RCAAP Repository

The main object of the present paper consists in giving formulas and methods which enable us to determine the minimum number of repetitions or of individuals necessary to garantee some extent the success of an experiment. The theoretical basis of all processes consists essentially in the following. Knowing the frequency of the desired p and of the non desired ovents q we may calculate the frequency of all possi- ble combinations, to be expected in n repetitions, by expanding the binomium (p-+q)n. Determining which of these combinations we want to avoid we calculate their total frequency, selecting the value of the exponent n of the binomium in such a way that this total frequency is equal or smaller than the accepted limit of precision n/pª{ 1/n1 (q/p)n + 1/(n-1)| (q/p)n-1 + 1/ 2!(n-2)| (q/p)n-2 + 1/3(n-3) (q/p)n-3... < Plim - -(1b) There does not exist an absolute limit of precision since its value depends not only upon psychological factors in our judgement, but is at the same sime a function of the number of repetitions For this reasen y have proposed (1,56) two relative values, one equal to 1-5n as the lowest value of probability and the other equal to 1-10n as the highest value of improbability, leaving between them what may be called the "region of doubt However these formulas cannot be applied in our case since this number n is just the unknown quantity. Thus we have to use, instead of the more exact values of these two formulas, the conventional limits of P.lim equal to 0,05 (Precision 5%), equal to 0,01 (Precision 1%, and to 0,001 (Precision P, 1%). The binominal formula as explained above (cf. formula 1, pg. 85), however is of rather limited applicability owing to the excessive calculus necessary, and we have thus to procure approximations as substitutes. We may use, without loss of precision, the following approximations: a) The normal or Gaussean distribution when the expected frequency p has any value between 0,1 and 0,9, and when n is at least superior to ten. b) The Poisson distribution when the expected frequecy p is smaller than 0,1. Tables V to VII show for some special cases that these approximations are very satisfactory. The praticai solution of the following problems, stated in the introduction can now be given: A) What is the minimum number of repititions necessary in order to avoid that any one of a treatments, varieties etc. may be accidentally always the best, on the best and second best, or the first, second, and third best or finally one of the n beat treatments, varieties etc. Using the first term of the binomium, we have the following equation for n: n = log Riim / log (m:) = log Riim / log.m - log a --------------(5) B) What is the minimun number of individuals necessary in 01der that a ceratin type, expected with the frequency p, may appaer at least in one, two, three or a=m+1 individuals. 1) For p between 0,1 and 0,9 and using the Gaussean approximation we have: on - ó. p (1-p) n - a -1.m b= &#948;. 1-p /p e c = m/p } -------------------(7) n = b + b² + 4 c/ 2 n´ = 1/p n cor = n + n' ---------- (8) We have to use the correction n' when p has a value between 0,25 and 0,75. The greek letters delta represents in the present esse the unilateral limits of the Gaussean distribution for the three conventional limits of precision : 1,64; 2,33; and 3,09 respectively. h we are only interested in having at least one individual, and m becomes equal to zero, the formula reduces to : c= m/p o para a = 1 a = { b + b²}² = b² = &#948;2 1- p /p }-----------------(9) n = 1/p n (cor) = n + n´ 2) If p is smaller than 0,1 we may use table 1 in order to find the mean m of a Poisson distribution and determine. n = m: p C) Which is the minimun number of individuals necessary for distinguishing two frequencies p1 and p2? 1) When pl and p2 are values between 0,1 and 0,9 we have: n = { &#948; p1 ( 1-pi) + p2) / p2 (1 - p2) n= 1/p1-p2 }------------ (13) n (cor) We have again to use the unilateral limits of the Gaussean distribution. The correction n' should be used if at least one of the valors pl or p2 has a value between 0,25 and 0,75. A more complicated formula may be used in cases where whe want to increase the precision : n (p1 - p2) &#948; { p1 (1- p2 ) / n= m &#948; = &#948; p1 ( 1 - p1) + p2 ( 1 - p2) c= m / p1 - p2 n = { b2 + 4 4 c }2 }--------- (14) n = 1/ p1 - p2 2) When both pl and p2 are smaller than 0,1 we determine the quocient (pl-r-p2) and procure the corresponding number m2 of a Poisson distribution in table 2. The value n is found by the equation : n = mg /p2 ------------- (15) D) What is the minimun number necessary for distinguishing three or more frequencies, p2 p1 p3. If the frequecies pl p2 p3 are values between 0,1 e 0,9 we have to solve the individual equations and sue the higest value of n thus determined : n 1.2 = {&#948; p1 (1 - p1) / p1 - p2 }² = Fiim n 1.2 = { &#948; p1 ( 1 - p1) + p1 ( 1 - p1) }² } -- (16) Delta represents now the bilateral limits of the : Gaussean distrioution : 1,96-2,58-3,29. 2) No table was prepared for the relatively rare cases of a comparison of threes or more frequencies below 0,1 and in such cases extremely high numbers would be required. E) A process is given which serves to solve two problemr of informatory nature : a) if a special type appears in n individuals with a frequency p(obs), what may be the corresponding ideal value of p(esp), or; b) if we study samples of n in diviuals and expect a certain type with a frequency p(esp) what may be the extreme limits of p(obs) in individual farmlies ? I.) If we are dealing with values between 0,1 and 0,9 we may use table 3. To solve the first question we select the respective horizontal line for p(obs) and determine which column corresponds to our value of n and find the respective value of p(esp) by interpolating between columns. In order to solve the second problem we start with the respective column for p(esp) and find the horizontal line for the given value of n either diretly or by approximation and by interpolation. 2) For frequencies smaller than 0,1 we have to use table 4 and transform the fractions p(esp) and p(obs) in numbers of Poisson series by multiplication with n. Tn order to solve the first broblem, we verify in which line the lower Poisson limit is equal to m(obs) and transform the corresponding value of m into frequecy p(esp) by dividing through n. The observed frequency may thus be a chance deviate of any value between 0,0... and the values given by dividing the value of m in the table by n. In the second case we transform first the expectation p(esp) into a value of m and procure in the horizontal line, corresponding to m(esp) the extreme values om m which than must be transformed, by dividing through n into values of p(obs). F) Partial and progressive tests may be recomended in all cases where there is lack of material or where the loss of time is less importent than the cost of large scale experiments since in many cases the minimun number necessary to garantee the results within the limits of precision is rather large. One should not forget that the minimun number really represents at the same time a maximun number, necessary only if one takes into consideration essentially the disfavorable variations, but smaller numbers may frequently already satisfactory results. For instance, by definition, we know that a frequecy of p means that we expect one individual in every total o(f1-p). If there were no chance variations, this number (1- p) will be suficient. and if there were favorable variations a smaller number still may yield one individual of the desired type. r.nus trusting to luck, one may start the experiment with numbers, smaller than the minimun calculated according to the formulas given above, and increase the total untill the desired result is obtained and this may well b ebefore the "minimum number" is reached. Some concrete examples of this partial or progressive procedure are given from our genetical experiments with maize.

