Prediction variance and G-criterion location for split-plot designs

2008 ◽  
Vol 25 (4) ◽  
pp. 381-395 ◽  
Author(s):  
Wayne R. Wesley ◽  
James R. Simpson ◽  
Peter A. Parker ◽  
Joseph J. Pignatiello
Keyword(s):  
Prediction Variance ◽  
Split Plot ◽  
Criterion Location

Maximum and Minimum Prediction Variance for Spherical and Cuboidal Split Plot Designs

2009 ◽  
Vol 38 (13) ◽  
pp. 2251-2266
Author(s):  
Wayne R. Wesley ◽  
James R. Simpson ◽  
Peter A. Parker ◽  
Joseph J. Pignatiello
Keyword(s):  
Prediction Variance ◽  
Split Plot

scholarly journals Missing Observations in Split-Plot Central Composite Designs: The Loss in Relative A-, G-, and V- Efficiency

2021 ◽  
Vol 25 (2) ◽  
pp. 239-247
Author(s):  
Y. Yakubu ◽  
A.U. Chukwu
Keyword(s):  
Model Parameters ◽  
Missing Observations ◽  
Prediction Variance ◽  
Efficiency Losses ◽  
Split Plot ◽  
Negative Effect ◽  
Central Composite Designs ◽  
Plot Structure ◽  
Composite Designs ◽  
Central Composite

The trace (A), maximum average prediction variance (G), and integrated average prediction variance (V) criteria are experimental design evaluation criteria, which are based on precision of estimates of parameters and responses. Central Composite Designs(CCD) conducted within a split-plot structure (split-plot CCDs) consists of factorial (𝑓), whole-plot axial (𝛼), subplot axial (𝛽), and center (𝑐) points, each of which play different role in model estimation. This work studies relative A-, G- and V-efficiency losses due to missing pairs of observations in split-plot CCDs under different ratios (d) of whole-plot and sub-plot error variances. Three candidate designs of different sizes were considered and for each of the criteria, relative efficiency functions were formulated and used to investigate the efficiency of each of the designs when some observations were missing relative to the full one. Maximum A-efficiency losses of 19.1, 10.6, and 15.7% were observed at 𝑑 = 0.5, due to missing pairs 𝑓𝑓, 𝛽𝛽, and 𝑓𝛽, respectively, indicating a negative effect on the precision of estimates of model parameters of these designs. However, missing observations of the pairs- 𝑐𝑐, 𝛼𝛼, 𝛼𝑐, 𝑓𝑐, and 𝑓𝛼 did not exhibit any negative effect on these designs' relative A-efficiency. Maximum G- and Vefficiency losses of 10.1,16.1,0.1% and 0.1, 1.1, 0.2%, were observed, respectively, at 𝑑 = 0.5, when the pairs- 𝑓𝑓, 𝛽𝛽, 𝑐𝑐, were missing, indicating a significant increase in the designs' maximum and average variances of prediction. In all, the efficiency losses become insignificant as d increases. Thus, the study has identified the positive impact of correlated observations on efficiency of experimental designs. Keywords: Missing Observations, Efficiency Loss, Prediction variance

Power of Modified Brown-Forsythe and Mixed-Model Approaches in Split-Plot Designs

Methodology ◽  
2017 ◽  
Vol 13 (1) ◽  
pp. 9-22 ◽  
Author(s):  
Pablo Livacic-Rojas ◽  
Guillermo Vallejo ◽  
Paula Fernández ◽  
Ellián Tuero-Herrero
Keyword(s):  
Repeated Measures ◽  
Statistical Power ◽  
Mixed Model ◽  
Covariance Structure ◽  
Simulation Method ◽  
Future Research ◽  
Repeated Measures Design ◽  
Fixed And Random Effects ◽  
Split Plot ◽  
High Level

