr tuyt i: =Abs(s). o Tr ln nht, nh nht: =Max(dy s), Min(dy s). o Cc hm lng gic: =Cos(s), =Sin(s), =tan(s). o Hm m, log: =Exp(s), =Ln(s), =Log(s). o Cn bc 2: =Sqrt(s).. o Sai tiu chuN mu cha hiu nh: =Stdevp(dy s); hiu nh =Stdev(dy n s). o Phng sai mu cha hiu nh: =Varp(dy s); hiu nh =Var(dy s). o Giai tha: =Fact(n). o S Pi: =Pi(). Tra cc gi tr T, F, 2: Chn 1 ly gi tr tra. Kch nt fx trn thanh cng c chuN Trong hp thoi Function Category, chn n. Statistical. Trong mc Function name, chn 1 trong cc hm: Hm Tinv: tra T. Hm Chiinv: tra 2. Hm Finv: tra F. Bm Next. Trong hp thoi tip theo: Function Wizard chn: o Probability (fx): G vo mc ngha =0.05 ; 0.01 hay 0.001. o Degrees Freedom (fx): G vo bc t do. i vi tiu chuN F cn ua vo 2 n t do. o Finish. 1.2. Tng qut v phn mm x l thng k Statgraphics Centurion y l mt phn mm chuyn dng trong x l thng k, bao gm cc chc nng: - To lp c s d liu di dng bng tnh - Tnh ton cc c trng mu, v s , th quan h - So snh hai hay nhiu mu bng cc tiu chuN thng k t, U, F v nhiu tiu chuN phi n n tham s khc. - Phn tch phng sai ANOVA. - Kim tra tnh chuN ca d liu v i bin s. n - Thit lp cc m hnh hi quy tuyn tnh hay phi tuyn tnh t mt cho n nhiu lp, t hp bin. Vi cch x l a dng chn la c cc bin nh hng n mt hu qa (bin ph thuc).
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Giao tip trong Statgraphics Centurion, s liu u vo c th c nhp trc tip trong file bng tnh v c s d liu; song vi cc lm ny i khi khng thun tin trong cc bc x l s liu th nh i bin s, tnh cc bin trung gian, m ha bin s. Do thng thng nn to lp c s d liu trong bng tnh Excel c th s dng nhng chc nng bng tnh mnh ca n trong x l d liu th, to lp c s d liu; sau s nhp vo Statgraphics Centurion tnh ton, thit lp m hnh, .... C s d liu lp trong Excel cn lu di dng phin bn ca Excel 97 2003, v n cha nhn c file Excel version 2007. Sau khi nhp d liu trong Excel 97-2003, ng file ca Excel v m n trong Statgrahics Centurion nh sau: File/Open/Open Data Source; chn External Data File OK. Trong hp thoi m file, chn kiu file Excel v chn file cn m to trc .
