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# Inferential Statistics Methods

Statistics is a science that has some significant specific features that distinguish it from other disciplines. It appeared from the practical requirements of society. Even in the ancient world, there was a need to count the number of residents of the state and people who were suitable for military affairs, determine the number of livestock, the size of land, and other property. This kind of information was necessary to collect taxes and warfare. In the future, with the development of social life, the circle of studied phenomenon expanded. These days, statistics deals primarily with the quantitative aspect of phenomenon and processes of social life and, thus, it is an extremely crucial field of science.

Statistics has a multitude of peculiar characteristics that are typical only for this science. These features are related to knowledge of the socio-economic phenomena and processes such as characteristic changes in population, its structure, output of products in various fields, a number of workers, alternations of performance indicators in the fields of economy, the ratio between the volume of produced and realized products, and others (Ross, 2010). Statistics closely examines quantitative aspects of these aspects and procedures because of their qualitative characteristics thereby enriching people’s knowledge and giving the opportunity to discover their essence. There are several definitions of statistics. In the book Introductory Statistics, it is affirmed that “statistics is the art of learning from data. It is connected with the collection of data, their subsequent description, and their analysis, which often leads to the drawing of conclusions” (Ross, 2010, p. 3). Such sciences as an economic theory, philosophy, and mathematics have a significant impact on the development of statistics.

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## Descriptive and Inferential Statistics

In accordance to a widespread division, statistical methods can be divided into statistical inference and descriptive statistics. Statistical inferences are fundamental for data received from the sample that could be spread to the entire population. Descriptive statistics is applied for the simple generalization of data obtained in the framework of sampling (Dietz & Kalof, 2009). The purpose of descriptive statistics is processing of empirical data, their classification, and visual representation in the form of graphs and tables as well as their quantitative description by means of basic methods of statistics. The main methods of descriptive statistics include measures of central tendency, percentages, paired coupling coefficients, and measures of variation. These procedures allow summarizing the data available in the sample. Unlike inferential statistics, descriptive statistics does not reach conclusions about the general population based on the results of the study of particular cases.

Statistical inference is the process of obtaining conclusions about a certain population dependent on randomly retrieved samples. In the book Introduction to Social Statistics, it is noted that “inferential statistics are tools used to make statements in the face of error” (Dietz & Kalof, 2009, p. 116). It is widely adopted in psychology. The logic of statistical inference does not rely on the specific problems and methods utilized (Dietz & Kalof, 2009). On a sample basis, the researchers make statements on issues that are likely to occur among population.

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## Hypothesis Development and Testing

Statistical hypothesis is a specific assumption of the probability of distribution underlying the observed sample data. Testing statistical hypothesis is the process of reaching a decision whether the observed statistical hypothesis contradicts data sample. The testing process is based on the formulation of two hypotheses – null and alternative. A null hypothesis is one of the absence of differences. According to this hypothesis, the difference between the values is sufficient and the independent variable contains no effect (Tanner & Youssef–Morgan, 2013). In the book Business Statistics, it is stated that “in the hypothesis-testing approach, the preliminary assumption is that the null hypothesis is true” (Black, 2009, p. 334). The alternative hypothesis deals with the significance of differences. It asserts the existence of differences or similarities. The alternative hypothesis is a “working” hypothesis of the study. Due to this hypothesis, the dissimilarities are significant enough and caused by the effect of the independent variable. Null and alternative hypotheses represent a complete group of incompatible events: the deviation of one implies the adoption of the other (Black, 2009). The basic principle of the method of testing hypotheses is that the null hypothesis is applied for attempting to refute it and, thus, confirm the alternative hypothesis. If the results of the statistical test adopted to analyze the difference between the averages are such that they will allow rejecting the null hypothesis, it would imply that the alternative hypothesis is correct. Consequently, a working hypothesis is confirmed.

Statistical hypothesis testing is performed with the usage of a statistical criterion for the general logic including finding a specific form of the function of the findings of observation that creates the basis of for affirming the final decision (Black, 2009). For example, a hypothesis about the general law of distribution of the studied random variable, the homogeneity of two or more processed samples, the numerical values of the parameters, general population, and others can be considered.

The test result can either be negative when observed data contradict a proposed hypothesis or non-negative. In the first case, the hypothesis is inaccurate while in the second it cannot be considered proved. It does not deny the available sample data. However, other hypotheses can also possess the same properties. Different criteria are applied for statistical hypothesis testing.

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## Selection of Appropriate Statistical Tests

There are two types of statistical tests to examine hypotheses: one-tailed and two-tailed. When the researchers are interested in the deviation of the measured characteristics from the fixed value in any particular direction, thus the alternative hypothesis is expressed directional, one-tailed tests are adopted. In case the researcher is concerned about the deviation of the measured characteristics from the fixed value, two-tailed tests are conducted. Besides, it excludes the matter whether it is a higher or lower deviation. In market researches, such tests have less practical importance since there is a commonly certain preferred direction of differences.

## Evaluating Statistical Results

The statistical evaluation is a function of the results of observations utilized for the estimation of unidentified probability of distribution parameters of studied random variables. The statistical evaluation is applied for estimation the unexplained parameters of random variable distributions. To evaluate the accuracy of the findings of the study means to establish the probability of the prediction due to which the study results based on the total sample can be transferred to the general population or the other research.

## Conclusion

Statistics is a field of social sciences that aims at collecting, organizing, analyzing, and comparing the facts related to a variety of mass phenomena. In such a manner, it is a highly significant area. Statistics develops as a separate science. Nevertheless, it is in close conjunction with other disciplines. It should be noted that statistics is divided into several fields such as descriptive and inferential statistics. Statistics is closely connected with the hypothesis, which can be null and alternative. There are various methods to develop and test hypotheses in a statistical science.        Discount applied successfully