Abstract. Low precision of the inferences of data analyzed with univariate or multivariate models of the Analysis of Variance (ANOVA) in repeated-measures design is associated to the absence of normality distribution of data, nonspherical covariance structures and free variation of the variance and covariance, the lack of knowledge of the error structure underlying the data, and the wrong choice of covariance structure from different selectors. In this study, levels of statistical power presented the Modified Brown Forsythe (MBF) and two procedures with the Mixed-Model Approaches (the Akaike’s Criterion, the Correctly Identified Model [CIM]) are compared. The data were analyzed using Monte Carlo simulation method with the statistical package SAS 9.2, a split-plot design, and considering six manipulated variables. The results show that the procedures exhibit high statistical power levels for within and interactional effects, and moderate and low levels for the between-groups effects under the different conditions analyzed. For the latter, only the Modified Brown Forsythe shows high level of power mainly for groups with 30 cases and Unstructured (UN) and Autoregressive Heterogeneity (ARH) matrices. For this reason, we recommend using this procedure since it exhibits higher levels of power for all effects and does not require a matrix type that underlies the structure of the data. Future research needs to be done in order to compare the power with corrected selectors using single-level and multilevel designs for fixed and random effects.

P—Zn kölcsönhatás mészlepedékes csernozjom talajon kukorica monokultúrában

2002 ◽  
Vol 51 (3-4) ◽  
pp. 381-394 ◽  
Author(s):  
Imre Kádár ◽  
Tamás Turán
Keyword(s):  
List Type ◽  
Split Plot

Szabadföldi P—Zn műtrágyázási tartamkísérletünket 1978 őszén állítottuk be löszön képződött, mély humuszrétegű, vályog mechanikai összetételű karbonátos csernozjom talajon, Intézetünk nagyhörcsöki kísérleti telepén. A talaj szántott rétege 5 % CaCO3-ot, 3 % humuszt tartalmaz; Ca, Mg, Mn és Cu elemekkel kielégítően, N és K elemekkel közepesen, P és Zn elemekkel gyengén ellátott. A talajvíz 13–15 m mélyen helyezkedik el, a termőhely aszályra hajló, vízmérlege negatív. A 4P × 3Zn = 12 kezelést 3 ismétlésben, split-plot elrendezésben állítottuk be. A parcellák mérete 4,9x15=73,5 m². Főparcellaként a 0, 100 kg/ha/év, 500 kg/ha/5 év, 1000 kg/ha/5 év P2O5-trágyázás, alparcellaként a 0, 20, 40 kg/ha/5 év Zn-trágyázás szolgált szuperfoszfát és ZnSO4 formájában. Alaptrágyaként az egész kísérletben egységesen 200 kg/ha N-és 200 kg/ha K2O-műtrágyát alkalmaztunk NH4NO3 és KCl formájában. A termesztett kukoricahibrid az Mv-SC 580 volt. Az első 4 év eredményei alapján levonható főbb következtetések: Kísérleti körülményeink között, ezen a foszforral gyengén ellátott talajon, az évenként adott 100 kg/ha P2O5-trágyázás kielégítheti a kukorica P-igényét. Előretrágyázás formájában ez a mennyiségű foszfor 4–5 évre számolva egyszerre is kiadható. Az 1000 kg/ha feltöltő P2O5-trágyázás gazdaságtalan és Znhiányt indukálva terméscsökkenéshez vezethet. Az AL-oldható P2O5-tartalom optimumát a 100–150 mg/kg érték jelezheti a szántott rétegben.Az egyoldalú, 1000 kg P2O5/ha adaggal előidézett P-túlsúlyt és szemterméscsökkenést a 40 kg/ha Zn-trágyázással lehetett ellensúlyozni. A KCl+EDTA módszerrel meghatározott Zn-tartalom optimumát 2–3 mg/kg talajbani koncentráció mutatta.Irodalmi adagokkal összhangban a kukorica kiegyensúlyozott tápláltsági állapotát a 4–6 leveles légszáraz hajtásban mért 0,3–0,5 % P és 30–60 mg/kg Zn, míg a címerhányáskori levél optimális összetételét 0,25–0,40 % P és 25 mg/kg feletti Zn-koncentráció-tartomány jellemezheti. A P/Zn arányának ideális értéke a vegetatív növényi részekben 50–150 közöttire tehető. Amennyiben ez a P/Zn arány jelentősen 200 fölé emelkedik, a Zn-trágyázás hatékony lehet.A P-túlsúly növelte a meddő tövek előfordulását 1978-ban, amikor szemtelítődés idején (augusztusban) aszály uralkodott. Ebben az évben a termő tövek 13–20 %-a bizonyult terméketlennek.

