Ordered probit regression analysis of the effect of brand name on beer acceptance by consumers

Ordered probit regression was used to analyze data of sensory acceptance tests designed to study the effect of brand name on the acceptability of beer samples. Eight different brands of Pilsen beer were evaluated by 101 consumers in two sessions of acceptance tests: blind evaluation and brand information test. Ordered probit regression, although a relatively sophisticated technique compared to others used to analyze sensory data, was chosen to enable the observation of consumers' behavior using graphical interpretations of estimated probabilities plotted against hedonic scales. It can be concluded that brands B, C, and D had a positive effect on the sensory acceptance of the product, whereas brands A, F, G, and H had a negative influence on consumers' evaluation of the samples. On the other hand, brand E had little influence on consumers' assessment.

An outline of military technological dynamics as restraints for acquisition, international cooperation and domestic technological development

The expectation that technological returns from defense expenditure through acquisition, international cooperation and domestic research would further national development underappreciates the different technological dynamic of the armed services. This paper outlines the technological dynamic the stems from fighting in the air, at sea and on land, exemplifying consequences for the case of acquisition.

Incidence and risk factors for intimate partner violence during the postpartum period

OBJECTIVE To estimate the incidence and identify risk factors for intimate partner violence during postpartum.METHODS This prospective cohort study was conducted with women, aged between 18-49 years, enrolled in the Brazilian Family Health Strategy in Recife, Northeastern Brazil, between 2005 and 2006. Of the 1.057 women interviewed during pregnancy and postpartum, 539 women, who did not report violence before or during pregnancy, were evaluated. A theoretical-conceptual framework was built with three levels of factors hierarchically ordered: women’s and partners’ sociodemografic and behavioral characteristics, and relationship dynamics. Incidence and risk factors of intimate partner violence were estimated by Poisson Regression.RESULTS The incidence of violence during postpartum was 9.3% (95%CI 7.0;12.0). Isolated psychological violence was the most common (4.3%; 95%CI 2.8;6.4). The overlapping of psychological with physical violence occurred at 3.3% (95%CI 2.0;5.3) and with physical and/or sexual in almost 2.0% (95%CI 0.8;3.0) of cases. The risk of partner violence during postpartum was increased for women with a low level of education (RR = 2.6; 95%CI 1.3;5.4), without own income (RR = 1.7; 95%CI 1.0;2.9) and those who perpetrated physical violence against their partner without being assaulted first (RR = 2.0; 95%CI 1.2;3.4), had a very controlling partner (RR = 2.5; 95%CI 1.1;5.8), and had frequent fights with their partner (RR = 1.7; 95%CI 1.0;2.9).CONCLUSIONS The high incidence of intimate partner violence during postpartum and its association with aspects of the relationship’s quality between the couple, demonstrated the need for public policies that promote conflict mediation and enable forms of empowerment for women to address the cycle of violence.

Response rate in the Study of Cardiovascular Risks in Adolescents – ERICA

ABSTRACT OBJECTIVE To describe the response rate and characteristics of people who either took part or not in from the Study of Cardiovascular Risks in Adolescents (ERICA) , according to information subsets. METHODS ERICA is a school-based, nation-wide investigation with a representative sample of 12 to 17-year-old adolescents attending public or private schools in municipalities with over 100,000 inhabitants in Brazil. Response rate of eligible subjects were calculated according to macro-regions, sex, age, and type of school (public or private). We also calculated the percentages of replacement schools in comparison with the ones originally selected as per the sample design, according to the types of schools in the macro-regions. The subjects and non-subjects were compared according to sex, age, and average body mass indices (kg/m2). RESULTS We had 102,327 eligible adolescents enrolled in the groups drawn. The highest percentage of complete information was obtained for the subset of the questionnaire (72.9%). Complete information regarding anthropometric measurements and the ones from the questionnaire were obtained for 72.0% of the adolescents, and the combination of these data with the 24-hour dietary recall were obtained for 70.3% of the adolescents. Complete information from the questionnaire plus biochemical blood evaluation data were obtained for 52.5% of the morning session adolescents (selected for blood tests). The response percentage in private schools was higher than the one in public schools for most of the combination of information. The ratio of older and male adolescents non-participants was higher than the ratio among participants. CONCLUSIONS The response rate for non-invasive procedures was high. The response rate for blood collection – an invasive procedure that requires a 12-hour fasting period and the informed consent form from legal guardians – was lower. The response rate observed in public schools was lower than in the private ones, and that may reflect lower school frequency of registered students.

