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De 1983 a 1985 se hicieron experimentos de campo en dos localidades de Puerto Rico para comparar la respuesta de tres genotipos de habichuela (Phaseolus vulgaris L.) a diferentes prácticas de cultivo. Los genotipos de habichuela variaron en hábito de crecimiento y en susceptibilidad a acamarse. Se utilizó un diseño de bloques completos aleatorizados con un arreglo de parcelas divididas con tres repeticiones. Las parcelas enteras consistieron de dos distancias entre surcos (0.5 y 1.0 m.). Las subparcelas consistieron de un arreglo factorial de tres densidades de siembra (6.6, 13.2, y 19.8 semillas/m.) y tres genotipos de habichuela. Con los tres genotipos se obtuvieron los mayores rendimientos en parcelas con 0.5 m. entre surcos y una densidad de siembra de 19.8 semillas/m. Los mayores rendimientos se debieron a un aumento en el número de vainas/ha. El genotipo 2W-33-2 produjo los mayores rendimientos, a pesar de que el acamado fue mayor que en los demás genotipos. En Fortuna los rendimientos de los genotipos fueron mayores de 2,000 kg./ha. cuando se sembraron en surcos de 0.5 m. de ancho. Con relación al índice de cosecha, en Fortuna no hubo diferencias significativas tanto en distancia entre surcos como en densidad de siembra. Por el contrario, en Isabela, el índice de cosecha disminuyó cuando se aumentó la densidad de siembra. La altura de la planta y el peso de 100 semillas no mostraron diferencias significativas al variar la distancia entre surcos y la densidad de siembra. En Fortuna el acamado fue mayor cuando la densidad de siembra se aumentó.

Following a method to analyze split-plot designs which have one "between subjects" variable with unequal n, and one "within subjects" variable, an extension is suggested to analyze more complicated designs. The technique presented is based on a program in Statistical Package for Social Sciences (SPSS) (Nie, Hull, Jenkins, Steinbrenner, and Bent, 1975).

Summary For a group of split-plot designs it is assumed that the error variance is constant for a particular experiment but it varies from experiment to experiment. Assuming error variances to be known, estimators of the treatment parameters are obtained by weighted (generalised) least squares method and the corresponding analysis is given. For unknown error variances, an adjustment of the statistics using estimated weights is proposed for removing much of the resulting bias. The adjustment stems from a theorem due to Meier (1953).

We propose an incomplete split plot design where levels of one factor (say A) are applied to the wholeplots and levels of the other (say B) to subplots, and where the number of subplots in each wholeplot may be less than the number of levels of factor B. The t levels of factor A are arranged in a completely randomized design. The s levels of factor B are arranged in a connected and proper incomplete block design within each level of factor A, by considering the wholeplots as blocks.

A total of 1200 poults were housed in a split plot arrangment to evaluate four different dietary treatments and three light treatments. Pre-starter and starter diets contained 0 or 10% Tower rapeseed meal (RSM), Candle RSM, combination of Tower and Candle RSM (50:50), and 0 or 20% of these RSM treatments, respectively. Grower, developer, and finisher diets contained 0 or 30% of these RSM treatments, respectively. The light treatments tested were continuous (23L:1D), intermittent (4L:2D), and total darkness. Tower and Candle RSM, singularly or in combination, when included in turkey diets resulted in significantly lower mortality, higher live weights, improved feed conversion, higher percentage Grade A carcasses, and improved monetary returns. There were no significant differences observed for any of these traits for turkeys raised under continuous or intermittent lighting or total darkness. There was, however, some indication that the turkeys tended to perform better under intermittent lighting. No light X diet interaction was observed for any of the traits measured indicating that the turkeys responded in a similar manner regardless of the diet or light treatment.

Six opaque-2 lines and their normal counterparts were crossed in diallel crosses. The crosses were grown in 1970 in a split plot randomized complete block design. Harvests were made at 7-day intervals starting at 28 days after pollination and countinuing through 63 days.

