Businesses today are faced with massive data from which they are to make decisions. But extensive data with no analysis is wasted data as no useful information can be drawn from it. Data is futile if not analyzed effectively and correctly. Statistics help in making the most critical decisions in businesses and other areas in society, such as in the criminal justice system, and help eliminate risks from decisions made subjectively, which are often wrong (Milgram, 2014). Statistics, therefore, help in decision-making more scientifically and objectively with a minimized chance of making errors in decision-making. The following assignment expands on the statistical test, the t-test, which analyses the differences between groups.
Statistics is crucial in management decision-making in a complex business environment. Williams (2019) asserted that statistics help focus on the big picture, back up assertions, make a connection between variables to establish relationships, and ensure product quality. In the modern world, organizations are faced with big data and statistical analysis is, therefore, a crucial part of these organizations to help draw useful information from the data.
After downloading the attached tutorial document, assignment three in the attached document provides data indicating data for ratings given before and ratings given after. The best statistical test to analyze is the paired t-test, which is an extremely useful and powerful tool to detect if there is a significant difference between the two groups. The paired t-test is used in experiments with data collected before and after for the same individuals. The data output for the sample data set, assignment three, is attached below.
Table 1: t-Test: Paired Two Sample for Means
|Ratings before||Ratings after Mean|
|Hypothesized Mean Difference||0 df||17 t|
|Stat||-0.676373538 P(T<=t)||one-tail 0.253951131 t|
|Critical one-tail||1.739606726 P(T<=t)||two-tail 0.507902262 t|
This data output seems to make more sense than just the previous raw data that had been provided. In this case, we interpret the results to make a meaningful conclusion that can be used for decision-making. In explaining the above output, we consider the P-value, P (T<=t) two-tail. To make use of the results, we first make a hypothesis for which the statistical test examines. The null hypothesis, in this case, is that the means for the ratings before and the ratings after are equal. In Excel analysis, we chose the alpha value of 0.05, implying that we are 95% confident in the obtained statistical output. The general criterion in making a decision is that we consider the p-value. If the value is greater than 0.05, we conclude that the means for the ratings before and after are not significantly different. In our case, the p-value is 0.507902262, which is greater than 0.5. This implies that there is no significant difference between the means in ratings before and ratings after.
Based on the output, we find that the mean for "ratings before" is 2.94, and the mean for "ratings after" is 3.22. If decisions were made from our own instincts, in most cases, we would be subjected to conclude that the means for the two groups are different. However, based on the statistical results, we see that there is no significant difference in the means. As such, we find the importance of statistical tests in helping make decisions in business and other areas such as the criminal justice system. We can conclude that statistical tests help eliminate decision-making errors or make decisions subjectively by scientific and objective decision-making criteria.
Milgram, A. (2014). Why smart statistics are the key to fighting crime [Video]. Retrieved from https://www.youtube.com/watch?v=ZJNESMhIxQ0
Williams, J. (2019). The Importance of Statistics in Management Decision Making. Retrieved 10 February 2020, from https://smallbusiness.chron.com/importance-statistics-management-decision-making-4589.html
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