Lymphocyte subpopulations and neutrophil function in chronic human Chagas' disease

The absolute numbers of total leukocytes, lymphocytes, T cells, helper/inducer, suppressor/cytotoxic and B cells were decreased in the peripheral blood of patients with chronic Chagas' disease. Since antilymphocyte antibodies were present only in a minority of patients they probably cannot account for the abnormalities in lymphocyte subsets. Patient neutrophils stimulated with endotoxin-treated autologous plasma showed depressed chemotactic activity and this seems to be an intrinsic cellular defect rather than plasma inhibition. Random migration of neutrophils was normal. Reduction of nitroblue tetrazolium by endotoxin- stimulated neutrophils was also decreased. These findings further document the presence of immunosuppression in human Chagas' disease. They may be relevant to autoimmunity, defense against microorganisms and against tumor cells at least in a subset of patients with more severe abnormalities.

Presence of Circulating Levels of Interferon-g, Interleukin-10 and Tumor Necrosis Factor-a in Patients with Visceral Leishmaniasis

Experimental murine L. major infection is characterized by the expansion of distinct CD4+ T cell subsets. The Th1 response is related to production of IFN-g and resolution of infection, whereas Th-2 response with production of IL-4 and IL-10 and dissemination of infection. The objective of this study was to measure the circulating levels of IFN-g, IL-10 and TNF-a in patients with visceral leishmaniasis (VL) before, during and at the end of therapy and to examine the association between cytokine levels and activity of VL. Fifteen patients with VL were evaluated. The cytokine determinations were done by using the enzyme-linked immunoassay (ELISA) before, during and at the end of therapy. At baseline, we detected circulating levels of IFN-g in 13 of 15 patients (median = 60 pg/ml); IL-10 in 14 of 15 patients (median = 141.4 pg/ml); and TNF-a in 13 of 14 patients (median = 38.9 pg/ml). As patients improved, following antimonial therapy, circulating levels of IL-10 showed an exponential decay (y = 82.34 e–0,10367x, r = –0.659; p < 0.001). IFN-g was no longer detected after 7/14 days of therapy. On the other hand, circulating levels of TNF-a had a less pronounced decay with time on therapy, remaining detectable in most patients during the first seven days of therapy (y = 36.99-0.933x, r = –0.31; p = 0.05). Part of the expression of a successful response to therapy may, therefore, include reduction in secretion of inflammatory as well as suppressive cytokines. Since IL-10 and IFN-g are both detected prior to therapy, the recognized cellular immune depression seen in these patients may be due to biological predominance of IL-10 (type 2 cytokine), rather than lack of IFN-g (type 1 cytokine) production.

The pattern of immune cell infiltration in chromoblastomycosis: involvement of macrophage inflammatory protein-1 alpha/CCL3 and fungi persistence

Chromoblastomycosis (CR) is a subcutaneous chronic mycosis characterized by a granulomatous inflammatory response. However, little is known regarding the pattern of leukocyte subsets in CR and the pathways involved in their recruitment. The objective of this study was to assess the cellular subsets, chemokine, chemokine receptors and enzymes in CR. The inflammatory infiltrate was characterized by immunohistochemistry using antibodies against macrophages (CD68), Langerhans'cells (S100), lymphocytes (CD3, CD4, CD8, CD45RO, CD20 and CD56) and neutrophils (CD15). The expression of MIP-1alpha (Macrophage inflammatory protein-1alpha), chemokine receptors (CXCR3 and CCR1) and enzymes (superoxide dismutase-SOD and nitric oxide synthase-iNOS) was also evaluated by the same method. We observed an increase in all populations evaluated when compared with the controls. Numbers of CD15+ and CD56+ were significantly lower than CD3+, CD4+, CD20+ and CD68+ cells. Statistical analysis revealed an association of fungi numbers with CD3, CD45RO and iNOS-positive cells. Furthermore, MIP-1alpha expression was associated with CD45RO, CD68, iNOS and CXCR3. Our results suggest a possible role of MIP-1alpha and fungi persistence in the cell infiltration in CR sites.