An extension of McNemar's test for correlated proportions was presented in which subjects falling into McNemar's A and D categories are nested under two or more levels of one or more between-subjects factors. The main effect for the within-subjects factor is tested with the McNemar chi-squared statistic used for correlated proportions after collapsing the one or more between-subjects factors. Two- and higher-way interactions between the one or more between-subjects factors and the correlated proportions factor are tested with the Pearson chi-squared statistic used for two- and higher-dimensional contingency tables, respectively, based on observations taken from independent samples.

The influence of gallamine, metocurine, pancuronium, and tubocurarine on depolarization of a mammalian muscle end-plate region was examined to determine whether the antagonists given in combination exerted a degree of block consistent with the simple classical competitive model. Depolarization was produced by carbachol in isolated guinea pig lumbrical muscles and recorded by the moving fluid electrode technique. The dose-response values obtained were fitted to a regression embedded in a split plot factorial experimental design such as both to control and to measure effects of variation among preparations, order of administration, time, and level of block. Of the six possible pairings of the four drugs, four showed the simple additivity expected from a competitive mechanism, while two (pancuronium plus metocurine and metocurine plus gallamine) showed potentiation beyond additivity. In these latter two pairs the combination shifted the carbachol dose-response curve, respectively, 41 and 21% further than predicted from the classical model. The significance of this deviation in the light of alternative receptor models is discussed, and a model consistent with the observed results is outlined.

The effects of a career course taught by 11 instructors (two sections each) for college students, who were undecided about a major field or career, were evaluated in a pre-post design using the Vocational Identity, Occupational Information, and Barrier scales of the My Vocational Situation ( J. A. Holland, D. C. Daiger, & P. G. Power, Palo Alto, Calif.: Consulting Psychologists Press, 1980 ). Large main effects were observed for the Identity and Occupational Information scales, but not for the Barriers scale. No interactions by instructor or student characteristics were found by using a simple ANOVA procedure or by using a split plot factorial design. The implications for new research and career instructors were discussed.

This paper treats the question, "How should one estimate the reliability of school (or classroom) means when persons are nested within schools (or classrooms)?" We begin by reviewing the use of variance components in the estimation of reliability from a randomized block (RB) design. Then we extend this rationale to the estimation of reliability (or generalizability) coefficients in a split-plot factorial (SPF) design with persons nested within schools. Through the use of variance components from the SPF design, we derive estimates of reliability for schools and for persons within schools. Then we compare the reliability for persons within schools from a SPF design with the reliability for persons from a RB design. Finally, we compare the reliability for schools from a SPF design with the reliability for school means from a RB design.

Cohen and Cohen (1983) and Pedhazur (1982) have describeddifferent procedures for the multiple regression analysis of split-plot factorial designs. In the present study both procedures wereapplied to a small data set previously analyzed by Kirk (1982), whonoted that two cases need to be distinguished when the groupscontain unequal numbers of subjects. The results demonstratedthat (a) Cohen and Cohen's procedure and Pedhazur's give thesame results when applied to the same data, and (b) both procedures address the case in which the investigator deliberatelyselected unequal numbers of subjects for the groups, proportionalto the sizes of the corresponding populations.

The effects of fertilizers on potato chip color were studied over a period of 11 years. Yield and specific gravity data also were taken. Single element and compete fertilizers were used in randomized block and split plot experiments. Most of the work was done with the Russet Burbank variety but in some experiments the Kennebec, White Rose, Norgold Russet and Cascade varieties were also included. Specific gravity and chip color data were taken immediately after harvest. Effects of storage and reconditioning on chip color were recorded in some cases.