NGHIÊN CỨU ẢNH HƯỞNG CỦA LƯỢNG GIỐNG GIEO ĐẾN NĂNG SUẤT MỘT SỐ GIỐNG LÚA CHẤT LƯỢNG TRONG ĐIỀU KIỆN THÂM CANH LÚA CẢI TIẾN (SRI) TẠI TỈNH QUẢNG BÌNH

2016 ◽  
Vol 119 (5) ◽  
Author(s):  
Dương Thanh Ngọc ◽  
Hoàng Thị Thái Hòa ◽  
Nguyễn Thị Hải Bình ◽  
Nguyễn Xuân Thủy
Keyword(s):  
Split Plot ◽  
Quang Ninh

Thí nghiệm gồm 4 lượng giống gieo (20, 40, 60 và 80 kg/ha) trên hai giống lúa HT1 và P6, bố trí theo kiểu ô lớn - ô nhỏ (split – plot) với 3 lần nhắc lại, được thực hiện trong vụ Đông Xuân và Hè Thu 2014 trên đất chuyên trồng lúa của huyện Quảng Ninh, tỉnh Quảng Bình nhằm đánh giá ảnh hưởng của lượng giống gieo theo hướng SRI đến một số chi tiêu sinh trưởng, phát triển, năng suất lúa và hiệu quả kinh tế trong sản xuất lúa. Kết quả nghiên cứu cho thấy lượng giống gieo khác nhau có ảnh hưởng đến sinh trưởng, phát triển và năng suất, hiệu quả kinh tế của hai giống lúa nghiên cứu. Nhìn chung lượng giống gieo 60 kg/ha ở vụ đông xuân và 40 - 60 kg/ha ở vụ hè thu có một số chỉ tiêu sinh trưởng tốt, cho năng suất và hiệu quả kinh tế cao nhất, tiếp đến là lượng giống gieo 80 kg/ha ở vụ hè thu và vụ đông xuân.

Induksi Akar dan Tunas Setek Batang Tanaman Pohpohan (Pilea trinervia Wight) dalam Media Air dengan Perlakuan IBA dan Aerasi

2018 ◽  
Vol 6 (3) ◽  
pp. 362
Author(s):  
Katerin Ninariyani ◽  
Darda Efendi ◽  
E. Gunawan
Keyword(s):  
Split Plot

Penelitian ini bertujuan untuk mempelajari pengaruh penggunaan aerasi dan hormon pertumbuhan tanaman Indol -3-butiryc acid (IBA) pada induksi tunas dan akar setek Pohpohan (<em>Pilea trinervia </em>Wight.) dalam media air. Penelitian dilaksanakan di Rumah Kaca Kebun Percobaan Pasir<strong> </strong>Kuda, Pusat Kajian Holtikultura Tropika (PKHT) IPB pada bulan Juni-Oktober 2016. Penelitian menggunakan rancangan split-plot dua faktor dengan empat ulangan. Faktor pertama sebagai petak<strong> </strong>utama adalah aerasi terdiri dari dua taraf yaitu aerasi dan tanpa aerasi. Faktor kedua sebagai anak petak adalah IBA dengan empat taraf konsentrasi yaitu 0.0, 0.5, 1.0, dan 2.0 mg L-1. Hasil penelitian menunjukan bahwa perlakuan aerasi dan IBA berpengaruh terhadap persentase setek bertunas, jumlah akar, panjang akar, jumlah tunas, dan panjang tunas, namun tidak berpengaruh pada persentase setek hidup dan setek berakar. Kombinasi perlakuan tanpa aerasi dan IBA 0.5, 1.0, dan 2.0 mgL-1 menghasilkan jumlah akar paling banyak.