ESTABLISHING THE REFERENCE RANGE FOR T LYMPHOCYTES SUBPOPULATIONS IN ADULTS AND CHILDREN FROM BRAZIL

SUMMARY In Brazil, the existing reference values for T-lymphocytes subsets are based on data originated in other countries. There is no local information on normal variation for these parameters in Brazilian adults and children. We evaluated the normal variation found in blood donors from five large Brazilian cities, in different regions, and in children living in Salvador, and Rio de Janeiro. All samples were processed by flow cytometry. The results were analyzed according to region, gender, and lifestyle of blood donors. A total of 641 adults (63% males), and 280 children (58% males) were involved in the study. The absolute CD3+, and CD4+ cells count were significantly higher for females (adults and children). Higher CD4+ cell count in adults was associated with smoking, while higher CD8+ count was found among female children. Higher counts, for all T-cells subsets, were detected in blood donors from southeast / south regions while those living in the northern region had the lowest values. Individuals from midwestern and northeastern regions had an intermediate count for all these cells subsets. However, these differences did not reach statistical significance. In Brazil, gender and smoking, were the main determinants of differences in T-lymphocytes reference values.

Atypical lymphocytosis in leptospirosis: a cohort of hospitalized cases between 1996 and 2009 in State of Rio de Janeiro, Brazil

INTRODUCTION: Leptospirosis is a zoonotic disease found in tropical and temperate countries, and its clinical diagnostic confusion with arboviruses (dengue fever, oropouche fever and yellow fever), Brazilian spotted fever, viral hepatitis and hantaviruses has been an ongoing public health concern. The aim of this observational study was to demonstrate an association between findings of atypical lymphocytosis and the progression of endemic leptospirosis. METHODS: A retrospective analysis was performed on the demographic, epidemiological, clinical and laboratory aspects of 27 human leptospirosis cases that occurred over a period of 13 years (1996-2009) with no reported epidemic outbreaks in Rio de Janeiro, Brazil. RESULTS: The overall mortality rate was 11.1% in our cohort of hospitalized cases. However, there was no mortality among patients with atypical lymphocytosis (OR = 11.1; 95% CI = 1.12-110.9; p = 0.04). Two patients who were in the septicemic phase showed signs of expansion of γδ T cell responses in peripheral blood. CONCLUSIONS: Atypical lymphocytosis may be observed in patients with leptospirosis. Our observations suggest that these atypical leukocyte subsets are associated with partial protection during the disease course of leptospirosis.

Leprosy and pregnancy: detection coefficient and proposal for a new index

Introduction Our study presents a method to generate a novel detection coefficient for the association between leprosy and pregnancy (DCLP). Methods The DCLP was calculated for women from the State of Pará (2007-2009), Brazil. Data were ordered, divided into five equal parts (corresponding to the P20, P40, P60, and P80 percentiles), and classified as low, medium, high, very high, or hyperendemic. Results Using the new index, we established the DCLP parameters for low (<0.36), medium (0.36-0.69), high (0.70-1.09), very high (1.10-1.50), and hyperendemic (>1.50). Conclusions The new DCLP is more appropriate than the overall detection coefficient (DC), which does not take into account the particularities of the interaction between a disease and a specific physiological state.

Tegumentary leishmaniasis in the State of Amazonas: what have we learned and what do we need?

