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Ashford UniversityStatistics Final PaperBUS/308ProfessorDateStatistics Final PaperIn the entire class BUS/308, a survey of statistics has been presented ranging from descriptive statistics to inferential statistics, and everything in between. Three of the most important elements of the course are descriptive statistics, types of hypothesis testing, and the use and appropriateness of hypothesis tests. Descriptive StatisticsDescriptive statistics is one of the first things discussed in BUS/308, and is the fundamental to more complicated statistical analysis. The topic is covered in many other courses including elementary mathematics courses due to the importance of descriptive statistic measures. Descriptive statistics measures are broken into two groups – measures of central tendency, measures of dispersion.Measures of central tendency include the three well-known mean, median, and mode. The mean is the average of the data set, and is a unique value. The median is a unique value which represents the middle of the data set; 50% of values lie above and below this value. Lastly, the mode is a sometimes unique value that represents the data value with the most occurrence. Each one of these three statistics are strong in analysis, but are only appropriate in certain areas. The mean and median are very strong all around, except the mean is weak when the data set has outliers, while the median is not. The mode, on the other hand, is one of the weakest and least-used measures due to its many disadvantages – it is usually not unique, meaning there can be no mode, one mode, or many modes, which make it a difficult measure to use to compare data sets. The second group of descriptive statistics are the measures of dispersion. There are several measures of dispersion, such as the range, IQR, standard deviation, variance, and skew. The most used are the standard deviation and variance, described as the amount of dispersion from the mean and the square of the former respectively. The standard deviation and variance are two measures that can be applied to almost every type of distribution, thus its strength. In most cases, the standard deviation trumps the range and IQR as useful measures of dispersion since knowing the range of distributions is a statistic that is of no use as it does not give an idea of a data value’s proximity to the central data point. The use of the two forms of descriptive statistics is the quintessence of statistics. Without the mean, median, standard deviation, and variance, a large majority of theoretical statistics would be unfounded and the basis of hypothesis testing would not exist. Descriptive statistics serves as the crux of the next major topic of the course – hypothesis testing and its types. Types of hypothesis testingWith the help of descriptive statistics, the use of hypothesis testing is possible. Hypothesis testing is the basic process of using statistical methods to test a hypothesis, or a claim/idea produced by a researcher. The hypothesis must be clearly defined, which is then used to formulate an appropriate research methodology (Curran-Everett, 2009). Depending on the hypothesis being tested, there are many different types of hypothesis tests that can be used. The first step to hypothesis testing is developing the hypothesis. The research/scientific hypothesis should be the status-quo; it is what the researcher is testing to determine if it is false. The hypothesis, commonly known as the null hypothesis, must be clear and testable by statistical means. After the null hypothesis is created, the alternate hypothesis can be created – which is the opposite of the null hypothesis, or the result that the researcher hopes to uncover. Since the null hypothesis is the status-quo, the goal of the researcher is usually to reject the null so he/she can report his/her conclusion to the public via professional journals (Fagerland et al, 2011).After the development of the hypotheses, the testing phase can be applied. There are many types of testing procedures that can be used, and they are all dependent on the hypothesis. Examples of hypothesis tests include one-sample z and t tests for sample means, two-sample z and t tests for sample means, t test for paired sample, tests for proportion, regression test for significance of slope, chi-square for independence/homogeneity, analysis of variance and more. All situations that can arise for a researcher are compatible with at least one of the scores of parametric and non-parametric hypothesis tests (Fagerland et al, 2011). The appropriateness of a hypothesis test is important, since each hypothesis test comes with its lists of assumptions, which if violated are not applicable to the research scenario.Appropriateness of hypothesis testingOf the hypothesis tests listed above, each is appropriate in its unique way. There are cases where research can be analyzed using only one of the ways above, two of the ways above, or none of the ways above. In situations where multiple tests can be used, using the most robust test will ensure results tested at rigorous levels. In a situation where none of the tests above are valid, a researcher might have to resort to non-parametric hypothesis testing (as opposed to the parametric tests listed above) since these tests are used when parametric assumptions are violated (Driscoll and Lecky, 2001). For example, a researcher wishes to determine whether an experimental drug for Alzheimer’s has an effect over a six month period. The researcher would apply a t-test for paired samples here since the same sample of people is being compared before and after treatment. In another case, a researcher wishes to determine the effects of classroom music and classroom atmosphere on testing with three levels of difficulty – easy, medium, or hard. The researcher would apply a factorial ANOVA to determine the significance of the variables upon each other. After the appropriate hypothesis testing procedure has been chosen, the rest of the procedure is a simple execution of the hypothesis testing process. The data is tabulated, important descriptive statistics are calculated, significance level and critical region are established, test statistic is calculated, and final conclusion is made. ConclusionIn conclusion, the BUS/308 course provides an entire survey of statistical analysis. The basics of statistical analysis begin with descriptive statistics, and progress onto with the development of inferential statistics and further usage of descriptive statistics. Both forms of statistics work hand in hand, and neither part can provide the complete functionality that is today used in almost every field of science without the other part. ReferencesCurran-Everett, D. (2009). Explorations in statistics: Hypothesis tests and P values.Advances in Physiology Education, 33(2), 81-86. Retrieved October 4, 2014, from http://advan.physiology.org/content/33/2/81Driscoll, P., & Lecky, F. (2001). Article 8. An introduction to hypothesis testing. Non-parametric comparison of two groups—1. Emerg Med J, 18(4), 276-282. Retrieved October 4, 2014, from http://emj.bmj.com/content/18/4/276.fullFagerland, M., Sandvik, L., & Mowinckel, P. (2011). Parametric methods outperformed non-parametric methods in comparisons of discrete numerical variables. BMC. Retrieved October 3, 2014, from http://www.biomedcentral.com/1471-2288/11/44Tanner, D., & Youssef-Morgan, C. (2013). Statistics for Managers. San Diego: Bridgepoint Education.
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