Table of Contents

- Introduction
- Descriptive Statistics
- Inferential Statistics
- Hypothesis Development and Testing
- Bivariate Measure of Association
- Multivariate Techniques
- The Analysis of “Questionnaire on Delinquency in Youth and Adults and Its Treatment by the Courts” by Leon A. Carley
- Conclusion
- Related Research essays

## Introduction

While analyzing various statistical approaches for a certain population, it is obvious that statistics involves a systematic collection of data to gain knowledge through deductive and inductive ways. In social sciences, particularly psychology and sociology, various statistical generalizations are made with the precise definition of population. For example, the article from *Journal of the American Institute of Criminal Law and Criminology* on crime and delinquency specifies the results received from a questioner and defines the subject of the research clearly. However, to reach the same results, it is vital to concentrate on the application of the following statistical methods. The purpose of this essay is to discuss the various analytical methods and their use in social science.

## Descriptive Statistics

The empirical research uses descriptive statistics in social sciences, particularly in psychology and sociology. Descriptive statistics summarizes and represents detailed data is a simple manner. Some examples of descriptive statistics include the average score of the sample that helps to understand the participants in the area of the study. Other examples include the median, standard deviation and the variance, the coefficient of variation and the range. Descriptive statistics is used to summarize the samples ad show the quantitative description in a convenient form. During the formation of statistics, measuring a large number of populations may be tedious, and, thus, descriptive statistics helps to simplify the massive amount of data in a friendly way that helps to reach a reasonable conclusion from analyzing the data set without the need to review it again.

## Inferential Statistics

As the word suggests, inferential statistics tends to extend beyond the immediate data collection. Inferential statistics is used to make a judgment and to infer from the data, for example, a t-test is useful in testing differences between groups of data when comparing the average performance between groups of students. A social researcher, such as a psychologist, must be familiar with the diversity of general linear models. There are other possible methods also, such as the analysis of variance, the analysis of covariance, the regression analysis, and others. Analyzing and understanding that data should be collected from a larger population automatically introduce the peculiarities of the analysis applied in social sciences.

## Hypothesis Development and Testing

A hypothesis is a precise, falsifiable statement subjected to the observational testing as a part of a scientific investigation. The practice of hypothesis testing in the social sciences started in the 1940s. Essentially, it constitutes the primary source of data analysis in the experimental psychology. Additionally, it is used to justify conclusion made from data gathering (Weakliem, 2016, p.107). In social sciences, the scientific method requires stating an answer to the question (the hypothesis) and testing it with the observations (the hypothesis testing). One of the major strategies for the hypothesis testing is a qualitative research. The focus is given on the quantification of social science concepts in order to compare and measure the hypothesis. An example of hypothesis testing could be similar to this statement, “If a prisoner learns a life skill in jail, then she is less likely to commit other crimes when she is released.” The tested hypothesis will state that “there is a positive correlation between training prisoners and the number of crimes committed when they are released.” The goals of the hypothesis testing are to explain the focus and the direction of the research. Finally, the explanation of the hypothesis will show the purpose and identify the variables used in research.

## Bivariate Measure of Association

A bivariate measure of association refers to the broad range of coefficients that assess a statistical strength of the relationships between the variables of interests. The results depend on their analysis. This step is explained in different ways, for example, a value of zero signifies that no connection exists. Regarding a linear relationship, the measure of association usually deals with predictive monotonic that could be both monotonic and strictly monotonic. It is worth noting that the measure of association identifies a defined relationship regarding the strict monotonicity. Thus, the one value will be achieved if two variables come from a similar marginal distribution. Besides, the measure of association also disregards those rows and columns which have null values.

## Multivariate Techniques

This technique examines multiple variables at the same time; it involves more than one dependent or independent variable. It could also examine both of them simultaneously. In social sciences, the researcher who uses this method presupposes that a given product of significance is influenced by a single unit. In fact, there are several statistical techniques used for evaluating multivariate analysis. The most suitable method for a given study depends on the type of the learning and critical research of the problem. However, the most used multivariate methods are multiple regression analysis, factor analysis, path analysis, and various analyzes of variance. Furthermore, the most applicable method is the multiple regression analysis since it evaluates the effects of multiple independent variables on the value of a dependent variable. Each independent variable coefficient is calculated using regression and its statistical implication. Each dependent variable that requires analysis with other factors is held constant. The psychologists often use regression analysis to study social and psychological phenomena.

## The Analysis of “Questionnaire on Delinquency in Youth and Adults and Its Treatment by the Courts” by Leon A. Carley

The article introduces the descriptive statistics. During the research, the mean to be tested is a group of seventy-three prisoners who are selected from the whole population of detainees. The selection technique may take various forms, for example, sampling. The answers to the questioner about which diagnosis method the prisoners think vary. The data is based on the sociological examination, physical examination, psychological examination including the background information of interviewed, such as the history of a home, school, and offenses. The received data shows that:

Physical ……………………………………..6

Mental……………………………………… 6

Sociological……………………………….... 3

All three…………………………………… 27

Physical and Sociological...............................1

Mental and Sociological …………………….3

From this set of data, the range is the difference between the largest binary number (27) and the lowest (1) which gives a range of 26. Besides, the mean can be calculated. The mode is six that is the most repeated numerical figure:

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(6+6+3+27+1+3)/6 =7.667

Certainly, the researchers apply hypothesis development. For example, in this situation, the hypothesis is that before determination of guilt or innocence of a suspect, a proper investigation of the cases should be performed. One can state that the defendants who are found guilty before the diagnosis do have a fair trial. Next step is the identification of the population to which the study results should apply, in this case, the population is the prisoners. After, it is required to perform a null hypothesis of the same which is HO: UH=UL, where UH is the mean number of detainees who support the diagnosis before the trial and UL is the average number of the prisoners who support the diagnosis after the trial. In the article, initially, the first group is bigger that the second one who support the diagnosis after the trial. It rejects the null hypothesis and accepts that a diagnosis performed before the prisoners are put on trial.

Having already conducted the hypothesis testing, the next step is to use the bivariate measures that will be tested on the examination of two variables. A cross-classification table is mostly used to determine independent and dependent variables. For example, if considering both females and males, it leads to the question whether there should be special treatment. In this case, the answers should be categorized on sex showing the relationships between the possible opinions and suggestions.

Finally, the examination of multivariate variables should be completed. It shows the relationships among variables that are performed simultaneously. The analysis of both bivariate and multivariate measures may not be realistic in our example due to the data arrangements.

## Conclusion

When the research should be performed, the psychologists have to remember every theory should be supported by the facts. There is a range of effective statistical methods which help make clear and precise predictions. Furthermore, they usually provide the operational definitions of the primary variables used in addition to the summary and explanation of the related facts. Thus, the use of statistical measures in social sciences is equally important to the other methods of gathering information. However, these measures may be based on the bias or other drawbacks. For example, failure to present the whole population in a study may give inappropriate results which will lead to the wrong generalization. Certain sets of data may not contain full information needed to perform all the analysis, for example, a multivariate analysis. The analyses, such as the linear regression, lead to the assumptions which do not correspond to the particular type of data. This assumption usually leads to the simplification of the whole population which might not be the case in the real world. Finally, the statistics give the researches of social science an opportunity to collect and interpret the data which help to define various social problems.