Statistics is a distinct mathematical science which involves the study of or use of both qualitative and quantitative principles in compilation, interpretation, analysis and representation of numerical data. It helps in explaining the different trends and patterns we witness in different phenomena in the society. It is divided into two major groups or subdivisions which include descriptive statistics and inferential statistics. Descriptive statistics is involved with analysis and representation of numerical data while inferential statistics is involved with techniques which make inferences based on the whole population out of the observation made from thesample population. The purpose of statistics is to infer, describe and make meaningful judgments from collected data. Data is collected from a population which could be a phenomenon, community, procedural process, a production line amongst other input data which have variability related to them (Florida State University, 2010). Statistical knowledge or study is crucial for individuals tasked with different research or investigative projects as it helps one to describe the different properties of a sample population and test or compare the same with other different populations. This paper is going to highlight what I have learned in statistics, particularly the application of various course elements in analyzing and makings decisions about data.
Compared to other types of data analysis, statistics is mostly concerned with variable data hence most of its results are articulated with respect to probabilities. Statistical models are built to analyze variables within data. Statistical models form a crucial basis for statistical analysis owing to the variability involved in the various aspects of data collected. The models or equations are used to explain and illustrate how data regularly would behave within an ideal environment or an ideal representation of the population (Kufs, 2011). Data is collected from a sample population, and it is evaluated in comparison to the ideal model to determine any deviations. Through the use of statistical techniques and statistical analyses, mathematical parameters for different variables in question within the model are built, followed by an error coefficient. The developed model will then be capable of providing an approximation of the measure being investigated along with the possibility or degree of chance that the event would have happened based on the model.
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Other than the two main subdivisions of statistics, descriptive, and inferential statistics, other divisions or elements of statistic include hypothetical development and testing, selection of appropriate statistical tests and evaluation of statistical results.
Descriptive Statistics
From its name, descriptive statistics is the wing of statistics whose aim entirely is to describe or summarize data (Mann, 1995). The descriptive statistic is the foundation of quantitative analysis of data providing simple deductions based on various measures and samples i.e. describes what data shows and simple relationships between variables (Trochim, 2006). It does not presume that the data came from a wider population. Some of the commonly used terms or measures were taken under descriptive statistic are central tendency and variability measures. These measures include the mean, median and mode for central tendency while a measure of variability includes the level of variance, maxima, and minima values. Descriptive statistics is not developed from probability theories as in the case of other statistical elements. The descriptive aspect of statistics is used during univariate analysis i.e. to analyze a single variable at a time and bivariate analysis i.e. analysis of two interdependent variables at a time (Tanner & Youssef–Morgan, 2013) . Descriptive statistic presents data in theform of tables, graphs and pie charts, which are manageable, easy to understand at first sight and very helpful in quick decision making.
Inferential Statistics
Inferential statistics is used when testing a hypothesis. It further from the immediate data collected by trying to make conclusions on the probability that an event is dependable on certain variables or whether they happened only by chance within the course of the study(Trochim, 2006). This branch of statistics is involved with random sampling and experimentation and tries to make deductions through regression analysis, t-tests, analysis of covariance and variance amongst other multivariate techniques or methods. Once these techniques have been used to analyze samples from an interested population, prepositions are made on the whole population. Dummy variables play a crucial role in forming the basis of how to compare the population and the sample. This type of statistic singles out random errors and the use of inadequate designs usually encounter two kinds of errors, sample error and sample bias. This type of statistical analysis is applicable when one is investigating different relations between several variables in a population. It allows one to use data from a sample to come up with crucial deductions about a whole population.
Hypothesis Development and Testing
Good research is dependent on the nature of its hypothesis. Development of the right research question is important in research. Also, testing of hypothesis or the research question is crucial in any statistical analysis. Testing of a hypothesis is done after its development to check its worth. Hypotheses should be definite in nature, changing the center of its attention from the general population of interest to the definite issue that needs to be investigated. As such, testing a hypothesis is important since it helps to check whether the research question extended beyond the sample into the population and is relevant to the target population. A hypothesis is first developed, based on the issues a researcher wants to explore and investigate from the population and with the intention putting it to the test. A null and an alternate hypothesis are developed at this stage. Once developed, the research question is then tested. Testing of hypothesis begins by first identifying independent and dependent variables crucial for testing of the research question. The independent variables are statistical assumptions presumed on the need for the study and are used to develop dependent variables. Once assumptions and the variables have been formulated, a relevant test is decided upon stating the acceptable test statistics.A significance level below which a null hypothesis can be rejectedis developed. Distribution of the test statistic is then put against the significant level to determine whether the null hypothesis will be accepted or rejected for the alternate hypothesis.
Selection of Appropriate Statistical Test
Selection of an appropriate statistical test is a very important feature in statistic since the accuracy of results found is heavily dependent on theappropriateness of the statistical tests used. The prerequisites of the appropriate statistical test include the kind of data dealt with, the purpose of the study and whether the analyzed data follow a normal distribution or not (Kluwer, 2011). Wrong statistical tests are seen in cases where parametric statistical tests are used for data which is inconsistent with the normal distribution or paired tests used for unpaired data. As such, to ensure that an appropriate statistical test is selected a researcher should consider whether the data being analyzed follows a normal distribution or not, the aim of the study, and the kind of data being dealt with during the study.
Evaluation of Statistical Results
Evaluation of statistical data is necessary for determining the validity of the statistical data. This is done by first bringing together all the relevant information from the sample used in the calculation of different statistical parameters. Out of this collection of statistical parameters a standard deviation and the sample, theaverage is then calculated. The calculation subsequently enables the identification of P-values. These values are important in the establishment of the variance between the null and alternate hypothesis. The values help in assessing the validity of the research question. Proper statistical tools are required during this process of thorough evaluation. The tools used during the evaluation of statistical results are dependent on the nature of statistical data under examination.
Conclusion
Statistics is an important wing of scientific mathematics which equips learners with the necessary knowledge required for the assessment of patterns and trends in different phenomena. It is very crucial for a research project. Statistics has different elements which equip an individual with necessary skills needed for developing a research question to the evaluation of statistical results. From the knowledge gathered in the descriptive statistic, an individual is capable of measuring different aspects of grouped and ungrouped data, presenting the data in histograms which enhances quick decision making. Inferential statistics enable one to assess the relationships between different variables within a population by analytically assessing a given population sample. Statistics also teaches one how to develop a hypothesis and an appropriate statistical test to help in assessing the validity of the research project. Statistics is a very important, necessary subject which enables learners to bring meaning to data which otherwise would have been considered useless.
References
Florida State University (2010 ) What Is Statistics? Retrieved from http://stat.fsu.edu/undergrad/statinf2.php
Kluwer, W (2011). ‘ How to select appropriate statistical test?’ Journal of pharmaceutical negative results , 1(2): 61-63
Kufs, C (2011). Five Things You Should Know Before Taking Statistics 101 . Retrieved from https://statswithcats.wordpress.com/2011/05/15/five-things-you-should-know-before-taking-statistics-101/
Mann, P (1995). Introductory Statistics (2nd Ed.)Wiley Publishers, New York.
Tanner, D. E., & Youssef–Morgan, C. M. (2013). Statistics for managers [Electronic version]. Retrieved from https://content.ashford.edu/
Trochim, W (2006). Descriptive data . Retrieved from http://www.socialresearchmethods.net/kb/statdesc.php