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2. THNG K M T c hiu bit r rng v mt i tng quan st nh sinh trng cy rng ca mt l rng, s a dng loi ca ca l rng, bin ng mt ti sinh, t l sng ca trng rng, ..... cn p dng thng k m t, bao gm tin hnh thu thp d liu ca mu v t tnh ton c trng ca mu c lng cc ch tiu thng k c bn ca tng th . y l cc thng tin c bn v mt i tng quan st, theo mt ch tiu, nhn t quan tm. Cc c trng mu c m t bao gm tnh cc ch tiu c bn: S trung bnh, phng sai, sai tiu chuN lch, nhn ca dy s liu quan st c v phm vi bin ng theo mt n, tin cy cho trc. V d: Kho st cc c trng c bn v sinh trng ca rng trng tch. S liu o D1,3 rng trng Tch 14 tui trong tiu chuN 500m2. n Cc c trng mu c th tnh ng thi trong Excel theo cc bc: Nhp s liu theo ct hoc hng. Menu Tools/Data Analyisis/Descriptive Statistics/OK (Hoc Data/Data Analysis trong MS. Ofice 2007). C hp thoi, trong cn xc nh: o Input range: Khai bo khi d liu. o Grouped by: Chn d liu nhp theo ct (Columns) hoc hng (Rows). o Label in first row: Nu a vo c hng tiu th nh du. o Output range: nh vo a ch trn tri ni a ra kt qu. o Summary Statistics: Thng tin tm lc cc c trng thng k (nh du). o Confidence Level for Mean: Chn tnh cy: 90% hoc 95% hoc 99% ty theo yu cu nh gi, phn tch ng lng. o Kch nt OK Bng nhp d liu ng knh D1.3 ca Tch
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Kt qu tnh c trng muD1,3 (cm)
Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count Confidence Level (95,0%)
18,98 0,442 19,1 19,42 3,16 9,986 0,852 -0,227 17,19 9,868 27,06 968 51 0,889
12 Gii thch kt qu: o Mean (Xbq): S trung bnh. o Standard Error: Sai s ca s trung bnh mu. o Median: Trung v mu. o Mode: Tr s ng vi tn s phn b tp trung nht. o Standard deviation (S): Sai tiu chuN mu. n o Sample variance: Phng sai mu. o Kurtosis (Ku): nhn ca phn b. o Skewness (Sk): lch ca phn b. o Minimum: Tr s quan st b nht. o Maximum: Tr s quan st ln nht. o Sum: Tng cc tr s quan st. o Count: Dung lng mu. o Cofidence level (95%): Sai s tuyt i ca c lng vi tin cy 95%. Vi kt qu phn tch c trng mu, rt ra c cc ch s thng k quan trng sau: - Gi tr trung bnh v cc bin ng nh sai tiu chuN phng sai, max, min n, - Mu quan st chuN hay cha thng qua Ku v Sk. Mu tim cn chuN th mi bo n n m s liu quan st v cc gi tr c lng l tin cy theo tin cy cho trc; nu khng th gi tr ny s sai lch trong thc t. Vi mt mu quan st t phn b chuN khi n Ku v Sk xp x bng 0. o Kurtosis: nhn ca phn b Ku = 0 phn b thc nghim tim cn chuN n. Ku > 0 ng cong c dng bt hn so vi phn b chuN n. Ku < 0 ng cong c nh nhn hn so vi phn b chuN n. V d Ku = Kurt(A2:A52) = 0.852. nh ng cong thp hn so vi phn b chuN n. o Skewness: lch ca phn b. Sk = 0 phn b i xng. Sk > 0 nh ng cong lch tri so vi s trung bnh. Sk < 0 nh ng cong lch phi so vi s trung bnh. V d trn Sk = Skew(A2:A52) = -0.227. ng cong hi lch phi. o Minimum: Tr s quan st b nht. Nu mu phn b cha chuN th cn b sung mu theo cng thc mu cn thit nct: n ?????????????????? ?????? . ??????% /% Trong V% l h s bin ng: ??????% = 100 v % l sai s tng i cho trc.
- c lng phm vi bin ng ca gi tr trung bnh, trong v d trn vi tin cy 95% th ng knh trung bnh ca khu rng tch 14 tui bin ng trong phm vi: 18.98 0.89 cm Hay P(Xbq - Cofidence level (95%) Xbq + Cofidence level (95%) = 0.95
3. SP XP V V BIU PHN B TN S XUT HIN THEO CP, C, HNGy l chc nng sp xp bng phn b tn s theo mt nhn t theo tng cp, hng, ... v v th phn b. Trong nghin cu x hi, ngi ta cn nghin cu tn s phn b s ngi theo cp tui bit s phn b con ngi theo cc th h c chin lc qun l ngun nhn lc.
