Construction of Split-Plot Designs with General Minimum Lower Order Confounding

Fractional factorial split-plot design has been widely used in many fields due to its advantage of saving experimental cost. The general minimum lower order confounding criterion is usually used as one of the attractive design criterion for selecting fractional factorial split-plot design. In this paper, we are interested in the theoretical construction methods of the optimal fractional factorial split-plot designs under the general minimum lower order confounding criterion. We present the theoretical construction methods of optimal fractional factorial split-plot designs under general minimum lower order confounding criterion under several conditions.

Individual Word Length Patterns for Fractional Factorial(Split-Plot)Designs

Fractional factorial(FF)designs are commonly used for factorial experiments in many fields.When some prior knowledge has shown that some factors are more likely to be significant than others,Li,et al.(2015)proposed a new pattern,called the individual word length pattern(IWLP),which,defined on a column of the design matrix,measures the aliasing of the effect assigned to this column and effects involving other factors.In this paper,the authors first investigate the relationships between the IWLP and other popular criteria for regular FF designs.As we know,fractional factorial split-plot(FFSP)designs are important both in theory and practice.So another contribution of this paper is extending the IWLP criterion from FF designs to FFSP designs.The authors propose the IWLP of a factor from the whole-plot(WP),or sub-plot(SP),denoted by the I_w WLP and Is WLP respectively,in the FFSP design.The authors further propose combined word length patterns C_(w) WLP and Cs WLP,in order to select good designs for different cases.The new criteria C_(w) WLP and Cs WLP apply to the situations that the potential important factors are in WP or SP,respectively.Some examples are presented to illustrate the selected designs based on the criteria established here.

高阿丁枫人工中龄林生长对坡向和密度的响应

为了解高阿丁枫人工林的生长过程,2021年对林龄21 a的高阿丁枫人工林进行每木检尺,以胸径作为标准木选择的依据,西南坡不同密度中各选择1株,南坡不同密度中各选择3株高阿丁枫标准木作为解析木,分析不同坡向和造林密度组合的林木生长差异。结果表明:林龄21 a时,不同坡向和造林密度组合的高阿丁枫林木的平均胸径、树高和材积分别为17.60~20.78 cm、25.73~28.51 m和0.3186~0.4293 m3,林木尚处于旺盛的生长阶段;处理组合间以上生长量均呈现极显著的差异。林龄1~9、1~10、8~16 a期间分别是胸径、树高和材积的速生期,其连年生长量最高分别达2.19 cm/a、2.74 m/a和4.3966×10^(-2)m^(3)/a。坡向、密度及其交互作用显著或极显著地影响高阿丁枫林木的生长。高阿丁枫隶属热区长寿命大径材树种,速生期延续较长,其生长对立地和密度较为敏感。优质高效的高阿丁枫人工林培育应选择最适宜的立地和造林密度,并且适时开展密度的动态调控。综上所述,造林密度通过影响树高生长从而影响材积生长,南坡采用3 m×2 m×5 m非均匀密度造林的单株总材积最大。研究结果可应用于生产实践中高阿丁枫优质高效人工林培育的立地选择和密度控制。

Bounds on the maximum numbers of clear two-factor interactions for 2^((n1+n2)-(k1+k2)) fractional factorial split-plot designs

Fractional factorial split-plot (FFSP) designs have an important value of investigation for their special structures.There are two types of factors in an FFSP design: the whole-plot (WP) factors and sub-plot (SP) factors,which can form three types of two-factor interactions:WP2fi,WS2fi and SP2fi.This paper considers FFSP designs with resolution Ⅲ or Ⅳ under the clear effects criterion.It derives the upper and lower bounds on the maximum numbers of clear WP2fis and WS2fis for FFSP designs,and gives some methods for constructing the desired FFSP designs.It further examines the performance of the construction methods.

Minimum secondary aberration fractional factorial split-plot designs in terms of consulting designs

It is very powerful for constructing nearly saturated factorial designs to characterize fractional factorial (FF) designs through their consulting designs when the consulting designs are small. Mukerjee and Fang employed the projective geometry theory to find the secondary wordlength pattern of a regular symmetrical fractional factorial split-plot (FFSP) design in terms of its complementary subset, but not in a unified form. In this paper, based on the connection between factorial design theory and coding theory, we obtain some general and unified combinatorial identities that relate the secondary wordlength pattern of a regular symmetrical or mixed-level FFSP design to that of its consulting design. According to these identities, we further establish some general and unified rules for identifying minimum secondary aberration, symmetrical or mixed-level, FFSP designs through their consulting designs.

