Hypothesis Testing as a Statistical Tool and Its Application in the Current Business Setup - Coursework Example

Hypothesis Testing Business statistics can be scientifically defined as a decision making tool using scientificprinciples to formulate workable solutions to existing problems. Within the business field, statistics can be applied to different capacities, and this technique is commonly used in financial analysis, operations management, marketing research and auditing among others. In reaching different decisions using statistical methods, hypotheses are often formulated to act as guidelines. Various techniques are then applied in attempts to test the validity of the hypotheses, which determines whether the formulated hypotheses ought to be accepted or rejected. In addition some of the commonly used hypotheses testing procedures involve use of the P- values as discussed in this case. Key words: hypothesis testing, parameters, sample, accept, rejecting a claim. Introduction Statistics is one of the oldest fields in business studies. For a remarkable period of time, statistical tools have often been used to ascertain facts and fictions commonly encountered in day to day business activities. In fact, current statistical techniques have aided in development of methodologies that can be effectively applied to solve difficult situations within business setups. Managerial decisions are often quite difficult to make, however, the study notes that through proper application of statistical methods, such decision making processes can be simplified thus creating a better working relationship within the firm (Arshamp4). Through proper data analysis tools, Williamspoints out that business managers can easily make proper decision aimed at propelling business growth(p2). It comes out that relating various operations ongoing within the firm is very essential. In addition, considerations need to be made before taking certain decisions that may affect the employees or clients, either directly or indirectly (Williamsp8). In such instances, statistical tools come in handy to aid in ensuring equity and equality, moreover, the aim of different firms is to grow and expand business operations. Sadly, most large businesses have often ended up failing in this prospect. It is therefore imperative that the firm carries out market research to determine feasibility of various business proposals (Shuklap5). In such instances, statistical tools are central in the collection, analysis and interpretation of business findings. This hence provides the management with an ideal ground on which to base their claims. During these business research ventures, various hypotheses are often raised. Analytic parameters such as central tendency and dispersion are then tested to ascertain the validity of the proposals (Davie p1). This case critically analyses hypothesis testing as a statistical tool and its application in the current business setup. Hypothesis Testing Analysis Statistical data vary in their properties, which implies that large firms must process large volumes of data before drawing any credible conclusions. As a result, most of the firms have resorted to keen study of specific statistical parameters, using definite sample sizes to predict the characteristics of the parent population. The use of samples in statistical analysis is essential not only in saving the business firm large sums of capital, but also ensures timeliness of business operations. It as well lowers labor costs, requiring fewer personnel to analyze (Williamsp4). In selecting the samples, the firm may opt to adopt random techniques which are credited for being less biased. During the data analysis, the management may find out whether the specific parameter in question is normally distributed or not (Davie p1). In many instances, it is also necessary to determine the confidence levels of the data attained. Based on Javanmard and Montanari’s observation, business research involves use of non- linear parameter estimation techniques (p. 2). As such, it is quite difficult to obtain exact values for the given traits. Consequently, it is essential to accommodate the margin of error attainable within the study so as to account for constant variations in data characteristics (Davie p. 2). Hypothesis Testing Hypothesis testing process involves four critical steps which include; formulation of hypotheses, determination of decision making criteria, computation of test statistics and decision making process (Williams p4). The process is mainly accomplished using a distribution table. This table or graph is often partitioned into two regions, the acceptance and rejection regions. Based on the statistics available, one test values are then computed. The obtained results are checked against the test graph, and in such an instance, any value falling within the acceptance region is accepted, while values falling within the rejection region are rejected (Skrivanek p. 2). The rejection of a test value implies that the null hypothesis is false, while acceptance implies the null hypothesis is true. In testing for hypotheses, the determination of the p-value, the measure of evidence available against a null hypothesis, is critical. Based on Arsham, a statistical data set may have a p-value for one sided alternative hypothesis or two-sided alternative hypothesis (p. 10). In the two side case, the rejection regions lie on either ends of the acceptance region, but this is contrary to the single tailed case in which the rejection region either lies on the left or right side of the acceptance zone. Working with one-sided data sets is often easier and more accurate. As such, it is necessary that two sided sets are converted to one sided probabilities to enhance statistical accuracy both in computation and interpretation of test results. The conversion process occurs as outlined below (Arshamp15); Taking C to be the probability for the two sided confidence interval (CI) for the given data estimate, Then probability (C1) that either estimate is greater than lower limit or lower than upper limit is given by; C1 = C/2 + ½ ........ (one sided) Another essential component in statistical analysis when testing hypotheses is the a-value, which specifies the chances of error in the test process (Shuklap4). It is often necessary to minimize errors in computations, and as such, the a-value should always be as minimal as possible, possibly below 5% (Skrivanekp2). Bonferroni Method and Hommels principle In some instances, businesses are forced into rapid decision making processes. Therefore, it becomes necessary to adopt data comparison techniques to help in reaching feasible, statistically proven conclusions. Therefore, the firms may adopt the Bonferroni method to combine many t-tests. This technique is, however, limiting since it is not suitable for comparison of more than 8 data sets (Skrivanekp1). The Bonferroni technique is based on the equation t = ( 1 -2 )/ ( s2 / n1 + s2 / n2 )1/2.... where s2 is the population variance. In other cases, Hommels principle for multiple p-values may be adopted. This method is summarized as; p(n-j+k) >ka/j,    for all k=1,..,j. In this technique, the hypothesis is rejected when no J relationships occur and accepted when the data sets portray J relationships (Arsham p18). Power of the Test Following completion of the hypothesis test, it is necessary to determine the power of the test, which acts as a tool for measuring the accuracy of the test. Besides, it provides an ideal avenue for comparing two related test techniques. As defined by Skrivanek, the power of a test is the likelihood of rejecting a false Ho when the null hypothesis is when the null hypothesis is false (p. 1). This determination is important in ensuring a large sample size is used to produce conclusive results (Skrivanekp1). It is hence recommended to perform the test after determining the power of the test. After calculating the recommended power of the test, backward calculation should be carried out to determine the appropriate sample size (Williamsp2). The calculation of the power is, however, subject to several factors, and first it is subject to difference between the alternative and null hypothesis, and this effect also varies with sample size and variability of the sample. Finally, the power is influenced by the significance level of the test (Skrivanek p. 2). Parametric, Non-parametric and Distribution-free Tests 1. With these four pieces of information, we calculate the following statistic, t: t =  =  = 898 2. The test statistic for the Mann Whitney U Test R1=6+7+8+9+10 = 40 and R2= 1+2+3+4+5 = 15, Non-parametric and Distribution free tests are based on fewer and weaker assumptions compared to the parametric tests. Therefore, the distribution free and the non-parametric tests can be used as substitutes to the parametric tests in instances where the principles and rules involved in parametric tests are likely to be violated. As observed by Davie, non-parametric technique should be applied when dealing with enumerative data measured using nominal or ordinal scales (p. 1). It is also applicable for random data based on assumptions. Conclusion In summary, hypothesis testing is an essential part of business research that should never be ignored. In many cases, it has often come out that what is perceived to be true may be false. As such, it is important to ascertain the proposals in order to develop confidence in business activities and ventures. According to Javanmard and Montanari, current business problems are highly complex hence need integrated approach to attain more accurate results (p. 1). Firms must develop techniques that not only guarantee maximal confidence interval (CI), but also ensure minimal assumptions are made in the process. In testing for hypothesis, it is necessary that one clearly specifies the hypothesis they are willing to test, and this implies that both the null and alternative hypothesis must be outlined. In some instances, the null hypothesis can be statistically proven wrong through statistical procedures, and such a case implies that the alternative hypothesis (Ha) is correct. However, statistical techniques may at times give wrong reflections of the statistical parameters. For instance, calculations may brand a true null hypothesis as false leading to rejection (type 1 error). Alternatively, the reflections obtained from the sample statistics may lead to false acceptance of a wrong alternative hypothesis, a situation referred to as type 2 error (Arshamp1). It is therefore necessary to conduct multiple hypothesis testing using different samples from the same population to ascertain the validity of the hypothesis. Cited Works Arsham, H. "Dr. Arshams Statistics Site." National Science Foundation, 2013.Web. 30 July 2014. . Davie, A M. "Distribution-free Statistical Methods, 2nd Semester 2010-2011."Home - School of Mathematics, University of Edinburgh, Jan. 2011: 1 - 9. Web. 30 July 2014. . Javanmard, Adel, and Andrea Montanari."Confidence Intervals and Hypothesis Testing for High-Dimensional Regression."Stanford University. Stanford University, 18 Apr. 2014: 1 - 80. Web. 30 July 2014. . Shukla, Paurav. "Marketing Research."UniverzitaKarlova v Praze, Fakultatělesnévýchovy a sportu.PauravShukla&Ventus Publishing ApS, June 2008: 3-25 Web. 30 July 2014. Skrivanek ,Smita. "Power of a Statistical Test." MoreSteam.com LLC, Apr. 2009: 1 -14 Web. 30 July 2014. . Williams, John T. "The Importance of Statistics in Management Decision Making | Chron.com."Small Business - Chron.com. Hearst Newspapers, LLC, Apr. 2014. Web. 30 July 2014. . Read More