Frederico Pimentel Gomes

Técnica de amostragem para comparar o dano causado pela lagarta-da-espiga, Heliothis zea (Boddie), em cultivares de milho

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 Agronomico, Campinas, State of Sao Paulo, Brazil. The treatments were: cultivar Asteca Prolifico 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.

Amostragem para estudos de resistência de milho a Sitophilus zeamais motschulsky

A study was made to determine the adequate sample size for research on corn resistance to maize weevil, Sitophilus zeamais Motschulsky. To evaluate the damage, the techniques described by Wiseman et alii and by Davis et alii were used. The relative merits of these two methods are discussed. The criteria used to select the sample size was such that a difference between two treatments of ten percent and of twenty percent of the overall mean should be detected by the statistical test, and that each treatment mean could be estimated with a standard error of 0.10 y or 0.20 y. The data were obtained from two laboratory experiments, in 1978/79, and 1979/80, at Instituto Agronomico, Campinas, State of Sao Paulo, Brazil. The treatments were: cultivar Asteca Prolifico VRPE VII, which is resistant to Sitophilus zeamais, Hmd 7974, a susceptible double hybrid; cultivar Maya XVI and HS 7777. A randomized complete block design with ten replications was used and each plot consisted of five rows of ten ears. The variance components method was used to define the type of sampling. The following minimum sample sizes can be used to detect differences of ten percent of the overall mean, between two treatments means: 6 blocks with 6 rows of 10 ears for the Wiseman method and 10 blocks with 6 rows of 10 ears for the Davis method of evaluation. To detect differences of 0.20 y, it can be used 6 blocks with 2 rows of 7 ears for Wiseman method and 6 blocks with 1 row of 10 ears for the Davis method of evaluation. According to each method of damage evaluation the following minimum sample sizes can be used for estimating the mean damage with 0.10 y as the half confidence interval: a) by Wiseman method, 270 ears for cultivar Asteca, and 70 ears for the cultivars Maya, Hmd 7974 and HS 7777; b) by Davis method, 450 ears for cultivar Asteca, and 300 ears for the other three cultivars. To estimate the mean damage with a 0.20 y as the half confidence interval it can be used: a) by Wiseman method, for cultivar Asteca, 5 blocks with 2 rows of 6 ears; for cultivars Hmd 7974, HS 7777 and Maya, 5 blocks with 2 rows of 3 ears; b) by Davis method, for cultivar Asteca, 5 blocks with 3 rows of 6 ears and for the other three cultivars, 5 blocks with 2 rows of 5 ears.

O regime de chuvas em Pesqueira

The authors studied the rainfall in Pesqueira (Pernambuco, Brasil) in a period of 48 years (1910 through 1957) by the method of orthogonal polynomials, degrees up to the fourth having been tried. None of them was significant, so that it seems that no trend is present. The mean observed was 679.00 mm., with standard error of the mean 205.5 mm., and a 30.3% coefficient of variation. The 95% level of probability would include annual rainfall from 263.9 up to 1094.1mm.

Determinação da média aritmética e desvio padrão de quocientes de séries independentes e dependentes

The authors prove some approximate formulas for the computation of the mean and the standard error of quotients of two variates, correlated or uncorrelated, with not too high coefficient of variation. The formulas obtained are subsequently applied to some date on mensuration of horses of the Brazilian breed Mangalarga, by the eclectic system of LESBRE. The relsults obtained directly by the actual computation of the quotients as well as by means of the formulas with the aid of statistics of the numerators and the denominators are given in table 3, showing excellent agreement.

Dois teoremas sôbre a função gama

This paper proves the following theorems on the gamma function: Theorem I The integral ∫O∞ tu e-t dt = Γ ( u + 1 ) , where u, real or complex, is such that R (u) > -1, will not change its value if we substitute z = Q (cos φ + i sen φ) for the real variable t, being jconstant and such that - Π/2 < φ < Π/2 , Theorem II The integral ∫-∞∞ w2u + 1 e -w2 dw = Γ ( u + 1 ) , where 2u + 1 is supposed to be a non negative even integer, will not change its value if we substitute z = w + fi, f being a real constant, for the real variable w. The proof of both theorems is obtained by means of the well known Cauchy theorem on contour integrals on the complex plane, as suggested by CRAMER (1, p. 126) and LEVY (3, p. 178).

A estimação do efeito residual de fertilizantes por meio da Lei de Mitscherlich

This paper deals with the estimation of the residual effect of fertilizers through the use of Mitscherlichs law. The formulas and reasonings now presented are a further development of those introduced previously by PIMENTEL GOMES (2). The new formulas allow the estimation of the residual effect h in cases where the experiments are carried out in the same plots for two or three subsequent years (or crops). In an experiment analysed as an example, the residual effect of calcium hydroxide was estimated to be h = 0.423, that is, about 42%, so that one should advise the use of frequent application of small amounts of lime instead of heavy quantities used at long intervals.