Split-plot designs with general minimum lower-order confounding

Split-plot designs have been widely used in industrial experiments.Up to now,most methods for choosing this kind of designs are based on the minimum aberration (MA) criterion.Recently,by introducing a new pattern,called aliased effect-number pattern (AENP),Zhang et al.proposed a general minimum lowerorder confounding (denoted by GMC for short) criterion and established a general minimum confounding (also denoted by GMC for saving notations) theory.It is proved that,the GMC criterion selects optimal designs in a more elaborate manner than the existing ones,and when an experimenter has a prior about the importance ordering of factors in experiments the GMC designs are better than other optimal designs.In this paper we extend the GMC criterion to the split-plot design case and give a GMC-FFSP criterion for ranking split-plot designs.Some comparisons of the new criterion with the MA-MSA-FFSP criterion are given,and the optimal 32-run split-plot designs up to 14 factors under the two criteria are tabulated for comparison and application.

Theory of optimal blocking for fractional factorial split-plot designs

The issue of optimal blocking for fractional factorial split-plot (FFSP) designs is considered under the two criteria of minimum aberration and maximum estimation capacity. The criteria of minimum secondary aberration (MSA) and maximum secondary estimation capacity (MSEC) are developed for discriminating among rival nonisomorphic blcoked FFSP designs. A general rule for identifying MSA or MSEC blocked FFSP designs through their blocked consulting designs is established.

Mixed Two-and Eight-level Fractional Factorial Split-plot Designs Containing Clear Effects

Fractional factorial split-plot （FFSP） designs are useful in practical experiments. When the num- bers of levels of the factors are not all equal in an experiment, mixed-level design is selected. This paper investigates the conditions of a resolution III or IV FFSP design with both two-level and eight-level factors to have various clear effects, including two types of main effects and three types of two-factor interaction compo- nents.

一种距离多普勒平面的二维点迹凝聚方法

本文提出了一种距离多普勒平面的二维点迹凝聚方法,该方法通过先对目标检测后点按一定顺序排列,接着在相同多普勒通道进行距离维归并,然后再进行多普勒维归并,接着将二维归并完的目标点根据目标判决条件剔除虚假点,最后将剩余的目标点按一定准则凝聚形成最终结果。通过二维归并凝聚可以避免目标分裂现象。

整区因子更重要时一般最小低阶混杂裂区设计

考虑当整区因子比子区因子更重要时一般水平的裂区设计,提出了这种情况下的一般最小低阶混杂准则.用有限投影几何作为工具,建立了裂区设计与其补设计字长型之间的关系.这对构造该准则下的最优设计是有帮助的.

磷钾肥和多效唑对高羊茅越夏性的影响研究 Ⅲ·高温对高羊茅叶片中N、P、K含量的影响

采用三因素三水平裂裂区试验设计,2004年夏季在草坪试验基地研究磷钾肥和多效唑对高羊茅Fes-tuca arundinacea越夏性的影响。结果表明:叶片中N、P、K含量的变化均达到了极显著差异。在A2B3C2(磷:60 kg/hm2,钾:140 kg/hm2,多效唑:250 mg/L)处理下,高羊茅叶片细胞中N、P、K含量相对较高,说明肥料和化控的较优搭配能促进N、P、K素营养在高羊茅草坪草中的大量积累,为高羊茅顺利越夏提供营养基础。

沼肥对保护地番茄生长发育及其产量的影响

采用二裂式区组设计的方法,以番茄为供试作物,以沼肥(沼液、沼渣)、猪粪和化肥为肥料,研究了不同施肥措施对番茄生长发育及其产量的影响。结果表明:与施用化肥相比,施用沼液的番茄植株平均株高及根系体积有所增加,番茄产量略有降低;与施用猪粪相比,施用沼渣可促进植株茎秆的健壮生长及根系发育,番茄产量提高20.8%;与沼渣和化肥配合施用相比,沼渣与沼液配合施用促进了番茄植株的生长发育,其植株生长稳健,根系发达,而且番茄产量增加;与猪粪和化肥配合施用相比,猪粪与沼液配合施用促进了番茄植株的生长发育,其株高较高、茎秆粗壮、根系发达,但番茄产量下降。

高温对高羊茅叶片中渗透调节物质的影响

采用了裂裂区设计,以耐热较强的冷季型草坪草高羊茅(Festuca arundinecea Schreb. cv. Huntdog 5)为实验材料,比较了不同磷钾肥施肥量和多效唑喷施浓度对高羊茅渗透调节物质的影响。结果表明:在自然高温胁迫下,27个处理组合之间的渗透调节物质(可溶性糖、可溶性蛋白、脯氨酸)的含量变化均达到了极显著水平,在A2B3C2(即P2O5:A=60 kg/hm2;K2O:B=140 kg/hm2,多效唑:C=0.25 kg/hm2)处理下,高羊茅的叶片细胞中渗透调节物质含量相对较高,说明肥料和化控的较优搭配能促进渗透调节物质在高羊茅草坪草中的大量积累,为高羊茅顺利越夏提供保障。