This study evaluated the occurrence of American tegumentary leishmaniasis (ATL) in the State of Amazonas, Brazil, in the last 30 years with emphasis on the last 10 years (2001 to 2010). The disease was predominantly observed in males (76.2%), in the 21- to 30-year-old age group (26.6%) and in extractive workers (43.7%); 3.3% of the cases were the mucosal form. The endemic channel shows the disease seasonality, with a predominance of cases at the beginning and end of each year. The number of cases by municipality in the period of 2001-2010 shows the maintenance of the endemic in the localities where the highest numbers of cases have always been registered, namely, Manaus, Rio Preto da Eva, Itacoatiara and Presidente Figueiredo. The comparison of data from 2001 to 2005 and from 2006 to 2010 showed the emergence of this disease in municipalities that had been previously unaffected. In the last years, there has been a significant increase in the activities of control, diagnosis and treatment of leishmaniasis in the State of Amazonas. In conclusion, the historical series of ATL analyzed in this study suggests that the transmission foci remain and are even expanding, though without continuous transmission in the intra- or peridomicile settings. Moreover, the disease will persist in the Amazon while the factors associated with infection acquisition relative to forest exploitation continue to have economic appeal. There is a real expectation of wide variations in disease incidence that can be influenced by climate and economic aspects.

Cataract surgery: expectations of patients assisted during a community project in São Paulo, state of São Paulo, Brazil

OBJECTIVE: To identify social characteristics and expectations of individuals seen during a community project for the treatment of senile cataracts. Expected results from their eye surgery and its consequences to their quality of life were studied as well. METHODOLOGY: Cataract patients (visual acuity equal to or lower than 0.2 in the more superior eye) aged 50 years or over, were surveyed by means of interviews held during their visit at the Cataract Project in São Paulo city, State of São Paulo, Brazil, in 1999. RESULTS: The sample was composed of 331 subjects of low socioeconomic level ranging in age from 50 to 97 years (average = 71.8 years). Expectation of total recovery from the cataract condition by means of surgery was declared by 80.0% of the respondents, with no significant differences between male and female subjects (P < 0.1723). Hope to resume manual activities was expressed by 59.8%. CONCLUSION: A predominance of expectations of resuming normal activity and achieving a better quality of life after cataract surgery were identified.

Guidelines on how to assess the validity of results presented in subgroup analysis of clinical trials

In observational studies, identification of associations within particular subgroups is the usual method of investigation. As an exploratory method, it is the bread and butter of epidemiological research. Nearly everything that has been learned in epidemiology has been derived from the analysis of subgroups. In a randomized clinical trial, the entire purpose is the comparison of the test subjects and the controls, and when there is particular interest in the results of treatment in a certain section of trial participants, a subgroup analysis is performed. These subgroups are examined to see if they are liable to a greater benefit or risk from treatment. Thus, analyzing patient subsets is a natural part of the process of improving therapeutic knowledge through clinical trials. Nevertheless, the reliability of subgroup analysis can often be poor because of problems of multiplicity and limitations in the numbers of patients studied. The naive interpretation of the results of such examinations is a cause of great confusion in the therapeutic literature. We emphasize the need for readers to be aware that inferences based on comparisons between subgroups in randomized clinical trials should be approached more cautiously than those based on the main comparison. That is, subgroup analysis results derived from a sound clinical trial are not necessarily valid; one must not jump to conclusions and accept the validity of subgroup analysis results without an appropriate judgment.