13 Trong qun l ti nguyn thin nhin, thng cn nghin cu s phn b s lng c th loi theo cp tui, cp kch thc bit c quy lut bin i c th theo th h, theo kch thc, cht lng, ... l c s qun l, bo tn v nh hng khai thc s dng bn vng. Trong lm nghip thng cn sp xp phn b s cy theo c knh (N/D), s cy theo c chiu cao (N/H), s cy theo cp th tch (N/V), s cy theo loi cy theo cc tng rng, th h t chc qun l iu ch rng. V d cng t s liu quan st rng trng Tch 10 tui, tin hnh sp xp phn b thc nghim N/H v v biu (cp H l 2m): Np s liu chiu cao vo bng tnh theo ct. Lp mt ct gii hn trn c knh. Vd: c 2m. Bng tm tt d liu u vo
Menu Tools/Data Analysis/Histogram/OK (Data/Data Analysis trong MS Office 20907). Xut hin hp thoi, xc nh: + Input range: Khai bo khi d liu + Bin range: Khai bo khi cha c ly t. + Output range: Khai a ch trn tri ni a ra kt qu. + Cumulative percentage: Tnh phn trm tn s tch ly.(nh du). + Chart output: V biu . (nh du chn). + OK.
14 Kt qa sp xp phn b tn s
Kt qu sp xp tn s cho c mt dy d liu theo cp v biu phn b. N phn nh c th hn c trng mu v cho thy hnh nh ca kiu dng phn b theo cp, th h; t gip cho vic phn tch qun th v a ra quyt nh qun l, s dng bn vng. V d trong biu trn, s cy phn ha kh mnh theo cp chiu cao, mt s cy sinh trng km cp chiu cao nh 8 12m, mt s cy vt tn c cp H trn 22m; gii php ngh y l ta tha loi b bt cy sinh trng km c H < 12m v c th ta tha mt s cy ln vi H>22m li dng trung gian, lc ny c th s c kch thc tp trung trong phm vi 14 22m v c khng gian dinh dng pht trin.
4. SO SNH 1 2 MU QUAN ST BNG TIU CHUN TKim tra mu bng tiu chuN t da vo gi thit phn phi chuN ca mu quan st. C hai n n loi kim tra t: kim tra t mt mu (one-sample t-test), v t cho hai mu (two-sample t-test). Kim tra t mt mu nh gi s trung bnh ca mt mu c phi tht s bng mt ga tr no hay khng?. Kim tra t hai mu th so snh hai mu c cng mt lut phn phi, hay c th hn l hai mu c tht s c cng tr s trung bnh hay khng? Hay ni khc i c s sai khc gia hai mu quan st hay khng? 4.1. So snh mt mu vi mt gi tr cho trc Kim tra T mt mu Trong m t quan st mt mu, ngi ta c th c yu cu nh gi gi tr trung bnh ca mu vi mt gi tr cho trc, v d t o m chiu cao ca cy ti sinh trong rng khp, so snh vi mt gi tr cho trc v chiu cao mong i cy rng vt qua c la rng, xem tht s chiu cao ti sinh ca l rng t yu cu hay cha?
15 gii quyt vn ny, s dng kim nh t mt mu. Theo l thuyt thng k cng thc t kim tra mt mu vi mt gi tr cho trc: ?????????????????? ?????? = ?????? ?????? Trong , Xbq l gi tr trung bnh ca mu, l trung bnh theo gi thuyt, S l sai tiu chuN v n l s lng mu quan st. n - Nu gi tr tuyt |t| tnh cao hn gi tr t l thuyt mc sai c ngha, thng l 5% th c th kt lun c s khc bit c ngha thng k gia trung bnh mu vi gi tr cho trc . V trong trng hp ny nu t tnh 0 th trung bnh ca mu ln hn c ngha so vi trung bnh l thuyt - Nu |t| tnh t(0.05, df) th c th kt lun mc sai 5% trung bnh mu quan st xp x vi trung bnh l thuyt. Trong t l thuyt c tnh theo hm =tinv(0.05, df), vi t do df = n-1. S liu o cao cy ti sinh rng khp trong ExcelChiu cao cy ti sinh (m) 1 2 3 4 5 6 7 8 9 10 11 58 59 60 61 1.5 1.3 0.8 1.9 1.7 2.2 2.5 1.0 0.7 1.9 1.8 1.6 2.0 1.9 1.7
Stt
tnh c gi tr t, cn tnh ton c trng mu c cc gi tr thng k v Xbq, S.
