Essay Example on Statistics: Math's Dominant Science for Data Analysis

Introduction

As expected, statistics is primarily grounded in mathematics along with other concepts that pertain the collection, analysis, interpretation, and presentation of data. Due to the dominant settlement on the empirical roots and application, statistics could be considered a distinct mathematical science rather than a mathematical branch. In as much as statistics are involved, other concepts including probability, distribution, samples, and population, estimation, and data analysis are critical in making decisions based on data and delivering a prediction (Patten & Newhart, 2017). However, this paper will provide statistics overview by considering the descriptive statistics, inferential statistics, hypothesis development and testing, selection of appropriate statistical tests, and evaluating statistical results.

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Descriptive and Inferential Statistics

Since statistic is the study of data, it includes descriptive statistics and inferential statistics. Descriptive statistics are brief coefficients that summarize a given data set which can be either a representation of a sample of a population of the entire population. Descriptive statistics are used to describe the feature of data and provide description through the use of graphs or tables, or numerical calculations. For instance, numerical descriptors include, mean, mode, and standard deviation while frequency and percentage are used in defining categorical data. Correspondingly, inferential statistics, are systems and techniques for making probability-based decisions and accurate predictions from data arising from systems affected by random variations like random sampling or random experimentation, or observational errors. Majorly, inferential statistics is a mathematical branch of statistics that involves concluding a population based on a sample drawn from it. The determination of the characteristics brings about the involvement of other methodologies used such as hypothesis testing, estimation of numerical data, correlation, and other modern relationships within data such as regression analysis (Byrne, 2007).

Hypothesis Development and Testing

In the utilization of descriptive and inferential statistics, the use of inferential statistics revolves around answering the yes or no questions concerning involved data which defines hypothesis testing. A hypothesis is an explanation that delivers an account of sets of facts that can be tested by further investigation. In the development of a hypothesis testing, it includes various concepts and terms such as Null hypothesis, alternative hypothesis, Type I error, Type II errors, one-tailed test, two-tailed tests, among others. The null hypothesis assumes that observation is a result of chance factor denoted as H0: m1 = m2 on the other hand, the alternative hypothesis depicts that observations are a real effect. When one rejects the null hypothesis even though it was true, it is defined as Type I error (denoted by alpha a) while when one accepts the null hypothesis even though it is false, it is defined as Type II error (indicated by beta v). When the given statistical hypothesis is in value such as H0: m1 = m2 is defined as a one-tailed test while the given hypothesis assumes a greater than or less than the value it is defined as the two-tailed test. Through the understating of such factor, it delivers the involvement of selection of appropriate statistical analyses (Murphy, Myors, & Wolach, 2014).Selection of Appropriate Statistical Tests

In the analysis of research data, the choice of an appropriate statistical test is imperative. It is because the use of inappropriate or wrong statistical tests has delivered various complications especially in the definition of results along with other findings. Majorly, the wrong statistical tests are evident in multiple conditions such as the use of a paired test for unpaired data for information that is incompatible with the type of data. In selecting the appropriate statistical tests, the researcher ought to consider the type of data involved. The types of data could include nominal data, ratio data, interval data, and ordinal data. Also, the selection of appropriate statistical tests is dependent on whether the data follows the normal distribution of not as well as the aims of the study. Furthermore, several statistical tools include the t-Test, the analysis of Variance (ANOVA), Correlation Co-efficient, Chi-squared Test, along with other regression analysis models.

Evaluating Statistical Results

In as much as various statistical evaluation tools are involved in statistics, it is critical to understand that the evaluation of statistical results is vital as well. In the assessment of analytical results, there is the need for a proper and appropriate way of presenting researched data in a meaningful way that will ultimately provide the of the study. To sum everything up, this phase of statistics, it looks at delivering the decision concerning the validity and reliability of data.

References

Byrne, G. (2007). A statistical primer: Understanding descriptive and inferential statistics. Evidence-based library and information practice, 2(1), 32-47.

Murphy, K. R., Myors, B., & Wolach, A. (2014). Statistical power analysis: A simple and general model for traditional and modern hypothesis tests. Routledge.

Patten, M. L., & Newhart, M. (2017). Understanding research methods: An overview of the essentials. Routledge.