Estudos experimentais sôbre a origem do milho

1) It may seem rather strange that, in spite of the efforts of a considerable number of scientists, the problem of the origin of indian corn or maize still has remained an open question. There are no fossil remains or archaeological relics except those which are quite identical with types still existing. (Fig. 1). The main difficulty in finding the wild ancestor- which may still exist - results from the fact that it has been somewhat difficult to decide what it should be like and also where to look for it. 2) There is no need to discuss the literature since an excellent review has recently been published by MANGELSDORF and REEVES (1939). It may be sufficient to state that there are basically two hypotheses, that of ST. HILAIRE (1829) who considered Brazilian pod corn as the nearest relative of wild corn still existing, and that of ASCHERSON (1875) who considered Euchlaena from Central America as the wild ancestor of corn. Later hypotheses represent or variants of these two hypotheses or of other concepts, howewer generally with neither disproving their predecessors nor showing why the new hypotheses were better than the older ones. Since nearly all possible combinations of ideas have thus been put forward, it har- dly seems possible to find something theoretically new, while it is essential first to produce new facts. 3) The studies about the origin of maize received a new impulse from MANGELSDORF and REEVES'S experimental work on both Zea-Tripsacum and Zea-Euchlaena hybrids. Independently I started experiments in 1937 with the hope that new results might be obtained when using South American material. Having lost priority in some respects I decided to withold publication untill now, when I can put forward more concise ideas about the origin of maize, based on a new experimental reconstruction of the "wild type". 4) The two main aspects of MANGELSDORF and REEVES hypothesis are discussed. We agree with the authors that ST. HILAIRE's theory is probably correct in so far as the tunicata gene is a wild type relic gene, but cannot accept the reconstruction of wild corn as a homozygous pod corn with a hermaphroditic tassel. As shown experimentally (Fig. 2-3) these tassels have their central spike transformed into a terminal, many rowed ear with a flexible rachis, while possessing at the same time the lateral ear. Thus no explanation is given of the origin of the corn ear, which is the main feature of cultivated corn (BRIEGER, 1943). The second part of the hypothesis referring to the origin of Euchlaena from corn, inverting thus ASCHERSON's theory, cannot be accepted for several reasons, stated in some detail. The data at hand justify only the conclusion that both genera, Euchlaena and Zea, are related, and there is as little proof for considering the former as ancestor of the latter as there is for the new inverse theory. 5) The analysis of indigenous corn, which will be published in detail by BRIEGER and CUTLER, showed several very primitive characters, but no type was found which was in all characters sufficiently primitive. A genetical analysis of Paulista Pod Corn showed that it contains the same gene as other tunicates, in the IV chromosome, the segregation being complicated by a new gametophyte factor Ga3. The full results of this analysis shall be published elsewhere. (BRIEGER). Selection experiments with Paulista Pod Corn showed that no approximation to a wild ancestor may be obtained when limiting the studies to pure corn. Thus it seemed necessary to substitute "domesticated" by "wild type" modifiers, and the only means for achieving this substitution are hybridizations with Euchlaena. These hybrids have now been analysed init fourth generation, including backcrosses, and, again, the full data will be published elsewhere, by BRIEGER and ADDISON. In one present publication three forms obtained will be described only, which represent an approximation to wild type corn. 6) Before entering howewer into detail, some arguments against ST. HILAIRE's theory must be mentioned. The premendelian argument, referring to the instability of this character, is explained by the fact that all fertile pod corn plants are heterozygous for the dominant Tu factor. But the sterility of the homozygous TuTu, which phenotypically cannot be identified, is still unexplained. The most important argument against the acceptance of the Tunicata faetor as wild type relic gene was removed recently by CUTLER (not yet published) who showed that this type has been preserved for centuries by the Bolivian indians as a mystical "medicine". 7) The main botanical requirements for transforming the corn ear into a wild type structure are stated, and alternative solutions given. One series of these characters are found in Tripsacum and Euchlaena : 2 rows on opposite sides of the rachis, protection of the grains by scales, fragility of the rachis. There remains the other alternative : 4 rows, possibly forming double rows of female and male spikelets, protection of kernels by their glumes, separation of grains at their base from the cob which is thin and flexible. 