16 Kt qu tnh c trng mu ti sinh rng khpChiu cao cy ti sinh (m) Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count Confidence Level(95.0%) 1.64 0.06318 1.7 1.9 0.49347 0.24351 -0.4499 -0.4627 1.8 0.7 2.5 100.3 61 0.12638
T tnh gi tr thng k t: So snh trung bnh chiu cao ti sinh vi gi tr l thuyt =2m 1.64 2 ?????? = = 5.63 0.493 61 V t l thuyt: t (0.05, df = n-1) = tinv(0.05, 60) = 2.00 Kt qu cho thy |t| = 5.63 > t(0.05, 60). Kt lun: C s sai khc c ngha gia trung bnh chiu cao cy ti sinh rng khp vi gi tr trung bnh l thuyt mong i l 2m. V t < 0 do c ngha l chiu cao trung bnh cy ti sinh nh thua c ngha khi so vi chiu cao mong i l 2m; hay ni khc nu vi yu cu cao trn 2m th mi thot c nh hng ca la rng, th l rng ny cy ti sinh cha t c. 4.2. So snh s sai khc gia trung bnh 2 mu Kim tra T 2 mu Trong cc th nghim thng ngi ta cn so snh kt qu ca 2 cng thc, v d: Bn phn khc nhau, tn che khc nhau, sinh trng ca cy c xut x khc nhau, ni b tc ng nh hng v ni khng, sinh trng cy rng ni chy v khng chy.....Vic kim tra tin hnh theo 2 mu trn c s so snh 2 s trung bnh bng cc tiu chuN t. n Cng thc tnh gi tr kim tra t: t= X1 X 2 ( n1 1) S1 + ( n 2 1) S 2 n1 + n 2 22 2
(
1 1 + ) n1 n 2
X1, X2: Trung bnh ca mu 1 v 2. S12, S22: Phng sai mu 1 v 2. n1, n2: dung lng 2 mu 1 v 2. Nu t tnh ln hn t bng vi =0.05 v t do K=n1+n2-2 th bc b gi thuyt Ho, c ngha trung bnh 2 mu sai khc c ngha, v ngi ta s chn mu c trung bnh cao.
Vi:
17 Trc khi s dng tiu chun t, cn kim tra 2 iu kin: o Hai mu c phn b chuN n. o Phng sai ca hai mu c bng nhau hay khng Hai mu c phn b chun: Trong thc t nghin cu sinh hc, trng hp dung lng mi mu >30 th c th xem l tim cn chuN n. Kim tra s bng nhau ca 2 phng sai ca 2 mu bng tiu chun F. Trc khi chn la tiu chuN t so snh trung bnh 2 mu, cn kim tra s sai khc phng n sai ca chng bng tiu chuN F. n V d: Kim tra sinh trng chiu cao H ca 2 phng php trng thng 3 l Pinus. kesiya bng cy con v r trn ti trm thc nghim Lang Hanh-Lm ng: Mi cng thc c rt mu theo tiu chuN 1000m2, o m chiu cao: n - Dung lng quan st mi mu >90cy, nn chp nhn gi thuyt phn b NH ca tng mu tim cn chuN hoc c th kim tra thm qua Sk v Ku n; mi mu. - Kim tra bng nhau ca 2 phng sai bng tiu chuN F: n Bng tm tt s liu sinh trng H ca hai muA 1 2 3 H (cy con) 13,6 14 13,8 13 11 12 93 94 12,5 B H (r trn) 13 13,5 12 13,5 15 14 10 9
Tnh F: Mt trong 2 cch: C1: Kch nt fx, c hp thoi: Chn: Statistical (trong Function Category) v Ftest-Next (trong Function name): Xut hin hi thoi tip theo: Array 1: a vo dy 1: A2:A93 Array 2: a vo dy 2: B2:B94 Finish. C2: a n kt qu: =Ftest(A2:A93,B2:b94) Enter. Nu gi tr xc sut P > 0.05, kt lun hai phng sai bng nhau, nu ngc li th bc b. Kt qu v d trn c P=0.40>0.05, kt lun phng sai hai mu bng nhau (cha c sai d r). Dng tiu chun t kim tra gi thuyt Ho theo trnh t:
18 Trong menu Tools/Data Analysis: Chn trong hp thoi mt trong hai trng hp tu theo phng sai hai mu c bng nhau hay khng qua kim tra bng F bc trc o t-Test: Two sample assuming equal variance (Trng hp phng sai bng nhau). o t-Test: Two sample assuming unequal variance (Trng hp phng sai khng bng nhau).
