Concordance between the size of the sign and the errors of first and second kind to investigations in medicine

Background: the relationship between sample size and errors of the first and second type, which are taken in those studies, where there are properly supported hypotheses, who is detailed in the classical literature; but without indicating a design of the methodology to follow. Aims: to design a methodology to establish the concordance between the sample size, the first and second gender errors of the experimental data. Method: mathematical and statistical methods, procedures, and algorithms are applied, combined with theoretical methods: analysis-synthesis, induction-deduction, and abstraction-concretion to determine the size of the sample, based on fixing the errors first and second gender. The empirical methods applied are framed mainly in the observation of the records of the experimental data, the bibliographic review, in order to deepen the problem and obtain information on the main difficulties that affect the research process. Results: a methodology is designed, in which the correspondence between the minimum size of the sample and the errors of the first and second gender is established with a preset significance level, according to the experimental data of the study. Conclusions: through elaborated health situations, the need to establish a methodology as a work tool to determine the concordance between the sample size, the errors of the first and second gender  and  is evidenced; in research with a predetermined significance level, based on experimental data in clinical trials, controlled and randomized studies in medicine.


INTRODUCTION
When developing mixed studies, it is necessary to specify the sample size, the first and second gender errors  and β, establish a relationship among these to ensure the veracity and reliability of the research, as well as the effectiveness of the results by hypothesis verification and interval estimation, using the working techniques of classical inference statistics.
The determination of these elements are not always used adequately, however the foundation of any research that is developed must be supported by these statistical tools and techniques, and work mathematics. (1 -3) For the analysis of the collected data, as well as the verification of the inferred results, from a study sample, they generally depend on an experimental design, where the reliability and efficacy of the study (minimum sample size) is ensured, in which the importance is emphasized, and the correspondence of the deductions, from the study sample to the population it represents. (4 -6) Some authors point out the need to interpret first and second gender errors in research to highlight the results achieved in the research; (1) but it is decisive to ensure their veracity and reliability from the beginning, therefore it is essential to specify the minimum size of the sample in such a way as to certify the inquiries obtained.
That is, ideas are retaken in depth, which acquire leading dimensions from the initial stages to the final ones, for which the objective is addressed: to design a methodology to establish the concordance between the sample size, the first and second errors gender of experimental data that ensure the reliability and veracity of research such as clinical trials, controlled and randomized studies in medicine.

MATERIALS AND METHODS
Mathematical and statistical methods, procedures, and algorithms are applied, combined with the theoretical methods: analysis-synthesis, induction-deduction, and abstractionconcretion to determine the minimum size of the sample, based on fixing the errors of the first and second gender.
A methodology is designed to ensure the processes of understanding, explanation and interpretation in the analysis of experimental data, (1)(2)(3) to guarantee the reliability and veracity of the study.
The empirical methods applied are framed mainly in the observation of the records of the experimental data, the bibliographic review, in order to deepen the problem and obtain information on the main difficulties that affect the research process, and the published reports, from of the search for methods and procedures. (7 -9) The document review method is used, through books, and articles referring to the topic Inferential Statistics in the Scielo, DOAJ, Latindex, Google Scholar Databases, Elsevier, among others. (10 -12)

RESULTS
The methodology designed to establish concordance between sample size, first and second gender errors,  and β, to ensure the reliability and veracity of research, such as clinical trials, controlled and randomized studies, is made up of the following steps: (I) Formulation of the statistical hypothesis.
(II) Determination of the minimum size of the study sample, based on prefixing the errors of the first and second gender  and β.
(III) Verification of the statistical hypothesis, preset a level of significance (reliability).
(IV) Construction of the confidential interval, which allows comparing the results obtained in the (III) verification of the statistical hypothesis (the veracity of the study is ratified).
(V) Interpretation of the results obtained, which allows to conclude the analysis of the transformation of the initial health situation.
Biomedical problems are elaborated to illustrate the application of the designed methodology. When deepening by means of the documentary review in the reports of studies in different databases, (13,14,15) no details are made that verify the concordance of aspects related to the experimental design, when continuing search no findings that ratify this gap are found (16,17,18) Thus, the aforementioned condition is not ratified from now on. Problem 3. The data contained in the technical certification of a drug show its effectiveness in 80 % of cases to cure a certain type of dermatitis. As a result of the modifications of the therapy, an increase in its effectiveness is expected. To verify this statement, checks are made, 121 patients are randomly selected, and 108 of them were cured with modifications in the treatment. Suppose that the sample of patients is obtained from a normally distributed mother population whose proportion is P = 0.80. Compare the reported results. (1) 1. What is the minimum size necessary to verify the null hypothesis: H 0 : Classical therapy is applied, which does not influence the increase in the effectiveness (proportion) of the drug, and the alternative hypothesis.

DISCUSSION
In solving the problems raised above, it is necessary to delve into the statistical tools and techniques supported by the methods, procedures and ways to stimulate the creative thinking of researchers. (1) The concordance of the study sample size and the errors of the first and second gender and are not specified in the reviewed research reports. Compare with analyzes presented in the scientific literature. (1,2,3) Through steps a in the designed methodology. According to the problem data, the following system is considered: If the hypothesis is verified , the confidential interval for the difference is examined. The hypothesis H 0 is accepted for the difference covers the null value (0).
Establish analogies with reports made. (1,2,3) The exception consists in the verification of the hypothesis about the equality of the variances since the confidential interval is constructed for the relation of the variables, the hypothesis H 0 in this case is accepted, if the interval in question covers the value equal to the Unit.

Problem 2. (IV)
The upper limit (upper bound) of the interval to the left is determined, that is ( ), for the parameter m, when the confidential probability of the percentile , is obtained: As the value of the mean m = 80 beats per minute of older adults is not covered by the interval, the null hypothesis H 0 : µ 0 = 80 must be rejected, which coincides with the result obtained when solving problem 1.
Problem 3. (I, II, III) 1. According to the data, the following system is considered: Thus, the system is solved by simplifying: The system is simplified, then The use of professional statistical programs is recommended, which ensure data processing with speed, precision, accuracy, and a high level of reliability. Compare with reports made.

CONCLUSIONS
It is necessary that the professionals of the Medical Sciences demonstrate in the analysis of the health situation, the application of the designed methodology, which ensures the reliability and veracity of the study to be developed, according to the steps to follow: (I) Formulation of the statistical hypothesis.
(II) Determination of the minimum size of the study sample, based on prefixing the errors of the first and second gender  and .
(III) Verification of the statistical hypothesis, preset a level of significance (reliability).
(IV) Construction of the confidential interval, which allows comparing the results obtained in the (III) verification of the statistical hypothesis (the veracity of the study is ratified).
(V) Interpretation of the results obtained, which allows to conclude the analysis of the transformation of the initial health situation.
It is recommended to deepen the application of statistical techniques to analyze the information collected, using inferential statistics work tools to model and simulate experimental data with the help of professional statistical programs.