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1 STATISTICS FOR MANAGERS BUS 308 Statistics for Managers Ashford University
Introduction
Statistics can be an intimidating term for many of the older generation. The first thoughts that come to mind at the mention of statistics for many are mathematical expressions and formulas. One example of the powerful intimidation was presented by Dr. Collin’s in his week 4, lecture 2, “…..we need to calculate a t-value for each correlation, using the formula: t = r * sqrt(n-2)/sqrt(1-r^2), df = n-2;” (Statistics For Managers, 2019). WOW, that looks a little complex to the average manager. Technological advancements and the availability of computers have simplified the use of statistics and data analysis. Modern statistics reported by J. Hand, “the modern discipline is all about: the use of tools to aid perception and provide ways to shed light, routes to understanding, instruments for monitoring and guiding, and systems to assist decision making” (Hand D. J., 2008). This paper will examine the role of both descriptive and inferential statistics in hypothesis development and proper statistical test selection for evaluating the statistical results.
Descriptive Statistics
Descriptive statistics is the gathering, sorting, and summarizing of data. The first step is collecting a sample from a population. It is much quicker to take a random sample of the
population than to test every individual within it. Descriptive statistics use the mean, median, and mode, to measure the sample. The mean is the average of the sample. The median is thevalue that occurs in the middle of the set. That leaves the mode which is the value that occurs or repeats the most in the sample. Variations and consistency are also important descriptive statistics. Variance and range are how consistency and variation are measured. Data with little variation allows the sample set to give a better representation of the population. This suggests that no matter how many different sample sets are taken the results will remain similar. The opposite would be a population with greater variations. In this case, the sample sets would not be a close representation of the whole; therefore, different samples would give varying results. The larger the sample size the better it will represent the population.
Inferential Statistics
Inferential statistics is another tool used in data analysis; unlike descriptive statistics, it lets one make predictions and draw conclusions about the population. Confidence intervals and the margin of error are two tools used to show probability and how sure one is of the conclusion. The descriptive statistics allow one to make inferences about the total population. To answer the question of equal pay for female workers; descriptive statistic allows us to compare both male and female salaries, years of service, and level of education. One could compare the midpoint for salary and see which is higher than the other. The mode would tell us the value that repeats the most. When comparing male and female modes we might find the female mode higher than the male. Descriptive statistics illustrate the sample being explored. Samples offer the opportunity to discover the variable distribution of populations without testing every individual within the population. The shape of the data gives a visual understanding or translation of its distribution within the sample. The empirical rule of probability implies that 95% of data observed in a normal distribution lies within two standard
bias. Reject the Ho hypothesis if the P-value is less than alpha 0.05. Excel will be used to perform the testing. Both the F-test and T-test a function in excel, one just needs to use the data to decide which test to use. The final step is interpreting the results of the test. This is done by looking at the appropriate p-value. One needs to compare the p-value with the value set for alpha 0.05. The value will allow one a decision; if the p-value is less than or equal to alpha 0.05 the null hypothesis is rejected. If the value is more than alpha the null hypothesis is not rejected.
Selection of appropriate statistical test
The type of data and the question determine the statistical test selection. Is the male salary mean equal to the female mean? The F-test will be used to find the answer to this question. If the data is interval level the F-test is used. Interval data is measured along a numerical scale and has no true zero. The F-test is used to determine if a difference between the two groups has a large level of significance. This test will show if the difference is substantial or just the result of sampling error. The T-test is used for testing hypotheses through making inferences. Is the male salary mean greater than or equal to the female salary mean? The t-test in excel would provide a value for one to compare and draw a scientific conclusion. If the P-value for the male salary mean is greater than the P-value for the female, we have determined that maybe females are not receiving equal pay for equal work. Before the conclusion is reached more variables will need to be analyzed.
Evaluating the statistical results
The confidence interval is a range of values that is based on the results of a sample taken from a population that contains the actual population parameter. Confidence interval
levels can be created with the use of the T-test. They are generally expressed as a 95% level. This means the margin of error is only 5%. Another way to evaluate the statistical results is the effect size. The effect size is only used after the null hypothesis is rejected and labeled large moderate or small. When the effect size is large the variable caused the rejection of the null hypothesis; therefore, the results have a strong practical significance. If the results are small the sample size caused the rejection of the Ho and has no practical significance.
Conclusion
In conclusion, the gathering, sorting, and summarizing of data or descriptive statistics creates the opportunity for inferential statistics; this allows statistical testing that concludes with an evaluation of the results, which drive data-based decisions and assure one’s best chance for success. The availability of computers and Excel have brought statistical testing to a large percentage of the population. The use of Excel functions such as the T-test and ANOVA among others will allow managers the opportunity to eliminate variables and make data-based decisions with their desired level of a confidence interval. REFERENCES Collins, B., Dr. (n.d.). Lecture. Retrieved October 19, 2020, from https://ashford.instructure.com/courses/72779/pages/week-4-weekly-lecture Hand, D. J. (2008). Statistics : A very short introduction. ProQuest Ebook Centralhttps://ebookcentral- proquest-com.proxy-library.ashford.edu