Trong Hp thoi: Xc nh: o Variable 1 range: Khi d liu mu 1 (A1:A93) o Variable 2 range: Khi d liu mu 2 (B1:B94) Nn a c tiu . o Hypothesized mean diference: a vo 0 (C ngha gi thuyt Ho=0). o Label: Nu c a hng tiu vo th cn nh du vi label o Output range: a a ch trn tri ni xut kt qu. o OK. Nu: P(T F(0,05) = 1,89. Kt lun: Cc xut x khc nhau c s sai khc v sinh trng ng knh. i vi cc cp t (Ct Collumns): F = 1,62 < F(0,05) = 2,81. Kt lun: Cc cp t khc nhau cha c nh hng n sinh trng. Nh vy 16 xut x khi trng Lang Hanh c sinh trng khc nhau, do vic cp t khng nh hng rt, nn nh gi chnh xc hn ch cn phn tch phng sai 1 nhn t (xut x):
27 Phn tch phng sai 1 nhn tAnova: Single Factor SUMMARY Groups 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 ANOVA Source of Variation Between Groups Within Groups SS 82.11826 34.9684 df 15 48 MS 5.474551 0.728508 F 7.514741 P-value 3.59E-08 F crit 1.880174 Count 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Sum 46.9 44.8 48.6 49.1 55.1 48.5 50.0 55.7 49.7 47.0 49.3 46.1 48.9 37.4 39.9 43.9 Average 11.7 11.2 12.2 12.3 13.8 12.1 12.5 13.9 12.4 11.7 12.3 11.5 12.2 9.3 10.0 11.0 Variance 1.253512 0.156318 0.268337 0.933224 0.049285 1.064903 0.975826 0.926688 0.817143 0.107475 1.054463 0.664541 1.255351 0.85117 0.763403 0.514494
Total
117.0867
63
Kt qu t bng ANOVA cho thy F = 7,51 > F(0,05) = 1,88. Kt lun: Sinh trng ng knh ca 16 xut x l khc nhau khi trng Lang Hanh.
28 Sinh trng bnh qun ng knh cc xut x theo th t t cao n thp bng sau: Th t sinh trng ng knh t tt n xuXut x 8 5 7 9 11 4 13 3 6 10 1 12 2 16 15 14 D1,3 tb(cm) 13.9 13.8 12.5 12.4 12.3 12.3 12.2 12.2 12.1 11.7 11.7 11.5 11.2 11.0 10.0 9.3
Xut x 8 c gi tr trung bnh cao nht, sau dng tiu chuN t so snh sinh trng n ng knh ln nht ca xut x 8 vi cc xut x c ng knh ln lt nh hn. Kt qu cho thy xut x 8 khng c sai d vi xut x c trung bnh th hai l xut x 5. Nh vy, xt theo ch tiu ng knh, xut x ti u trong 16 xut x kho nghim l 8 v 5, hai xut x ny c ch tiu D ln nht, cha c sai d vi nhau v c sai khc r rt vi cc xut x cn li. l 2 xut x: Doiinthranon v Lang Hanh. 5.1.2. Phn tch phng sai 2 nhn t m ln lp Trng hp ny mi t hp nhn t A v B c lp li m ln mt cch ngu nhin. Lc ny ngoi vic nh gi nh hng ca tng nhn t A, B cn phi tnh nh hng qua li ca chng n kt qu th nghim. V d: Nghin cu nh hng ca hai nhn t th nghim l mt v bn phn n nng sut ca bng. o Nhn t A: Mt chia lm 3 cp. o Nhn t B: Phn bn c chia lm 4 mc o Mi t hp c th nghim lp li ngu nhin 4 ln.