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A presente experiência foi realizada afim de se constatar a influência de dois tipos de milho comerciais, com grãos coloridos de amarelo-laranja, como precursores de vitamina A no crescimento de pintos. Um deles, denominado "Cateto", duro, de côr laranja muito forte e outro, chamado "Armour", dente, de coloração amarelo-laranja. Para testemunha foi empregado o milho "Cristal", duro e branco. Uma análise dos pigmentos dos dois tipos de milho com gráos coloridos mostrou que o milho Cateto, com grãos de coloração laranja forte, tem aproximadamente o dobro de pigmentos, tanto total como quanto a parte ativa em relação à vitamina A, quando comparado com o milho dente amarelo-laranja. Três lotes de pintos de 3 semanas foram utilizados, cada um recebendo a mesma ração onde variava somente o tipo de milho. Nas três primeiras semanas os três lotes reagiram bem, sem quaisquer diferenças apreciáveis. Após a terceira semana, o lote que recebeu milho branco apresentou uma queda sensível de peso dos pintos, os quais apresentaram todos os sinais de avitaminose A. Os outros dois lotes que receberam ração contendo milho de grãos coloridos não apresentaram sinal de avitaminose A. Os resultados obtidos indicam assim que a) o milho "Armour", dente, de grãos amarelo-laranja, embora possua, em relação ao milho "Cateto", duro, de grãos coloridos de laranja forte, cerca da metade da quantidade de pigmentos ativos em relação a formação de vitamina A no organismo animal, é capaz de prevenir a avitaminose, quando empregado em cerca de 70% da ração, b) que a ração contendo o milho "Cristal", duro, de grãos brancos, é deficiente, produzindo uma acentuada avitaminose A, que deverá ser corrigida, na falta de milho de grãos amarelo-laranja, por alimento verde ou outro alimento fornecedor dessa vitamina e c) que sendo o milho "Cateto", mais caro de Cr.$2,00 a 8,00 por saco de 60 quilos, há vantagem econômica no emprego do milho tipo "Armour" na constituição das misturas para aves.