The objective was to evaluate the use of prediction equations based on the chemical composition of feedstuffs to estimate the values of apparent metabolisable energy corrected for nitrogen balance (AMEn) of corn and soybean meal for broilers. For performance and carcass characteristics, 1,200 one-d-old birds (male and female) were allotted to a completely randomised factorial 28 (two genders and eight experimental diets) with three replicates of each sex with 25 birds. In the metabolism trial, 240 eight-d-old birds were distributed in the same design, but with a split plot in time (age of evaluation) with five, four and three birds per plot, respectively, in stages 8 to 21, 22 to 35, and 36 to 42 d of age. The treatments consisted of the use of six equations systems to predict the AMEn content of feedstuffs, tables of food composition and AMEn values obtained by in vivo assay, totalling eight treatments. Means were compared by Scott-Knott test at 5% probability and a confidence interval of 95% was used to check the fit of the energy values of the diets to the requirements of the birds. As a result of this study, the use of prediction equations resulted in better adjustment to the broiler requirements, resulting in better performance and carcass characteristics compared to the use of tables, however, the use of energy values of feedstuffs obtained by in vivo assay is still the most effective. The best equations were: AMEn = 4,021.8-227.55 Ash (for corn) combined with AMEn = -822.33+69.54 CP-45.26 ADF+90.81 EE (for soybean meal); AMEn = 36.21 CP+85.44 EE+37.26 NFE (nitrogen-free extract) (for corn) combined with AMEn = 37.5 CP+46.39 EE+14.9 NFE (for soybean); and AMEn = 4,164.187+51.006 EE-197.663 Ash-35.689 CF-20.593 NDF (for corn and soybean meal). (Key Words: Broiler, Feed, Energy Value)

Experimental plans are presented for split plot experiments in which the whole plot treatments and the split plot treatments each consist of combinations of two-level factors. The technique of split plot confounding, whereby interactions among split plot factors are confounded with various whole plot contrasts, is utilized to construct some full and fractional replicate plans.

Maximum ratios of 96 to 1 in 1946 and of 44 to 1 in 1947 in the seasonal levels of aphid abundance on potato plants of the Green Mountain variety resulted in no difference in specific gravities of the tubers. In general, similar results were obtained for potatoes of the Katahdin variety in 1956, 1957, 1958 and 1960. Aphids had no important effect on the specific gravity of tubers. Any reduction in starch content caused by the aphids was of no commercial significance and probably was too small to be reflected in the cooking or eating qualities of the tubers.

Four dent corn hybrids (3 in 1974 and one in 1975) were tested in split plot experiments that included arificial vs. natural infestation of ears with Heliothis zea (Boddie), inoculation of ears with Aspergillus flavus Link ex Fries vs. no inoculation, and ears sprayed with stirofos vs. nonsprayed ears in 1974; included inoculation vs. noninoculation and stirofos treated bags vs. nontreated bags in 1975. Aflatoxin B1 production and corn earworm injury were recorded. No evidence was found in either year for a significant relationship between corn earworm injury and the presence of aflatoxin B1. The insecticide regimen which was designed to totally control insects in both years did not eliminate insect damage nor did it effectively preclude A. flavus infection of the ears and subsequent aflatoxin production.

Holstein heifers, which weighed an average of 154 kg, were randomly assigned to three dietary treatments in a split plot in time design. Differences in diets were fiber source: solka floc, corn cobs, and corn silage. The major source of added protein was corn gluten meal. Total collection metabolism periods were the final 7 d of each of two 30-d periods. Several heifers had simple digestive disturbances, which appeared to be related to low ruminal pH, while consuming the solka floc diet. Average daily gains were .78, .83, and 1.02 kg/d for treatments solka floc, corn cobs, and corn silage, respectively. Gains were within the range of acceptable growth standards and were higher than reports in the literature for semipurified and purified diets. Protein in corn gluten meal appeared to be utilized efficiently by the heifers for growth. The solka floc and corn cob diets are acceptable for growing dairy heifers where a low mineral content is desired but normal growth rates need to be maintained. The solka floc diet might be improved by including a buffer to help stabilize rumen pH.

In order to provide an understanding of covariance analyses for split plot designs, analyses are first conducted on a data set without the covariate. Then an analysis with the covariate is performed. The third example has a different experiment design for the whole plots and the covariate is constant for all split plots within the whole plot. Computer packages may only give portions of the analysis correctly. Some packages require two procedural calls to obtain a portion of the correct results. BMDP 2V falls in the above category. Keywords: Analysis of variance; Experimental design.

In an experiment with at least two factors, it is sometimes convenient to apply some of the factors to large experimental units (called whole plots) and then to split the large units into smaller parts on which the remaining factors are applied. The subdivisions of the whole plots are called subplots or split plots.