29 Bng s liu sn lng bng theo t hp 2 nhn t v lp li 4 ln mt t hp (/v: T/ha)A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 B4 B3 B2 B\A B1 B A1 16 14 21 16 19 20 23 19 19 21 22 20 20 24 21 17 C A2 17 15 17 19 19 18 18 20 21 21 22 23 20 20 22 19 D A3 18 18 19 17 20 23 21 21 22 18 21 21 25 22 21 23
Phn tch phng sai 2 nhn t m ln lp: o Tools/Data Analysis/Anova: Two Factor With Replication- OK. o Hp thoi: Xc nh: Input range: Nhp khi d liu k c hng ct tiu . Vd: A1:D17. Rows per sample: Nhp s ln lp. Vd: 4. Output range: Nhp a ch trn tri ni xut kt qu. OK.
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Khai bo phn tch phng sai 2 nhn t m ln lp
Kt qu phn tch phng sai 2 nhn t m ln lpAnova: Two-Factor With Replication SUMMARY 1 Count Sum Average Variance 2 Count Sum Average Variance 3 Count Sum 4 82 4 87 4 82 12 251 4 81 20,25 3,583333 4 75 18,75 0,916667 4 85 21,25 1,583333 12 241 20,08333 2,810606 4 67 16,75 8,916667 4 68 17 2,666667 4 72 18 0,666667 12 207 17,25 3,659091 1 2 3 Total
31Average Variance 4 Count Sum Average Variance Total Count Sum Average Variance ANOVA Source of Variation Sample Columns Interaction Within 16 312 19,5 7,2 16 311 19,4375 4,529167 16 330 20,625 4,783333 4 82 20,5 8,333333 4 81 20,25 1,583333 4 91 22,75 2,916667 12 254 21,16667 4,878788 20,5 1,666667 21,75 0,916667 20,5 3 20,91667 1,901515
SS 116,2292 14,29167 21,20833 110,25
df 3 2 6 36
MS 38,74306 7,145833 3,534722 3,0625
F 12,65079 2,333333 1,154195
P-value 8,45E-06 0,111468 0,352014
F crit 2,866265 3,259444 2,363748
Total
261,9792
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Bng Summary: Cho kt qu tnh ton tng t hp nhn t A/B v chung cho tng nhn t B, nhn t A, gm cc ch tiu: Dung lng (Count), Tng (Sum), Trung bnh (Average), Phng sai (Variance). Bng ANOVA: Ct u tin l cc ngun bin ng: o Sample: Bin ng do nhn t B to nn (do c xp theo hng). o Columns: Bin ng do nhn t A to nn (do c xp theo ct). o Interaction: Tc ng qua li. o Within: Bin ng ngu nhin. o Total: Bin ng chinh ca n gi tr quan st. T kt qu ny cho thy: FB = 12.65 > F0.05 = 2.87. Kl: Phn bn c tc ng r rt n nng sut bng. FA = 2.33 < F0.05 = 3.26. Kl: Mt nh hng khng r n nng sut bng. FAB = 1.15 < F0.05 = 3.36. Kl: ng thi thay i mt v phn bn nh hng khng r n nng sut. Lc ny ch cn vic la chn cng thc bn phn ti u. Qua s trung bnh nng sut theo tng cng thc bn phn cho thy cng thc 4 c nng sut cao nht l 21.16 t/ha. C th dng tiu chuN t kim tra li xem cng thc 4 c sai khc vi cng thc no cn li la n chn cng thc c hiu qu nht.