Respon Pertumbuhan dan Produksi Kacang Tanah (Arachis hypogaea L.) terhadap Sistem Tanam Alur dan Pemberian Jenis Pupuk

2017 ◽  
Vol 5 (3) ◽  
pp. 342
Author(s):  
Rizal Mahdi Kurniawan ◽  
Heni Purnamawati ◽  
Yudiwanti Wahyu E. K
Keyword(s):  
Arachis Hypogaea ◽  
Arachis Hypogaea L ◽  
Split Plot ◽  
Plot Design

<p><em>Penelitian ini bertujuan untuk mempelajari pengaruh sistem tanam alur dan pemberian jenis pupuk terhadap pertumbuhan dan produksi kacang tanah (Arachis hypogaea L.). Penelitian dilaksanakan di KP Leuwikopo IPB Dramaga, Bogor pada bulan Februari - Juni 2013. Percobaan menggunakan rancangan petak terbagi (Split Plot Design) dengan perlakuan terdiri dari dua faktor, yaitu sistem tanam alur sebagai petak utama dan jenis pupuk sebagai anak petak. Hasil penelitian menunjukkan bahwa perlakuan sistem tanam alur meningkatkan daya hasil pada produktivitas biji kering, produktivitas polong kering, dan bobot kering biji per tanaman lebih baik dibandingkan sistem tanam konvensional. Hal tersebut ditunjukkan dengan perlakuan sistem tanam alur yang memiliki produktivitas 2.93 ton/ha polong kering, sedangkan sistem tanam konvensional sebesar 2.55 ton/ha polong kering. Sistem budidaya kacang tanah pada sistem tanam alur dapat meningkatkan efisiensi tanaman dalam memanfaatkan unsur hara yang telah diberikan baik pupuk organik maupun anorganik, sehingga pertumbuhan dan hasil tanaman kacang tanah menjadi lebih baik. Pemberian jenis pupuk kandang ayam + Dolomit + NPK memberikan respon terhadap pertumbuhan dan  daya hasil rata-rata tanaman yang lebih baik dibandingkan jenis pupuk lainnya.</em></p>

scholarly journals Interaction of dicamba, fluthiacet-methyl, and glyphosate for control of velvetleaf (Abutilon theopharsti) in dicamba/glyphosate-resistant soybean

2021 ◽  
pp. 1-21
Author(s):  
Jose H. S. de Sanctis ◽  
Amit J. Jhala
Keyword(s):  
United States ◽  
Field Experiments ◽  
The United States ◽  
Application Rate ◽  
Herbicide Application ◽  
Soybean Yield ◽  
Agronomic Crops ◽  
Split Plot ◽  
Main Plot ◽  
Biomass Reduction

Abstract Velvetleaf is an economically important weed in agronomic crops in Nebraska and the United States. Dicamba applied alone usually does not provide complete velvetleaf control, particularly when velvetleaf is greater than 15 cm tall. The objectives of this experiment were to evaluate the interaction of dicamba, fluthiacet-methyl, and glyphosate applied alone or in a mixture in two- or three-way combinations for velvetleaf control in dicamba/glyphosate-resistant (DGR) soybean and to evaluate whether velvetleaf height (≤ 12 cm or ≤ 20 cm) at the time of herbicide application influences herbicide efficacy, velvetleaf density, biomass, and soybean yield. Field experiments were conducted near Clay Center, Nebraska in 2019 and 2020. The experiment was arranged in a split-plot with velvetleaf height (≤ 12 cm or ≤ 20 cm) as the main plot treatment and herbicides as sub-plot treatment. Fluthiacet provided ≥ 94% velvetleaf control 28 d after treatment (DAT) and ≥ 96% biomass reduction regardless of application rate or velvetleaf height. Velvetleaf control was 31% to 74% at 28 DAT when dicamba or glyphosate was applied alone to velvetleaf ≤ 20 cm tall compared with 47% to 100% control applied to ≤ 12 cm tall plants. Dicamba applied alone to ≤ 20 cm tall velvetleaf provided < 75% control and < 87% biomass reduction 28 DAT compared with ≥ 90% control with dicamba at 560 g ae ha−1 + fluthiacet at 7.2 g ai ha−1 or glyphosate at 1,260 g ae ha−1. Dicmaba at 280 g ae ha−1 + glyphosate at 630 g ae ha−1 applied to ≤ 20 cm tall velvetleaf resulted in 86% control 28 DAT compared with the expected 99% control. The interaction of dicamba + fluthiacet + glyphosate was additive for velvetleaf control and biomass reduction regardless of application rate and velvetleaf height.

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