When measurements developed for the diagnosis of patients are used to detect treatment effects in clinical trials with chronic disease, problems in definition of response and in the statistical distributions of those measurements within patients have to be resolved before the results of clinical studies can be analyzed. An example of this process is shown in the development of the analysis of single-dose bronchodilator trials.

Submitted by Guilherme Lemeszenski (guilherme@nead.unesp.br) on 2013-08-22T18:42:26Z No. of bitstreams: 1 S0071-12761982000100001.pdf: 1191475 bytes, checksum: f74a5d1018fb8f443cf0d676694234b3 (MD5) Made available in DSpace on 2013-08-22T18:42:26Z (GMT). No. of bitstreams: 1 S0071-12761982000100001.pdf: 1191475 bytes, checksum: f74a5d1018fb8f443cf0d676694234b3 (MD5) Previous issue date: 1982-01-01 Made available in DSpace on 2013-09-30T19:29:41Z (GMT). No. of bitstreams: 2 S0071-12761982000100001.pdf: 1191475 bytes, checksum: f74a5d1018fb8f443cf0d676694234b3 (MD5) S0071-12761982000100001.pdf.txt: 1968 bytes, checksum: 3962dccec60db941d3cd4bda9203037f (MD5) Previous issue date: 1982-01-01 Submitted by Vitor Silverio Rodrigues (vitorsrodrigues@reitoria.unesp.br) on 2014-05-20T15:08:09Z No. of bitstreams: 2 S0071-12761982000100001.pdf: 1191475 bytes, checksum: f74a5d1018fb8f443cf0d676694234b3 (MD5) S0071-12761982000100001.pdf.txt: 1968 bytes, checksum: 3962dccec60db941d3cd4bda9203037f (MD5) Made available in DSpace on 2014-05-20T15:08:09Z (GMT). No. of bitstreams: 2 S0071-12761982000100001.pdf: 1191475 bytes, checksum: f74a5d1018fb8f443cf0d676694234b3 (MD5) S0071-12761982000100001.pdf.txt: 1968 bytes, checksum: 3962dccec60db941d3cd4bda9203037f (MD5) Previous issue date: 1982-01-01 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. This paper deals with the study of split plot design in balanced incomplete blocks in order to increase the usage of such designs in the agricultural research. The mathematical model adopted was the one traditionally used in the complete design. The presence of constant correlation between two subplots of the same plot and the subplots of distinct plots were considered as well. The estimates of the main treatments adjusted by block effects were analogous to those found in the literature of the balanced incomplete block design, while the other estimates were analogous to the correspondent ones in the split plot randomized block design. UNESP Instituto Básico de Biologia Médica e Agrícola E.S.A. Luiz de Queiroz Departamento de Matemática e Estatística UNESP Instituto Básico de Biologia Médica e Agrícola

A convenient method of introducing into a field experiment additional factors which can be applied to smaller areas than that of the whole plots is to use split plots: each whole plot is split into sections, and the different combinations of the additional factors are randomized over each set of sub-plots. An extension of this idea is the device of split-plot confounding, by which not all the combinations of the additional factors are used in every whole plot; instead, the possible combinations are subdivided into two or more sets which are then assigned to blocks and whole-plot treatments in a balanced manner, in such a way as to confound certain interactions of the additional factors between whole plots and certain higher order interactions between blocks.