8) Three successive stages in the reconstruction of wild corn, obtained experimentally, are discussed and illustrated, all characterized by the presence of the Tu gene. a) The structure of the Fl hybrids has already been described in 1943. The main features of the Tunicata hybrids (Fig. -8), when compared with non-tunicate hybrids (Fig. 5-6), consist in the absence of scaly protections, the fragility of the rachis and finally the differentiation of the double rows into one male and one female spikelet. As has been pointed out, these characters represent new phenotypic effects of the tunicate factor which do not appear in the presence of pure maize modifiers. b) The next step was observed among the first backcross to teosinte (Fig. 9). As shown in the photography, Fig. 9D, the features are essencially those of the Fl plants, except that the rachis is more teosinte like, with longer internodes, irregular four-row-arrangement and a complete fragility on the nodes. c) In the next generation a completely new type appeared (Fig. 10) which resembles neither corn nor teosinte, mainly in consequence of one character: the rachis is thin and flexible and not fragile, while the grains have an abscission layer at the base, The medium sized, pointed, brownish and hard granis are protected by their well developed corneous glumes. This last form may not yet be the nearest approach to a wild grass, and I shall try in further experiments to introduce other changes such as an increase of fertile flowers per spikelet, the reduction of difference between terminal and lateral inflorescences, etc.. But the nature of the atavistic reversion is alveadwy such that it alters considerably our expectation when looking for a still existing wild ancestor of corn. 9) The next step in our deductions must now consist in an reversion of our question. We must now explain how we may obtain domesticated corn, starting from a hypothetical wild plant, similar to type c. Of the several changes which must have been necessary to attract the attention of the Indians, the following two seem to me the most important: the disappearance of all abscission layers and the reduction of the glumes. This may have been brought about by an accumulation of mutations. But it seems much more probable to assume that some crossing with a tripsacoid grass or even with Tripsacum australe may have been responsible. In such a cross, the two types of abscission layer would be counterbalanced as shown by the Flhybrids of corn, Tripsacum and Euchlaena. Furthermore in later generations a.tu-allele of Tripsacum may become homozygous and substitute the wild tunicate factor of corn. The hypothesis of a hybrid origin of cultivated corn is not completely new, but has been discussed already by HARSHBERGER and COLLINS. Our hypothesis differs from that of MANGELSDORF and REEVES who assume that crosses with Tripsacum are responsible only for some features of Central and North American corn. 10) The following arguments give indirects evidence in support of our hypothesis: a) Several characters have been observed in indigenous corn from the central region of South America, which may be interpreted as "tripsacoid". b) Equally "zeoid" characters seem to be present in Tripsacum australe of central South-America. c) A system of unbalanced factors, combined by the in-tergeneric cross, may be responsible for the sterility of the wild type tunicata factor when homozygous, a result of the action of modifiers, brought in from Tripsacum together with the tuallele. d) The hybrid theory may explain satisfactorily the presence of so many lethals and semilethals, responsible for the phenomenon of inbreeding in cultivated corn. It must be emphasized that corn does not possess any efficient mechanism to prevent crossing and which could explain the accumulation of these mutants during the evolutionary process. Teosinte which'has about the same mechanism of sexual reproduction has not accumulated such genes, nor self-sterile plants in spite of their pronounced preference for crossing. 11) The second most important step in domestication must have consisted in transforming a four rowed ear into an ear with many rows. The fusion theory, recently revived byLANGHAM is rejected. What happened evidently, just as in succulent pXants (Cactus) or in cones os Gymnosperms, is that there has been a change in phyllotaxy and a symmetry of longitudinal rows superimposed on the original spiral arrangement. 12) The geographical distribution of indigenous corn in South America has been discussed. So far, we may distinguish three zones. The most primitive corn appears in the central lowlands of what I call the Central Triangle of South America: east of the Andies, south of the Amazone-Basin, Northwest of a line formed by the rivers São Prancisco-Paraná and including the Paraguay-Basin. The uniformity of the types found in this extremely large zone is astonishing (BRIEGER and CUTLER). To the west, there is the well known Andian region, characterized by a large number of extremely diverse types from small pop corn to large Cuszco, from soft starch to modified sweet corn, from large cylindrical ears to small round ears, etc.. The third region extends along the atlantic coast in the east, from the Caribean Sea to the Argentine, and is characterized by Cateto, an orange hard flint corn. The Andean types must have been obtained very early, and undoubtedly are the result of the intense Inca agriculture. The Cateto type may be obtained easily by crosses, for instance, of "São Paulo Pointed Pop" to some orange soft corn of the central region. The relation of these three South American zones to Central and North America are not discussed, and it seems essential first to study the intermediate region of Ecuador, Colombia and Venezuela. The geograprical distribution of chromosome knobs is rapidly discussed; but it seems that no conclusions can be drawn before a large number of Tripsacum species has been analysed.

A determinação dos números de indivíduos mínimos necessários na experimentação genética

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= δ. 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 = δ2 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 = { δ 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) δ { p1 (1- p2 ) / n= m δ = δ 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 = {δ p1 (1 - p1) / p1 - p2 }² = Fiim n 1.2 = { δ 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.