BASIC METHODS OF MATHEMATICAL STATISTICS DESIGNED TO PROCESS DATA OBTAINED IN THE STUDY OF BIOLOGICAL AND MEDICAL PATTERNS
BASIC METHODS OF MATHEMATICAL STATISTICS DESIGNED TO PROCESS DATA OBTAINED IN THE STUDY OF BIOLOGICAL AND MEDICAL PATTERNS
Marina Votyakova
Lecturer Russian Academy of National Economy and State Construction KMPO,
Russia, Moscow
Igor Andreev
Lecturer Russian Academy of National Economy and State Construction KMPO,
Russia, Moscow
ABSTRACT
A large number of statistical methods in research help researchers manage the data obtained and analyze the results of research. What is statistical evidence? A study whose conclusions are based solely on concrete, verifiable results.
Keywords: statistical methods, research, hypotheses, data processing, data analysis, sample error and variance.
Mathematical statistics is a branch of mathematics that can answer any question in life. You put forward a hypothesis and you need to confirm or disprove it.
Statistical methods come to the rescue. Statistical methods are the basis in scientific research. These are planning, design, data collection, analysis and conclusion regarding the result of the study. The data set generated during the course of a study is a meaningless raw value unless it is analyzed using statistical methods. Thus, the definition of statistical data in studies is essential to substantiate the results of the study.
Not using statistics in research leads to a huge set of results that are difficult to analyze. Statistics helps the researcher to carry out a scientific experiment in stages. You need to set the sample size for successful operation. Statistics teaches how to choose a sample size and reduce experimental error and errors. The next step involves testing the proposed hypothesis.
And the final stage of the study is the analysis of the obtained data.
Statistical methods help researchers draw conclusions from experiment and observations. Completing the study manually or by visual observation may give erroneous results. Statistical analysis takes into account all indicators and variance in the sample.
The identification of patterns and relationships between different indicators in medicine requires the study of data processing methods, the basics of biometrics and mathematical statistics. Our study showed that in most experimental works in medicine, mathematical data processing consists in determining the arithmetic mean, the standard error of the arithmetic mean, variance, and criteria for the significance of differences. Based on the confidence factor t, using the number of degrees of freedom or the number of observations, the Student-Fisher tables determine the error probability coefficient (p).
The difference between the arithmetic means is considered significant at p<0.05. The value of p reflects the level of reliability of the result of the study, that is, the expressed quantitative degree of confidence that the results of the experiment can be extended to the entire population, and the probability of error associated with the distribution of the observed result to the entire population. The higher the level, the lower the degree of confidence in the found dependency. Thus, p=0.05 is more reliable than p=0.1.
Value p = 0.05 indicates a 5% probability that the relationship between the variables established in the course of observations is random and is characteristic only for this sample.
As a rule, in the course of the experiment, a control and an experimental group of patients are distinguished. At the same time, the similarity and difference of quantitative characteristics in the main and control groups are determined by their average values. For example, such as the level of hemoglobin, erythrocytes, leukocytes, meiosis indicators. For this, a test with different variances over data series can be used. This criterion is used when comparing the average of two samples, with even comparisons, when evaluating the effectiveness of the “before and after exposure” methodology. The so-called "null hypothesis" implies the equality of the means of the two samples. Determining the absolute value of the t-statistic allows you to accept or, conversely, refute the null hypothesis. A null hypothesis is rejected if the means of the two samples are significantly different.
Many researchers in the field of medicine use X±1.96s to determine the confidence interval, where X is the arithmetic mean of the data series; 1.96 is the value of the Laplace function at a = 0.05 or the level of reliability is 95%; s is the standard deviation.
For example, when developing a method for predicting the development of nephrogenic hypertension in glomerulonephritis in children, we compared two groups of data by their arithmetic means, then checked the significance of the difference using a two-sample t-test with different variances. 20 quantitative traits were analyzed. As a result, indicators were obtained indicating the existence of significant differences in the average value of indicators, 95% reliability, between the compared groups with arterial hypertension (AH) and without AH. The chi-square test was used to compare the distributions of quantitative and qualitative traits.
When comparing the distributions of quantitative and qualitative characteristics using the standard error, indicators were identified for which there is a difference in frequency between groups with arterial hypertension (AH) and without it (without AH).
As a result of the calculations, it was found that the mean square error in these groups significantly exceeded the value of 3.8. This meant that, according to the probability of 95-99%, the compared groups of patients differ in this indicator, regardless of the cause of the disease. According to other qualitative and quantitative characteristics, no significant differences in the frequency of this or that indicator were found. The error was below 3.8. Evidence of the occurrence of nephrogenic hypertension in patients with diffuse kidney disease formed the basis of a method for predicting the development of nephrogenic hypertension through a comprehensive study of biomedical, clinical, laboratory and functional parameters of patients.
The study showed that the use of biometric indicators and methods of mathematical statistics is the basis for processing biomedical data, choosing a therapy option taking into account the prognosis of the development of the disease and improving treatment outcomes.
References:
- Agapov E.G., Luchaninova V.N., Popova V.V., Sycheva E.V. A method for the development of nephrogenic hypertension in children with glomerulonephritis: Patent of the Russian Federation / Vladivostok State Medical University; Published 2004.08.10. 16 p.
- Ivanter E.V., Koros A.V. Fundamentals of Biometrics: An Introduction to the Statistical Analysis of Biological Phenomena and Processes: Proc. help. Petrozavodsk: Publishing House of PetrGU, 1992. 168 p.