Este trabalho foi feito afim de determinar uma hipotética correlação existente entre a forma do ôvo e o sexo do pinto. Dois métodos foram utilizados. No primeiro considerou-se apenas a "ponta" do ôvo, dividindo-se um lote de 1100 ovos em dois grupos, um considerado ponteagudo e outro arredondado. Os resultados totais mostraram a nenhuma influência da forma da ponta na determinação do sexo, isto é, a falta de correlação era completa. No segundo método, determinou-se a média da relação entre a largura e o comprimento do ôvo, e adotou-se essa medida como linha divisória de dois grupos : um de ovos grossos com 223 ovos e outro de ovos finos, com 183 ovos. A relação sexual foi respectivamente de 38.60 e 37.07 o que mostra a falta de correlação. Os dez ovos mais compridos e os dez mais redondos, incubados separadamente, confirmaram os resultados anteriores. A determinação do sexo dos pintos foi feita pelo método de JAAP, aperfeiçoado nesta Seção. O Autor conclui, que na população estudada, da raça Rhode I. Red, não existe absolutamente a menor correlação entre a forma do ôvo e o sexo do pinto que êle possa determinar. Acredita que essas conclusões possam se aplicar a todas as variedades industriais, mas acha possível, que em raças muito antigas não provenientes de cruzamentos, talvez nalguma raça de briga, tal correlação possa existir.

The three species studied have 19 chromosomes, being one heterochromosome, one pair of microchromosomes and 8 pairs of autosomes. The microchromosomes of Hypselonotus fulvus are amongst the largest we know. During the synizesis, in Hypselonotus fulvus, we can see in several strands that scape from the chromatic knot a place in which they are widley open. As, in that phase the chromosomes have both ends converging to the same place, the openings suggest a side-to-side pairing of the chromosomal threads. The tetrads are like that studied by Piza (1945-1946). The bivalents are united side by side at their entire length. The unpaired part at the midle of the bivalents gives origin to the arms of the cross-shapede tetrads. The chromosomes have a kinetochore at each end. The bivalents sometimes unite their extremities to form ring-shaped figures, which open themselves out before metaphase. The tetrads are oriented parallelly to the spindle axis. At telophase the kinetochores repeli one another, the chiasmata, if present, slip toward the acentric extremities and the chromosomes rotate in order to arrange themselves parallelly to the axis of the new spindle. Separation is therefore through the pairing plane. In the spermatogonial anaphase of Hypselonotus subterpunctatus the chromosomes are curved to the poles, like those described by PIZA (1946) and PIZA and ZAMITH (1946). The sex chromosomes in Hypselonotus interruptus and Hypselonotus fulvus appears longitudinally divided. It is oriented with the ends in the plane of the equator and its chomatids separate by the plane of division. In the second division the sex chromosome, provided as it is with an actve klnetochore at each end, orients itself with its length parallelly to the spindle axis and passes undivided to one pole. Sometimes it is distended between the poles. This corresponds to case (a) established by PIZA (1946) for the sex chromosomes of Hemiptera In Hypselonotus subterpunctatus the sex chromosome, in the first division of the spermatocytes, orients like the tetrads and divides transversaly. In the second division, as its kinetochore becomes inactive, it remans monocentric, does not orient in the spindle, and is finally enclosed in the nearer nucleus. In the secondary telophase it recuperates its dicentricity like the autosomal chromatids. This behavior corresponds to case (c) of PIZA (1946).

La connaissance de la puissance nécessaire au broyage de la canne à sucre, est d'une très grande importance, tant pour les fabricants de moulins, que pour l'usinier et le téchnicien. Les auteurs en se réferant au procédé utilise par LEHKY dans le calcul de la puissance des moteurs destines aux moulins des usines de sucre: 1.° - expliquent la deduction des formules presentées par le remarcable ingénieur des Establissements Skoda; 2.° - modifient le facteur 1,305 de la formule originale employee dans le calcul de la puissance nécessaire pour vaincre le frottement de la bagassière par 1,2987, quand on considère la vitesse lineaire des cylindres en mètres par minute; 3.° - presentent des exemples numériques de l'application directe des formules pour differentes types de moulins. démontrant que le procèdé utilise para LEHKY est pratiquement applicable à n'importe quel moulin.

