Concepts and Applications of Inferential Statistics

Question: What have you learned about statistics? In developing your responses, consider at a minimum and discuss the application of each of the course elements in analyzing and making decisions about data (counts and/or measurements)? Answer: I had already attended the class on the statistics. The succinct thesis statement from this class on statistics is that statistics is a subject, which deals with organising and analysing the data that are either numeric in nature or it has to be converted to numeric data by the researcher. In the class, various topics on statistics were discussed and the application of these topics; i.e. the course elements and their analysis and decision-making properties were explored. Based on this exploration about statistics in the class, I am developing a response on the study of the course elements and their uses. Descriptive statistics Descriptive statistics was a course element in the class of the statistics, which deals with the summarisation of the given data and describing them using the basic statistical tools of mean, median, mode, standard deviation, quartiles, skewness and kurtosis. This course element mainly gives the summary of the samples used in the analysis. This kind of analysis is the 1st type of analysis done to the data sets which give a vivid idea about the nature of the data set available to us. The use of descriptive statistics is to present quantitative descriptions in a form that can be managed and understood easily. Descriptive statistics is mainly an indicator of the measure of central tendency of the data, variability of the data, the maximum and minimum value of the data and the tailed-ness and the asymmetry of the probability distribution of the data (Bickel Lehmann, 2012). Inferential statistics It is not always possible to get the whole population for analysis. We, therefore, use the samples from the population, for our further analysis. Therefore, it is very important for the sample to represent the population accurately. Inferential statistics is the process that allows us to conclude about the population from which the sample is drawn. The process of doing performing this inferential statistics is known as sampling and this process incurs sampling errors, thus a perfect representation of the population by the samples is not expected. There are two processes of inferential statistics and they are the estimation of parameters , and Testing of hypothesis. Thus, inferential statistics infers information about the underlying population on analysing the samples from the population and considering the sampling errors (Lowry, 2014). Hypothesis development and testing Development and testing of hypothesis is an important method for statistical inference. Here, the given statistical data set is compared with the idealized model of the population in accordance with a given significance level. In development and testing of hypothesis, we were taught to on is identify a research question at first so that the area of interest for the testing narrows down to a more specified area. After this, the specific issue is created in the area of interest and the specific questions are framed for the hypothesis. The next step is to create the hypothesis. Here, the hypothesis is mainly the relationship between the variables, which is to be studied. Two types of hypothesis are created, one is null hypothesis and the other is called alternative hypothesis. The hypothesis is then tested using various tests, depending on the variables and then conclusion is drawn depending upon the result from the test. The conclusion is either acceptance or rejection of null hypothes is (Lehmann, 2012). Selection of appropriate statistical test Statistical tests are selected on the type of the sample data. At first, we have to check what type of data is our sample data; i.e. whether the data is nominal data, or ordinal data or interval data or ratio data. Our next aim is to know whether the given set of data follows normal distribution or not normal distribution. Once we know the types of data and the distribution of the data, we can easily select the appropriate statistical test. However, there is no need to check the distribution for ordinal and nominal data, but the distribution must be checked in case of ratio data and interval data. In addition, if the distribution of the data is normal distribution, then we will use different types of parametric tests whereas, if the data is not normal distribution, then we will use different types of non-parametric tests. Thus, the above process does selection of appropriate statistical test (Stanojevic Rosenfeld, 2015). Evaluating statistical results After selecting the appropriate statistical test, the test is performed and we get a value of the test statistic. We then find the p-value and see the alpha error. Ifwe find the p-value to be less than 0.05, then we can say that data is not following the normal distribution and we should use the non-parametric test for this kind of data set whereas if he p-value is more than 0.05, then we can conclude that the data follows normal distribution and we accept the null hypothesis for this test (Tanner Youssef-Morgan, 2013). The chances of a data set to follow non normal distributions increases if the sample size is less. The statistical results from descriptive statistics are evaluated and this evaluation helps us to know about the basic properties of the data set. The descriptive statistics tells us about the mean, median, mode, skewness, kurtosis, quartiles of the given data set (Tanner Youssef-Morgan, 2013). In addition, data analysis can be done based on the dependency of a variable on other variable and on the extent at which a variable can describe another variable. Thus, we can also get the correlation and regression of the variables. This is how evaluation of different statistical results takes place. (Mohimani, Kim Pevzner, 2013). Conclusion of the thesis On attending the class on statistics, I have got to know about the various steps in the analysis of the data set. The thesis tells us about the various processes that are done on a data set to analyse it. At first we have to check the descriptive statistics and then select the appropriate issue for analysis. After selecting the appropriate issue, we are to form the hypothesis whether to accept or reject the given hypothesis. Then we have to conduct the appropriate statistical test based on the type of the sample and then analyse its result to accept or reject the null hypothesis. Thus, this thesis deals on the appropriate evaluation of the sample we got from the population. Reference Bickel, P. J., Lehmann, E. L. (2012).Descriptive statistics for nonparametric models. III. Dispersion(pp. 499-518). Springer US. Lehmann, E. L. (2012).Some principles of the theory of testing hypotheses(pp. 139-164). Springer US. Lowry, R. (2014). Concepts and applications of inferential statistics. Mohimani, H., Kim, S., Pevzner, P. A. (2013). A new approach to evaluating statistical significance of spectral identifications.Journal of proteome research,12(4), 1560-1568. Stanojevic, S., Rosenfeld, M. (2015). Selection and Appropriate Use of Spirometric Reference Equations for the Pediatric Population. InDiagnostic Tests in Pediatric Pulmonology(pp. 181-193). Springer New York. Tanner, D., Youssef-Morgan, C. (2013). Statistics for Managers. Bridgepoint Education.