Immunologic maturation of the chicken is dependent upon the thymus and the bursa of Fabricius. The bursa is responsible for antibody-mediated immune responses. The thymus is responsible for the cellular type or delayed sensitivity mechanism. A controversy exists as to whether or not thymectomy and/or bursectomy must be followed by X-irradiation (LD50) to insure that no immunologically competent cells exist. It is of fundamental and practical importance. The thymus consists of 5 to 7 paired lobes located bilaterally to the cervical vertebrae. Its removal is tedious, and there are surgical losses. If an LD50 of X-irradiation were not necessary, experiments would require one-half the number of thymectomized chickens, and only normal chickens as controls. Furthermore, uniform irradiation of all chickens is rarely accomplished. The study reported here included four groups of chickens: (i) thymectomized (Tx), (ii) normal (N), (iii) X-irradiated (X) and (iv) thymectomized X-irradiated (Tx-X). Thymectomies-were performed on day old chicks. An LD50 of 800 roentgens of X-irradiation was administered to 3 day old chicks, and by rotation during irradiation, a dosage variable of less than 2% was accomplished. Five blood samples for differential and total counts were collected at intervals up to 5 months of age. The data were analyzed as a split plot because of repeated measurement of each chicken. The results indicate a decrease in total lymphocytes in thymectomized X-irradiated and in thymectomized chickens, not in X-irradiated chickens. Moreover, chickens receiving X-irradiation showed an increase in total number of lymphocytes by 5 months of age. It is concluded that thymectomy of day old chicks results in a long lasting depletion of vascular lymphocytes and that coupling X-irradiation with thymectomy does not result in further depletion of vascular lymphocytes.

A split plot design for the factorial treatment combinations of factors A and B with t and s levels respectively, consists of wholeplots made up of s subplots or experimental units with each level of A applied to r wholeplots and the levels of B applied to the s subplots within each wholeplot. Often this process increases the amount of information for the estimates of the main effect B and the interaction A X B at the expense of information for the main effect A. There may arise situations where the number of subplots in each wholeplot is restricted to say, kc < s. An incomplete split plot design can now be set up with each level of factor A applied to r wholeplots and the s levels of factor B arranged in a balanced incomplete block design within each level of factor A by considering the wholeplots as blocks. That is, on a particular level of factor A each level of factor B occurs R times and each pair of levels of factor B occur in the same wholeplot X times, where R = rk/s and X = R(k l)/(s 1). Here r must be chosen so that the design exists and in some cases this may be so large that it will be impractical. Throughout this paper the wholeplot design will be considered as a conmpletely randomized design. However, it will sometimes be possible to have block designs for the wholeplots, but these will not be considered here.

Split-plot experiments are commonly used in industry for product and process improvement. Recent articles on designing split-plot experiments concentrate on minimum aberration as the design criterion. Minimum aberration has been criticized as a design criterion for completely randomized fractional factorial design and alternative criteria, such as the maximum number of clear two-factor interactions, are suggested (Wu and Hamada (2000)). The need for alternatives to minimum aberration is even more acute for split-plot designs. In a standard split-plot design, there are several types of two-factor interactions, not all of them equally interesting. However, minimum aberration is not designed to distinguish among the different types of two-factor interactions. It should be noted that this criticism is valid not only for the minimum aberration but also for any other design criteria originally proposed for completely randomized designs. Consequently, we provide a modified version of the maximum number of clear two-factor interactions design criterion to be used for split-plot designs.

The main purpose of this study was to evaluate the effect of drought stress on seed yield of some winter rapeseed cultivars and to study relevant drought tolerance indices, along with identifying resistant cultivars to drought stress. Plant materials were sown in split plot arrangement based on a randomized complete blocks design, at Islamic Azad University of Tabriz research field. Three drought stress levels which include 80, 130, and 180 mm water evaporation from class A pan were considered as the main factor levels, while seven winter rapeseed cultivars which include Licord, Okapi, Opera, S.L.M.046, Zarfam, Modena, and Talaye were arranged to sub plots. Studied quantitative drought tolerance indices were, tolerance index (TOL), mean productivity (MP), stress susceptibility index (SSI), stress tolerance index (STI), geometric mean productivity (GMP), yield index (YI), yield stability index (YSI), and percentage of yield reduction (%Reduction). The yield stability analysis of the studied cultivars was done by GGE biplot method. According to the results derived from principal component analysis and regarding evaluation of correlation coefficients among indices, STI and GMP were selected as the two superior indices for identifying drought resistant cultivars. Three dimensional scatter plots based on STI and GMP indices showed that Licord and Talaye were the most suitable cultivars, and were situated in group, A. In addition, Modena and Zarfam were identified as sensitive and resistant to drought stress, respectively.Key words: Brassica napus L, principal component analysis, drought stress, drought tolerance indices, stability analysis (GGE biplot), 3D scatter plot.