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6. PHN TCH TNG QUAN - HI QUYTrong thc t ngi ta cn lp cc m hnh tng quan hi quy v cc mc ch: o c lng mt nhn t kh o m (gi l bin ph thuc y) thng qua mt hay nhiu bin d quan st, o m (gi l bin c lp x) v tt nhin l phi c mi lin h gia y v x. T y c th lp cc biu iu tra phc v cho vic gim nh cc quan st o m mt s nhn t phc tp o d bo mt nhn t trong tng lai (gi l bin d bo y) vi mt s bin c lp, u vo (gi l l bin c lp x) o nghin cu tc ng, nh hng ca mt hoc nhiu nhn t n mt yu t cn quan tm nh sinh trng, sn lng, cht lng rng, xi mn t, dng chy lu vc. Trn c s c gii php k thut thch hp hoc cc bin php qun l quy hoch cp v m. Mc ch l s dng chng trnh Excel hoc Statgraphics thit lp cc m hnh tng quan/hi quy tuyn tnh t mt cho n nhiu bin s c lp. Trong chng trnh ny, cc tham s c c lng bng phng php bnh phng ti thiu. Ring cc dng phi tuyn khi ng dng chng trnh ny cn i bin s quy v dng tuyn tnh. 6.1. Hi quy tuyn tnh 1 lp Hi quy tuyn tnh mt lp c ngha l c mt bin s c lp x c nghin cu nh hng n bin ph thuc y, dng quan h c xc nh l ng thng. C ngha l khi x tng hoc gim th y cng tng hoc gim u theo dng c thng. Dng phng trnh tng qut: Y = A + B.X. Vd: Lp m hnh tng quan gia chiu cao di cnh (Hdc) vi chiu cao c cy (H) rng Tch dng ng thng: Hdc = A + B.H. V Hdc l ch tiu kh o m hn H, nn dng quan h ny xc nh Hdc thng qua H. Nhp s liu theo bng: Cc cp s liu Hdc - HA 1 2 3 4 ..... 40 41 Hdc(m) 22,0 21,8 21,5 ..... 9,7 9,8 B H(m) 23,0 23,0 22,3 ..... 10,9 11,1
c lng tng quan hi quy ng thng: o Tools/Data Analysis/Regression (Data/Data Analysis/Regression trong MS. Office 2009). OK. o Hp thoi: Input Y range: Nhp a ch ct bin Y (C th nhp c nhn). Vd: A1:A41. Input X range: Nhp a ch ct bin X (C th nhp c nhn). Vd: B1:B41. Label: nh du nu nhp c hng u lm nhn.
33 Output range: Nhp a ch trn tri ni xut kt qu. OK. Khai bo chy tng quan tuyn tnh 1 lp
Kt qu c lng hi quy tuyn tnh 1 lpSUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error ObservationsANOVA df Regression Residual Total 1 38 39 SS 1060,180842 3,84926708 1064,030109 MS 1060,181 0,101297 F 10466,12 Significance F 5,24804E-48
0,998189546 0,99638237 0,996287169 0,318271114 40
Coefficients Intercept Hgo(m) -0,715306008 0,994341123
Standard Error 0,127254043 0,009719471
t Stat -5,62109 102,304
P-value 1,88E-06 5,25E-48
Lower 95% -0,972918358 0,974665081
Upper 95% -0,457693658 1,014017165
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Phng trnh tng quan: Hdc = - 0.715 + 0.994.H Vi N = 40 R = 0.998 Fr = 10466.12 vi
