Tests of sunspot number sequences: 1. Using ionosonde data

More than 70 years ago it was recognised that ionospheric F2-layer critical frequencies [foF2] had a strong relationship to sunspot number. Using historic datasets from the Slough and Washington ionosondes, we evaluate the best statistical fits of foF2 to sunspot numbers (at each Universal Time [UT] separately) in order to search for drifts and abrupt changes in the fit residuals over Solar Cycles 17-21. This test is carried out for the original composite of the Wolf/Zürich/International sunspot number [R], the new “backbone” group sunspot number [RBB] and the proposed “corrected sunspot number” [RC]. Polynomial fits are made both with and without allowance for the white-light facular area, which has been reported as being associated with cycle-to-cycle changes in the sunspot number - foF2 relationship. Over the interval studied here, R, RBB, and RC largely differ in their allowance for the “Waldmeier discontinuity” around 1945 (the correction factor for which for R, RBB and RC is, respectively, zero, effectively over 20 %, and explicitly 11.6 %). It is shown that for Solar Cycles 18-21, all three sunspot data sequences perform well, but that the fit residuals are lowest and most uniform for RBB. We here use foF2 for those UTs for which R, RBB, and RC all give correlations exceeding 0.99 for intervals both before and after the Waldmeier discontinuity. The error introduced by the Waldmeier discontinuity causes R to underestimate the fitted values based on the foF2 data for 1932-1945 but RBB overestimates them by almost the same factor, implying that the correction for the Waldmeier discontinuity inherent in RBB is too large by a factor of two. Fit residuals are smallest and most uniform for RC and the ionospheric data support the optimum discontinuity multiplicative correction factor derived from the independent Royal Greenwich Observatory (RGO) sunspot group data for the same interval

Specific residue: application of orthogonal contrasts when heteroscedasticity is present Resíduo específico: aplicação de contrastes ortogonais na presença da heterocedasticidade

When experimental data are submitted to analysis of variance, the assumption of data homoscedasticity (variance homogeneity among treatments), associated to the adopted mathematical model must be satisfied. This verification is necessary to ensure the correct test for the analysis. In some cases, when data homoscedascity is not observed, errors may invalidate the analysis. An alternative to overcome this difficulty is the application of the specific residue analysis, which consists of the decomposition of the residual sum of squares in its components, in order to adequately test the correspondent orthogonal contrasts of interest between treatment means. Although the decomposition of the residual sum of squares is a seldom used procedure, it is useful for a better understanding of the residual mean square nature and to validate the tests to be applied. The objective of this review is to illustrate the specific residue application as a valid and adequate alternative to analyze data from experiments following completely randomized and randomized complete block designs in the presence of heteroscedasticity.<br>Ao realizar-se a análise da variância de um conjunto de dados, pressupõe-se que o critério de homocedasticidade (homogeneidade de variâncias entre tratamentos), associada ao modelo matemático adotado, seja satisfeito. Esta verificação se faz necessária para a correta aplicação dos testes de significância. Quando não é satisfeita, em certos casos, compromete a normalidade dos erros. Uma alternativa para contornar essa deficiência é a aplicação do resíduo específico, que consiste em decompor a soma de quadrados do resíduo em componentes, correspondentes aos contrastes ortogonais de interesse, apropriados para testar cada contraste ortogonal entre médias de tratamentos. A decomposição da soma de quadrados do resíduo é um procedimento pouco utilizado, mas é útil para melhor compreensão da natureza do quadrado médio residual e garantir a validade dos testes aplicados. Nessa revisão avaliou-se a aplicação dos resíduos específicos como alternativa válida e adequada, na análise de dados obtidos de experimentos que seguem a estrutura dos delineamentos inteiramente casualizados e em blocos casualizados, na presença da heterocedasticidade

Técnica de amostragem para comparar o dano causado pela lagarta-da-espiga, Heliothis zea (Boddie), em cultivares de milho Sampling techniques to compare the damage by Heliothis zea (Boddie) in corn varieties

Neste trabalho, realizado no Instituto Agronômico, determinou-se o tamanho da amostra para estudos de danos causados pela lagarta-da-espiga, Heliothis zea (Boddie), avaliados pelo método de Widstrom. Foram utilizados dados de dois experimentos de campo, com um cultivar resistente (Asteca Prolífico VRPE VII), um suscetível (híbrido duplo IAC Hmd 7974), o 'Maya XVI' e o híbrido simples HS 7777, em 1978/79 e 1979/80. O critério para estimar o tamanho da amostra foi de que esse tamanho permitisse detectar uma diferença de 10 ou de 20% da média geral entre médias de danos, em cultivares de milho, e avaliar o dano médio por cultivar com erro-padrão de 10 ou de 20% da média. Para definir o processo de amostragem, utilizou-se o método de componentes de variância, estimados a partir de dois modelos matemáticos. O tamanho da amostra foi bastante variável entre cultivares, sendo maior no resistente. Entre os possíveis tamanhos mínimos de amostra para detectar uma diferença de 10% da média geral entre médias de danos de tratamentos, podem ser utilizados seis blocos com quatro linhas de 24 plantas; para uma diferença de 20% de média, cinco blocos com três linhas de seis plantas são suficientes. Para estimar a média de danos por cultivar, com erro-padrão de 10% de média, são necessários sete blocos com quatro linhas de 30 plantas, no cultivar Asteca, e cinco blocos com duas linhas de 24 plantas nos cultivares Hmd 7974, HS 7777 e Maya e, com erro-padrão de 20% de média, cinco blocos de três linhas com doze plantas, no 'Asteca', e cinco blocos com duas linhas de seis plantas nos demais cultivares.<br>A study was made to determine the sample size for research on corn resistance to corn ear worm Heliothis zea (Boddie). The damage was measured using the Widstrom centimeter scale. The criteria used to select the sample sizes were such that a difference between two treatments of ten percent or twenty percent of the overall mean should be detected by the statistical test, and that each treatment mean can be estimated with a standard error of 0.10 y or a standard error of 0.20 y. The data were obtained from two field experiments, carried out in Instituto Agronômico, Campinas, State of São Paulo, Brazil. The treatments were: cultivar Asteca Prolífico VRPE VII, which is resistant to Heliothis zea; Hmd 7974, a susceptible double hybrid; cultivars Maya XVI and HS 7777. A randomized complete block design with ten replicates was used, and each plot consisted of four rows with 50 plants per row. The variance components method was used to define the type of sampling. The most important variance component was due to the variability among units within rows. The following minimum sample sizes can be used to detect the difference between two means: 6 blocks with 4 rows of 24 plants for a difference of 0.10 y and 5 blocks with 3 rows of 6 plants for a difference of 0.20 y. For estimating the mean damage with 0.10 y as the half confidence interval on the mean of the population, the following minimum sample sizes can be used: for cultivar Asteca, 7 blocks with 4 rows of 30 plants per row; for the hybrids Hmd 7974, HS 7777 and cultivar Maya, 5 blocks with 2 rows of 24 plants per row. If a 0.20 y is specified, as the half confidence interval on the mean, it can be used 5 blocks with 3 rows of 12 plants for cultivar Asteca and 5 blocks with 2 rows of 6 plants for the other three cultivars