Plant growth regulators can influence fruit yield and quality. This study aimed to evaluate the effect of cytokinin and gibberelin on the agronomic and physicochemical characteristics of banana fruits cv. ‘Prata’ (Musa spp. AAB), according to the formation period and position in the bunch. The experiment was conducted in a completely randomized 2 x 5 factorial design, two periods of bunch development (summer and winter), five treatments and ten replicates. To study the effect of position in the bunch, split plot was adopted, considering in the plot, 2 x 5 factorial and in subplots, hand 1, hand 4 and last hand. Treatments consisted of 2 pulverizations with water, 150 mg L-1 cytokinin, 200 mg L-1 of gibberellic acid, 100 mg L-1 of cytokinin plus 200 mg L-1 of gibberellic acid and 200 mg L-1 of cytokinin plus 200 mg L-1 of gibberellic acid, applied from the fourth to the last hand of the bunch. Cytokinin and gibberellin, alone or associated, regardless of formation period and position, did not affect the size and physicochemical characteristics of fruits, only delayed the bunch harvest. RESUMO Reguladores vegetais podem influenciar na produção e na qualidade do fruto. O objetivo do estudo foi avaliar o efeito de citocinina e giberelina nas características agronômicas e físico-químicas de frutos de banana ‘Prata’ (Musa spp. AAB), em função do período de formação e posição no cacho. Adotouse o delineamento inteiramente casualizado, em esquema fatorial 2 x 5, dois períodos de formação do cacho (verão e inverno) e cinco tratamentos e dez repetições. Para estudo do efeito da posição no cacho, adotaram-se parcelas subdivididas, considerando na parcela o esquema fatorial 2 x 5, e na subparcela, a penca 1, penca 4 e última penca. Foram duas pulverizações com água, 150 mg L-1 de cinetina, 200 mg L-1 de ácido giberélico (AG3), 100 mg L-1 de cinetina mais 200 mg L-1 de AG3 e 200 mg L-1 de cinetina mais 200 mg L-1 de AG3, da quarta penca até a última penca do cacho. Citocinina e giberelina, isoladas ou associadas, independentemente do período de formação e posição, não afetam o tamanho e as características físico-químicas do fruto, apenas atrasam a colheita do cacho.

Three separate sources provide incomplete information on the computer analysis of the split-plot factorial analysis of variance. Illustrative data are used to point out the mathematical and logical inconsistencies that arise from this deficiency.

Highlight: An Atriplex canewelts introduced to Iran and two weighed and recorded separately. This study was continued for about native species, Artemisiu herba alba and Kochiaprostrata, were fed 1 year. to sheep throughout a year to determine the comparative palataFor the statistical analysis, the analysis of variance was made on the bility of theAtriplex. The Kochia has the highest and Artemisia has mean grams used data, calculated from data for each species, amount, the lowest palatability when provided at two amounts on adjacent and lot summed over the days the study was conducted. The design days. Atriplex is of intermediate palatability in comparison with was a randomized block with amount on adjacent days as a split plot. the two native species. Significance was based on 95% probability.

The terms “split plot” and “repeated measures” are used by many authors throughout the statistical literature. However, the former is not used in a consistent manner, since many authors use this term in reference to inherently different experimental situations, each requiring a different analysis. Conversely, quite often inherently different experiments share a common analysis, as is the case with some types of split-plot and repeated measures experiments. Four distinct analyses are employed by various authors when describing split plot and repeated measures experiments in the classic literature. Four linear models, accounting for the four analyses, are stated in this article. Detailed examples are given that illustrate the relationships between experimental setup, model specification, and subsequent analysis.

In diallel cross experiments with reciprocal crosses present, crosses with the same maternal line are sometimes planted together or otherwise segregated. The results of Griffing (1956) for tho analysis of dianel cross experiments in randomized blocks are extended to give an analysis for this split-plot situation.

