In our revision we were very comfortable in the hypothesis testing procedures which we learned as the process by which a researcher conducts tests and also experiments in order to prove that a proposed explanation of a phenomenon under observation really works in practice (Wise GREEK). As individuals and as a team we have learned the processes that include the steps of testing a research hypothesis which in this case includes identifying the research problem, determining the hypotheses, calculating the t-statistics, determining the probability of the rejected region and finally making interpretations and conclusions by comparing two or more groups by computing the correlation between two variables. All of these gave us the ability to systematically gather and calculate data while following a scientific approach. However, we found some few challenges in the calculations of probability value which is compared to the value of the significance to determine if it is significantly different in order to make final conclusions. In addition, we discovered the importance of statistical skills which are useful in the calculation of correlations between two or more variables, determining T- Statistics and F-Statistics which are helpful statistical formulas.
In comparing the means of two or more groups, we use two methods known as the ANOVA (Analysis of the Variance) with the fisher’s formula; and the t-test, with a formula, t ,where r is coefficient of correlation n is sample size while (n-2) is the degree of freedom..
The two methods depends on the different degree of freedoms and the difference between them in comparing means is that, the ANOVA is able to compare the similarities between two or more class of means while on the other hand the t-test can only compare two class of means and it tells us whether two categories of means are significantly different from each other. We also learned on how to use the probability tables in determining the values of these methods. In our findings, we learnt that the F-distribution table is used to determine the probability value when using ANOVA while the T-distribution table is used to determine the probability value using the t-test method. The values on the LHS (left hand side) are called dependent variables because they are caused to change as a result of a change in the independent variables which are at the RHS (right hand side) of a linear equation.
Many businesses have applied these comparing techniques in their activities, for example, when comparing different products of the competitors in order to respond to the threat posed in the market by the competitors. An example of such business is Chevrolet Motor Company which uses statistics in determining the amount of gasoline used over the similar distances by the cars. From a large group, the determination of a grand mean from two or more means are computed by adding the common variance from the sample means represented as (x1-x2) and then it is multiplied by (x1-x2) (McClave, Benson, & Sincich, 2011). Through this formula the Company could determine that two cars could use between 30-40 gallons of gasoline per mile travelled. In its conclusion Chevrolet may set the above average as the benchmark in its manufacturing lines in that any car consuming more if not produced anymore. In some cases, the business may use the t-distribution tables when the sample size if small i.e. n<30, because the variance is insignificant (McClave, Benson, & Sincich, 2011). Here the sums of the squares of means are divided by the sample size and subtracting two. Similarly, we also learnt how to compute the degree of variations between two variables called correlation. The correlation between two variables is shown by the degree of change of one of the depended variable caused by a change in the independent variable. The correlation coefficient is denoted by letter ‘r’. Its formula is; Where, rxy – is coefficient of correlation, cov (x,y) denotes covariance of variables x and y while sx.sy denotes the products of the standard deviation of x and y respectively. The coefficient correlation is said to be positive when, rxy > 0, while it is said to be negative when rxy < 0. There is no correlation between two variables when, rxy = 0. The closer the coefficient of correlation to 1, the stronger is the positive relation between the two variables. This comparison technique is applied in business to compare different the effects of change in consumers’ income on their purchases (Sighn, D. & Wang, Y. 2011).
In conclusion, Statistics indeed helps managers make business short-term decisions as they anticipate for the long-term changes of the business. For example, the average amount of dollars spent in a specific area such as electronics versus the average amount of dollars spent in softlines helps management to determine where they can be the most profitable. As a manager at Target, I use statistics to track the performance of my employees by using time specific goals and determining the average amount of time the team spends stocking each area. I can determine what areas the team is slowest at and create innovative ideas to help boost my team's performance in those weak areas.
Lorelei Howard and Nick Wright (2008). t-tests, ANOVA and regression - and their application to the statistical analysis of fMRI data. Retrieved from:
Sighn, D. & Wang, Y (2011). Business Statistics. Hochschule Bonn-Rhein-Sieg University of applied science. Retrieved from: http://www.slideshare.net/divyanshu22/correlation-analysis-12140817