Studying the application of those methods of microanalysis which avoid costly instalations and atempting to combine high precision with low cost, the author recomends a new method consisting of the following : a) exposure of a surface of 530.66 mm2 of Zn to the action of the acid. b) instalation of 3 series of HgBr2 paper in test tubes with an internal diameter of respectively 3,5 and 9 mm. c - mouting between two slides, covering the margins (with parafin etc.) with parafin in order to conserve the results of the determination without change due to the action of light or moisture. d) the results can be compared at a level of 0.00001 mgr. A203 or 0.000007575 mgr. As.

The effect of different feeds in comparison with that of maize grains on the egg yolk color was observed. It was found that deep orange and yellow orange maize give satisfactory coloration to the yolk, respectively orange and yellow. The most intense color was observed when green feed was used in combination with deep orange maize. Green feeds as chicory, alfafa, cabbage, welsh onion and banana leaves and alfafa or chicory meal proved to be good in giving orange color to the yolk. Yellow yolk was obtained when Guinea grass or carica fruit were used in the ration. Carrot and beet without leaves did not give satisfactory color to the egg yolk. The observations with other feeds are being continued.

This paper refers to sex differentiation in one day chicks of the Rhode Island Red Breed, which has been selected by the laying capacity in the flock pertaining to the Escola Superior de Agricultura "Luiz de Queiroz". The A., taking as a basis the light staining of the anterior edge of the wing, the fair ring of down of the chick leg, immediately a bove the tibiotarsic joint, and dark spot that occurs sometimes near the posterior angle of the eye, besides other characters of minor importance, was able to separate correctly 197 out of 201 chicks, what represents 98,01% of the total number.

This paper deals with the results obtained in one experiment with rabbits, made in order to see which treatment should be the best one against ear canker. Five treatments, each one with 3 rabbits, were tried : Detefon, Insect-o-Blitz, Turpentine with oil, DDT with 10% of vaseline and Kerozene. The best results were obtained with DDT-10% and vaseline-90% which proved to be more efficacious, saving the animals quickly than the other treatment.

Size and shape in eggs of Rhode Island Red and Light Sussex breeds and in the hibrid Rhode x Sussex were studied. These characters are influenced by quantitative genes. Major and minor diameter were used for estimating size of the eggs and the ratio minor/major diameter for shape indice. It was found, in the material analyzed, that: a) the eggs laid by the sa- me chick are pratically uniform; b) the correlation coeficient between major and minor diameter is weak; c) Rhode Island Red has short eggs than Light Sussex; d) short eggs is dominant on long eggs; e) egg shape is the same in Rhode Island Red and Light Sussex breeds and different in the hibrid, which has rounder eggs than the breeds.

Three years of observations on Light Sussex breed conducted at the Poultry Departament of "Luiz de Queiroz" School of Agriculture are reported in this paper. The breed was compared mainly with the Rhode Island Red and the following conclusion obtained : The Light Sussex is fast growing, early maturing heavier, fine fleshed, more persistent and with greater dutchs. greater groodiness and lays larger eggs. The breed shows quality of adaptation being recommended for town or farm flocks in the same way generally used in England. Exceptionally could be recommended for commercial flocks.

In the present paper the author gives the final results of his studies about the significance of the two annex cells of the stomata of the Rubiaceae as anatomical family character, part of which has been previously published. After having verified that in the Order Rubiales the Family Rubiaceae is the unique to show stomata provided with two annex cells differing in size and shape, the author has extended his observation over 553 species belonging to 107 genera, having not found till the present time a single discrepant case. Even though in the future some species not yet investigated come to show stomata devoid of ajinex cells, even In this case the annex cells do not lose their importance at least as specific or generic character. However, the author is inclined to consider, on the light of-the facts in hand, the two annex cells of the Rubiaceae stomata as good anatomical family character.

The breeds Light Sussex, Rhode Island Red and the hibrid Light Sussex x Rhode Island Red, from the Poultry Department of "Luiz de Queiroz" School of Agriculture, at Piracicaba, S. Paulo, were studied in this paper, Tre authors, analysing eggs, pullets and chick growing arrived to the following conclusion: a) eggs of the Light Sussex breed were haevier; b) the Light Sussex breed was early maturing; c) the cross studied did not show hibrid vigor.

A test was conducted at Poultry Department of "Luiz de Queiroz" School of Agriculture to prove the effect of green feed on egg production. One hundred Rhode Island Red hens at plain laying period were divided in ten pens. The lot A was constituted of pens 1 to 5 and the lot B of pens 6 to 10. During 16 days the pens 1 to 5 did not receive green feed and the pens 6 to 10 received it with abundance. After and for a period of 30 days the situation was inverted. The analysis were made considering, a) the production of all chickens and b) discarding the chickens with irregular laying. In both cases the results were statistically insignificant, proving that green feed did not improve egg production.