云南松胚根与胚轴伸长对遮荫、微波和IBA处理的响应

全光照和75%遮荫作为裂区,微波辐射和IBA浸种采用L9(34)正交设计进行裂区下的正交试验,了解以上3因素对云南松苗木胚根和胚轴伸长的影响。结果表明,胚根和胚轴在全光照时的理论优水平组合分别为A2B1和A1B2;在75%遮荫时分别为A1B1和A2B2,仅胚轴在全光照时的理论优水平组合与实际试验结果相一致。全光照下微波辐射促进胚根伸长,而75%遮荫下其促进胚轴伸长。0.1 g/L的IBA浸种促进胚根和胚轴的伸长。

不同施氮量、密度对油研九号产量的影响

运用裂区试验研究了密度和施氮量对油研九号产量的影响。结果表明 ,密度、施氮量以及密度和施氮量的交互作用对产量的影响均达到显著或极显著水平。产量达 30 0 0kg/hm2 的栽培措施是每hm2 施纯氮 2 70kg、密度 18万株。产量性状间的相关与通径分析表明 :一次分枝数、二次分枝数、群体有效角果数、主花序长通过群体干物重对产量产生了较大影响 ,并与产量间均呈显著的相关性 。

气温对杂交水稻Ⅱ优718产量优势的影响分析

本文采用5个品种,6个播期的裂区试验设计,3次重复,研究不同播期和气温对水稻Ⅱ优718与对照Ⅱ优838不同性状及产量杂种优势的影响。结果表明:①Ⅱ优718和Ⅱ优838不同性状的杂种优势强弱均表现不同;②F1代产量高的并不一定是中亲优势强的,这主要取决于亲本的自身表现;③不同的环境对产量优势的表现都具有不同的影响,其影响的大小取决于环境因素是否有利于F1代的生长发育和双亲的遗传基础是否正常表达;④采用逐步回归分析后发现F1代及其父母本不同生育阶段的活动积温和有效积温对Ⅱ优718和Ⅱ优838的产量优势均有不同程度的影响。

施肥对保护地番茄果实品质及其产量的影响

采用二裂式区组设计的方法,以番茄为供试作物,以沼肥(沼液、沼渣)、猪粪和化肥为肥料,研究了不同施肥措施对番茄果实品质及其产量的影响。结果表明:与施用化肥相比,施用沼液番茄果实硝酸盐及Vc含量降低,总糖、总酸含量提高,糖/酸比均较适宜,番茄产量略有降低;与施用猪粪相比,施用沼渣降低了番茄果实硝酸盐及总酸含量,提高了Vc及总糖含量,糖/酸比值增大,番茄产量提高20.8%;与沼渣和化肥配合施用相比,沼渣与沼液配合施用改善了番茄果实的品质,其番茄果实硝酸盐含量降低,Vc、总糖、总酸含量和糖/酸比值均提高,而且番茄产量增加;和猪粪与沼液配合施用相比,猪粪与化肥配合施用番茄果实硝酸盐、Vc、总糖、总酸含量和糖/酸比值均提高,番茄产量增加。

裂-裂区设计及其方差分析

目的介绍裂-裂区设计及其方差分析。方法结合实例介绍裂-裂区设计中实验单位、实验因素级别的正确识别和合理安排,以便正确选择方差分析模型。结果只有正确识别裂-裂区设计中实验单位、实验因素的级别,才能获得正确的方差分析模型以及相应的分析结果。结论裂区及裂-裂区设计是采用区组化控制技术进行的多因素研究设计,是完全随机区组设计、拉丁方设计等的综合运用。

裂区试验资料均值的多重比较及错误辨析

裂区设计是农作物田间试验中运用较多的一种试验设计,笔者发现人们在进行裂区试验资料的统计分析,尤其是多重比较时存在一些问题,许多重要的结果没有被总结出来,造成了损失。为此,结合实例介绍了裂区设计试验F检验和多重比较的方法,并对公开发表文献中的部分问题进行了辨析。

单因素随机区组试验中重复测量数据分析及其SAS实现方法

结合两个实例,讨论了单因素随机区组试验中重复测量数据的分析方法,并用SAS程序进行了统计计算。对于不同地点的重复测量数据,在其变异来源中增加了一个地点取样误差,其SAS程序中,采用了Proc Anova语句,巧妙地在Model语句后加入了Test语句。对于不同时间点的重复测量数据,可以将单因素随机区组设计转化为裂区设计,单因素为主区因素,时间因素为副区因素,其SAS程序中,采用了Proc Mixed语句,并进行了同质性检验。