Efecto de la violaci??n de la normalidad y esfericidad en el modelo lineal mixto en dise??os split-plot

Resumen tomado de la publicaci??n

Split-mouth designs in orthodontics: an overview with applications to orthodontic clinical trials

SUMMARY Split-mouth designs first appeared in dental clinical trials in the late sixties. The main advantage of this study design is its efficiency in terms of sample size as the patients act as their own controls. Cited disadvantages relate to carry-across effects, contamination or spilling of the effects of one intervention to another, period effects if the interventions are delivered at different time periods, difficulty in finding similar comparison sites within patients and the requirement for more complex data analysis. Although some additional thought is required when utilizing a split-mouth design, the efficiency of this design is attractive, particularly in orthodontic clinical studies where carry-across, period effects and dissimilarity between intervention sites does not pose a problem. Selection of the appropriate research design, intervention protocol and statistical method accounting for both the reduced variability and potential clustering effects within patients should be considered for the trial results to be valid.

Statnote 12: the split-plot analysis of variance

In some experimental situations, the factors may not be equivalent to each other and replicates cannot be assigned at random to all treatment combinations. A common case, called a ‘split-plot design’, arises when one factor can be considered to be a major factor and the other a minor factor. Investigators need to be able to distinguish a split-plot design from a fully randomized design as it is a common mistake for researchers to analyse a split-plot design as if it were a fully randomised factorial experiment.

ANÁLISE DE REGRESSÃO em EXPERIMENTOS em PARCELAS SUBDIVIDIDAS COM DADOS NÃO-BALANCEADOS: UMA SOLUÇÃO NA LINGUAGEM GLIM

São estabelecidas as matrizes necessárias para a realização da análise de variância de experimentos em parcelas subdivididas, com dados não-balanceados e balanceados, quando os tratamentos aplicados às parcelas e os tratamentos aplicados às subparcelas são ambos fatores quantitativos, usando a teoria de modelos lineares e de modelos lineares generalizados. Foi desenvolvido um programa computacional, na linguagem GLIM, para a realização da análise.

Multistratum response surface designs

Response surface designs are usually described as if the treatments have been completely randomized to the experimental units. However, in practice there is often a structure to the units, implying the need for blocking. If, in addition, some factors are more difficult to vary between units than others, a multistratum structure arises naturally. We present a general strategy for constructing response surface designs in multistratum unit structures. Designs are constructed stratum by stratum, starting in the highest stratum. In each stratum a prespecified treatment set for the factors applied in that stratum is arranged to be nearly orthogonal to the units in the higher strata, allowing-for all the effects that have to be estimated. Three examples are given to show the applicability of the method and are also used to check the relationship of the final design to the choice of treatment set. Finally, some practical considerations in randomization are discussed.

The application of analysis of variance (ANOVA) to different experimental designs in optometry

Analysis of variance (ANOVA) is the most efficient method available for the analysis of experimental data. Analysis of variance is a method of considerable complexity and subtlety, with many different variations, each of which applies in a particular experimental context. Hence, it is possible to apply the wrong type of ANOVA to data and, therefore, to draw an erroneous conclusion from an experiment. This article reviews the types of ANOVA most likely to arise in clinical experiments in optometry including the one-way ANOVA ('fixed' and 'random effect' models), two-way ANOVA in randomised blocks, three-way ANOVA, and factorial experimental designs (including the varieties known as 'split-plot' and 'repeated measures'). For each ANOVA, the appropriate experimental design is described, a statistical model is formulated, and the advantages and limitations of each type of design discussed. In addition, the problems of non-conformity to the statistical model and determination of the number of replications are considered. © 2002 The College of Optometrists.

Ensaios em parcelas subdivididas delineados em blocos incompletos balanceados. I - Equações normais

Com o objetivo de ampliar o uso dos ensaios com parcelas subdivididas na pesquisa agropecuária, realizou-se um estudo de tais ensaios delineados em blocos incompletos balanceados. Adotou-se, para tanto, o modelo tradicionalmente usado no delineamento completo. Optou-se pela existência de correlação constante entre subparcelas distintas. A obtenção das estimativas para efeitos de blocos ocorreu como nos ensaios em blocos incompletos balanceados, enquanto que as estimativas para efeitos de tratamentos secundários e para a interação tratamentos principais x tratamentos secundários portaram-se como nos ensaios com parcelas subdivididas em blocos (completos), casualizados.