The author studied in this paper the substitution of a balanced ratio for an economic ratio composed of 50% of sugar beet and 50% of balanced ratio, in feeding ducks egg production. It was found that the combination had no advantage since the production of eggs was very much reduced.

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The main object of the paper is a revision of the methods for the statistical analysis of qualitative variation in small samples. In general, this analysis is carried out by means of two tests, which are mathematically different, but give identical statistical results : the analysis of relative deviates, i.e. of te quotients between the deviate of the observed frequency, with regerds to the expected frequency divided by its standard error, or an analysis using the X2-test. We must distinguish, in our discussion, two cases, which are quite different. The basic distribuition of all cases of qualitative variation is the binomial. If we expect any qualitative result to occur with probability p ,its non-occurence having probability q equal to (1-p>;, the expectancy to have, 0, 1, 2... m cases or individuals of the expected type in N trials may be calculated by expanding the binomial. (P + q)N Such a binomial may be substituited by other distributions in two special cases: a) If p is very small and thus q is aproaching the value one, we may substitute the binomial by a Poisson series. b) If the exponent N becomes very large, the binomial is approaching a continous distribution, i.e. the normal or Gaus-sean distribution. Only in the second case, the application of the X2-test is really justified, and in all other cases, we are dealing only with approximations. Indvidual values of X2- should follow a modified distribution of Pearson, with nl = 1; n2 = inf. Since this distributon corresponds exactly to one half of the Gaus-sean dstribution, it follows that the b lateral limits of the latter are equal to the unilateral limits of the former. These points have been explained fully elsewhere (BRIEGER, 1945, 1946). We have row to decide which value of p may be accepted as a satisfactory limit between a Poisson and a binomial series. Quadros 1-3, show that the conventional limit of pr=0,l is fully justified, from a practical point of view. In these tables we find in the second column from the left the frequencies of a Poisson series, and in the second column from the night the values of X2 based, as explained, on a modified Gaussean distribution. The two columns in the centre correspond to two binomials and it is evident that the first with p=0,05 has its limits of precision almost at the same level as the Poisson series, while the other with p=0,l agrees fairly well with the limits of the X2 series. Thus is seems justified to treat separately the cases with expected frequencies of p equal or smaller that 0,1 and those with p larger than 0,1. A) When the different classes, wich may be two (alternative variability) or more (multiple variability, have all expected frequences of p between 0,1 and 0,9, we may use practically the X2 test with out any restriction. Quadros 8 and 9 show that the limits calculated for two binomials are practically identical with those of the X2 total. Nevertheless a special table is given (table 11) for the limits of binomials with p equal 0,5 and 0,25 and expected class frequencies of less than 10. One must not forget that in these cases the individual values of X2 for each class are of less importance than their sum, the X2 total. The value of X2 for each class may be calculated either with the general formula, using actual numbers or with a modified formula using percentages : X² = ( f obs - f esp)² = (f esp - NP)² f esp NP = (f obs - p%)2.N p% 100 In the case of alternative variability, we may calculate directly the value of the X2 total, by squaring the relative deviate : x² total = (f obs - f esp)² = (f obs - Np)² f esp NP = ( f obs % - p %) 2. N p % (100 - p%) B) If we have one or more classes with expected frequencies equal os smaller than 0,1 we have to deal with a Poisson series. As shown in Quadro 7 the agreement between the limits of the Poisson series and the X2-test for one classe (simple X2) is only satisfactory when the expected frequency, is larger than 10 and tolerable when it is between 5 and 10. If the expected number should be smaller still, we cannot use anymore the X2-test, but should use the values given in table I, calculated for Poisson series witr expected frequencies (in numbers) from 1 to 15. Very frequently the X2-test is used for comparing in detail observed and expected distributions, a test called sometimes "homogeneity test". Since generally the frequencies in the marginal classes are less than five, we have to accumulate by summing the frequencies from the more extreme classes towards the center, untill all accumulated and remaining values are at least equal to five. The statistical information, lost in this accumulating process, may be recovered when comparing the individual class frequencies with the limiting values in table 1. As ilustration, a concrete exemple is discussed. (Quadro 10). The formulas and tables of this paper have been tried out first during sometime and, having been found of considerable value in the execution of statistical analysis, are now published. In order to permit a more general use, a table of ordinary limits for the X2-test is included, taken from a recent paper (BRIEGER, 1946).