Occasionally statisticians are confronted with data arising from a complex experimental design and not necessarily satisfying the traditional assumptions of analysis of variance; namely those of independence, variance homogeneity, and normality. Sometimes the analyst handles such situations by adjusting the data with transformations or by discarding certain extreme observations, etc. Although this may often lead to a satisfactory analysis, the results may be questionable in some cases. The purpose of this paper is to show that non-parametric methods provide realistic alternatives in analyzing such data. The procedures to be discussed are based on ranks. As such, they are valid under fairly general conditions and have good power properties. Moreover, they involve reasonably simple calculations describable with algorithms, for which computer programs are available.

A random error component is ilntroduced into linear models for analyzing data from designed experiments. This error component is called a 'restriction error' because it is used whenever a restriction on randomization occurs in the design. Discussion of the usefulness of this restriction error in randomized complete block designs, nested factorials, and split plot designs is given. Accompanying each discussion is an example of an experiment on prosthetic cardiac valves. Further, the restrictioin error concept is used to look at the controversy regarding a pooled split plot error.

A crucial question in the analysis of split-plot experiments is whether or not the interaction between subplot treatments and replications should be pooled with the three-factor interaction of main-plot treatments, subplot treatments, and replications, the result being called subplot error. A brief history of the disagreement over this question is given, along with a rule for deciding, on the basis of a preliminary test of significance, whether or not to pool. Several numerical examples are cited, and one of these is worked out in detail.

The rapid developments in the field of experimental design have provided many designs which appear to be extremely complicated. It seems desirable to publish examples of the use of various designs so that other research men will have the benefit of knowing how the design actually worked in practice. It is the purpose of this paper to present an example of the use of a complex design in vegetable crops research. The reasons for the choice of the design and the various steps involved in the analysis and interpretation of the data are given in sufficient detail so that the non-statisticians will be able to utilize such a design. One of the major projects of the Long Island Vegetable Research Farm is the determination of the fertilizer requirements of the various vegetable crops including potatoes. Recommendations have been made for fertilizing potatoes, but the advent of extensive irrigation of potatoes on Long Island raised the question as to how much difference there would be in fertilizer requirements of potatoes under irrigated conditions compared to potatoes grown without irrigation. Many new varieties of potatoes have been recently introduced and preliminary information indicated that some of the newer varieties had fertilizer requirements which differed considerably from the requirements of the standard varieties in use on Long Island. The specific problem for which this experiment must furnish an answer could be stated as follows: "What influence does irrigation have on the nitrogen, phosphorus, and potash requirements of different varieties of potatoes grown under Long Island conditions?" Thus there were five factors to be investigated, namely irrigation, nitrogen, phosphorus, potash and variety.

Background Bolting reduces the quality and commercial yield of Welsh onion (Allium fistulosum L.) in production. However, seed production is directly dependent on flower induction and bolting. The Welsh onion belongs to the green plant vernalisation type, specific seedling characteristics and sufficient accumulated time at low temperature are indispensible for the completion of its vernalisation process. Only if these conditions for vernalisation are fulfilled, the plants will bolt in the following year. The present investigation evaluated the effects of cultivar, sowing date and transplant location in field on the bolting of Welsh onion at the Horticultural Farm of the College of Horticulture, Northwest A&F University, Yangling, Shannxi Province, China in two succeeding production years: 2010–2011 and 2011–2012. A strip split plot layout within a randomised complete block design with three replications was used. Results The results revealed that all three factors (cultivar, sowing date and transplant location) and their interaction had significant effects on the initiation and final rate of bolting observed by 30 April. The earliest bolting date (14 February, 2011 and 15 February, 2012) and the highest bolting rate (100% in 2011 and 62% in 2012) occurred when the JinGuan cultivar was sown on 20 August and transplanted in a plastic tunnel, whereas the latest date and lowest rate (no bolting observed until 30 April) of bolting occurred when the XiaHei cultivar was sown on 29 September and transplanted in an open field. Conclusions These results suggest that we can control bolting in Welsh onion production by choosing an appropriate cultivar, sowing date and transplant location. Choosing a late bolting cultivar, such as cultivar XiaHei, sowing around October, and transplanting in the open field can significantly delay bolting, while a sowing date in late August should be selected for seed production, and the seedlings should be transplanted in a plastic tunnel to accelerate development of the flower buds.