Statnote 13: a more complex analysis of variance incorporating a 'repeated measures' factor

Experiments combining different groups or factors and which use ANOVA are a powerful method of investigation in applied microbiology. ANOVA enables not only the effect of individual factors to be estimated but also their interactions; information which cannot be obtained readily when factors are investigated separately. In addition, combining different treatments or factors in a single experiment is more efficient and often reduces the sample size required to estimate treatment effects adequately. Because of the treatment combinations used in a factorial experiment, the degrees of freedom (DF) of the error term in the ANOVA is a more important indicator of the ‘power’ of the experiment than the number of replicates. A good method is to ensure, where possible, that sufficient replication is present to achieve 15 DF for the error term of the ANOVA testing effects of particular interest. Finally, it is important to always consider the design of the experiment because this determines the appropriate ANOVA to use. Hence, it is necessary to be able to identify the different forms of ANOVA appropriate to different experimental designs and to recognise when a design is a split-plot or incorporates a repeated measure. If there is any doubt about which ANOVA to use in a specific circumstance, the researcher should seek advice from a statistician with experience of research in applied microbiology.

Data methods in optometry Part 9: experimental design and analysis of variance

The key to the correct application of ANOVA is careful experimental design and matching the correct analysis to that design. The following points should therefore, be considered before designing any experiment: 1. In a single factor design, ensure that the factor is identified as a 'fixed' or 'random effect' factor. 2. In more complex designs, with more than one factor, there may be a mixture of fixed and random effect factors present, so ensure that each factor is clearly identified. 3. Where replicates can be grouped or blocked, the advantages of a randomised blocks design should be considered. There should be evidence, however, that blocking can sufficiently reduce the error variation to counter the loss of DF compared with a randomised design. 4. Where different treatments are applied sequentially to a patient, the advantages of a three-way design in which the different orders of the treatments are included as an 'effect' should be considered. 5. Combining different factors to make a more efficient experiment and to measure possible factor interactions should always be considered. 6. The effect of 'internal replication' should be taken into account in a factorial design in deciding the number of replications to be used. Where possible, each error term of the ANOVA should have at least 15 DF. 7. Consider carefully whether a particular factorial design can be considered to be a split-plot or a repeated measures design. If such a design is appropriate, consider how to continue the analysis bearing in mind the problem of using post hoc tests in this situation.

Nitrous oxide emissions from irrigated wheat in Australia : impact of irrigation management

Background and Aims: Irrigation management affects soil water dynamics as well as the soil microbial carbon and nitrogen turnover and potentially the biosphere-atmosphere exchange of greenhouse gasses (GHG). We present a study on the effect of three irrigation treatments on the emissions of nitrous oxide (N2O) from irrigated wheat on black vertisols in South-Eastern Queensland, Australia. Methods: Soil N2O fluxes from wheat were monitored over one season with a fully automated system that measured emissions on a sub-daily basis. Measurements were taken from 3 subplots for each treatment within a randomized split-plot design. Results: Highest N2O emissions occurred after rainfall or irrigation and the amount of irrigation water applied was found to influence the magnitude of these “emission pulses”. Daily N2O emissions varied from -0.74 to 20.46 g N2O-N ha-1 day-1 resulting in seasonal losses ranging from 0.43 to 0.75 kg N2O N ha-1 season -1 for the different irrigation treatments. Emission factors (EF = proportion of N fertilizer emitted as N2O) over the wheat cropping season, uncorrected for background emissions, ranged from 0.2 to 0.4% of total N applied for the different treatments. Highest seasonal N2O emissions were observed in the treatment with the highest irrigation intensity; however, the N2O intensity (N2O emission per crop yield) was highest in the treatment with the lowest irrigation intensity. Conclusions: Our data suggest that timing and amount of irrigation can effectively be used to reduce N2O losses from irrigated agricultural systems; however, in order to develop sustainable mitigation strategies the N2O intensity of a cropping system is an important concept that needs to be taken into account.

Physiological Basis for Genotypic Variation in Tolerance to and Recovery from Pre-flowering Drought in Peanut.

Drought during the pre-flowering stage can increase yield of peanut. There is limited information on genotypic variation for tolerance to and recovery from pre-flowering drought (PFD) and more importantly the physiological traits underlying genotypic variation. The objectives of this study were to determine the effects of moisture stress during the pre-flowering phase on pod yield and to understand some of the physiological responses underlying genotypic variation in response to and recovery from PFD. A glasshouse and field experiments were conducted at Khon Kaen University, Thailand. The glasshouse experiment was a randomized complete block design consisting of two watering regimes, i.e. fully-irrigated control and 1/3 available soil water from emergence to 40 days after emergence followed by adequate water supply, and 12 peanut genotypes. The field experiment was a split-plot design with two watering regimes as main-plots, and 12 peanut genotypes as sub-plots. Measurements of N-2 fixation, leaf area (LA) were made in both experiments. In addition, root growth was measured in the glasshouse experiment. Imposition of PFD followed by recovery resulted in an average increase in yield of 24 % (range from 10 % to 57 %) and 12 % (range from 2 % to 51 %) in the field and glasshouse experiments, respectively. Significant genotypic variation for N-2 fixation, LA and root growth was also observed after recovery. The study revealed that recovery growth following release of PFD had a stronger influence on final yield than tolerance to water deficits during the PFD. A combination of N-2 fixation, LA and root growth accounted for a major portion of the genotypic variation in yield (r = 0.68-0.93) suggesting that these traits could be used as selection criteria for identifying genotypes with rapid recovery from PFD. A combined analysis of glasshouse and field experiments showed that LA and N-2 fixation during the recovery had low genotype x environment interaction indicating potential for using these traits for selecting genotypes in peanut improvement programs.

补充灌溉及氮磷配施对黄土塬区冬小麦水分利用及产量的影响

采用裂区试验设计,对黄土塬区补充灌溉及氮磷配施条件下麦田土壤水分动态、作物产量及水分利用效率等进行研究。结果表明:1)冬小麦对土壤水分的利用深度随小麦生长发育逐渐加深,在越冬前期和孕穗期分别达1.2和2.2 m土层以下,不同处理土壤含水量在小麦生育前期差异不明显,孕穗后氮磷配施处理的土壤含水量显著低于不施肥处理;2)试验条件下,补充灌溉后同样施肥处理的作物产量与雨养相比,虽有增加但不显著;不论是雨养水平,还是补充灌溉水平,氮磷配施均表现出显著的增产效果,从低氮低磷到高氮高磷,增产幅度在134%到240%之间;3)氮磷配施能显著提高冬小麦水分利用效率,而补充灌溉后水分利用效率降低3%~30%,但未达显著水平;4)不同氮磷配施的增产效应高于补充灌溉,补充灌溉与高氮高磷处理有显著的水肥协同效应,能显著提高作物产量并保持较高的水分利用效率。

Hacia una investigación agropecuaria eficiente : análisis de covariancia en el diseño en parcelas divididas

p.233-244

Comparison of consumer perception and acceptability for steaks cooked to different endpoints: Validation of photographic approach

Photographs have been used to enhance consumer reporting of preference of meat doneness, however, the use of photographs has not been validated for this purpose. This study used standard cooking methods to produce steaks of five different degrees of doneness (rare medium, medium well, well done and very well done) to study the consumer’s perception of doneness, from both the external and internal surface of the cooked steak and also from corresponding photographs of each sample. Consumers evaluated each surface of the cooked steaks in relation to doneness for acceptability, ‘just about right’ and perception of doneness. Data were analysed using a split plot ANOVA and least significant test. Perception scores (for both external and internal surfaces) between different presentation methods (steak samples and corresponding photos), were not significantly different (p > 0.05). The result indicates that photographs can be used as a valid approach for assessing preference for meat doneness.