What are Statistics

BUS308: Statistics for Managers

What are Statistics

**Introduction**

At the beginning of this course my understanding of statistics was that it was just another math class. Not only was statistics nothing close to math, it is a science. “Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data.” During these five weeks of class I was able run multiple statistics testing, interpret the results, and use excel to complete all the math I thought I was going to do. In the next few paragraphs I will go over some of the important parts of statistics such as descriptive statistics, inferential statistics, hypothesis development and testing, selection of appropriate statistical tests, and evaluating statistical results.

**Descriptive statistics**

In week one of the course, descriptive statistics was discussed and interpreted as measures that summarize characteristics of a group. Descriptive statistics are sample sets of data, that ultimately after breaking down with statistics, will provide a conclusion or finding. Within this data results are only applied to the specific data set being studied. Utilizing descriptive statistics one can gather information about an employee’s performance. You can use this to compare one data set such as male’s vs females to determine who gets paid more for the same job. It can be used for many things across the work industries. Data sets are a collection of data, data that eventually provides answers. Location measures consist of mean, median, and mode. These three provide additional information of the data sets such as average, mid points, and most frequent of the data sets. Descriptive measures describe data sets using the following measures:

**Inferential statistic**

- Range: Max value minus the min value
- Variance: the average of the square of sum between the difference of the value and mean
- Standard deviation: positive square root of variance.

Inferential statistics is in a sense descriptive statistic’s counterpart. When you are not using descriptive statistics, then you are using inferential statistics. When looking at data sets, and only concerned with using the group of data sets to “inferences, claims, and conclusions about a larger population, then we take a random sample from the population and use inferential statistics” (Week 1, Lecture 2, n.d, page 2). The difference between descriptive statistics and inferential statistics is that descriptive statistics describes a data set whereas inferential we can use to make claims or inferences based off a population/data set. Inferential statistics also consists of many statistics testing such as T-distribution, confidence intervals, hypothesis testing, and linear regression.

**Hypothesis development and testing**

According to K. Sethuraman and S.Mourougan, 2017 “Hypothesis testing is an important activity of evidence-based research”. The hypothesis testing allows for statistics to be used to examine what is found and make interpretations. The hypothesis testing procedure consists of six steps. The steps are as follows:

Look at the appropriate p-value (indicated in the test outputs, as we will see in lecture 2).

- State the null and alternate hypothesis: Ho, Ha; null hypothesis
- Select a level of significance:
*alpha*= 0.05 - Identify the statistical test to use this is determined by the data we have and what we are looking for.
- State the decision rule. Steps 1 – 4 are done before we examine the data: Reject the null hypothesis if the p-value is less than our alpha of .05
- Perform the analysis: Excel statistical function.
- Interpret the result (Week 2, Lecture 1, n.d, page 10):

Compare the p-value with our value for alpha (0.05).

Decide: if the test p-value is **less than or equal to **(<=) 0.05, we will **reject **the null hypothesis. If the test p-value is **more than **(=>) 0.05, we will **fail to reject **the null hypothesis.

Hypothesis testing is crucial to statistics and used to test a claim. Hypothesis testing allows us to reject the null hypothesis or fail to reject the null hypothesis. When rejecting the null hypothesis, you are indicating that the alternative hypothesis is the most accurate of the two.

- Rejecting the null hypothesis means that we feel the alternate hypothesis is the more accurate statement about the populations we are testing. This is the same for all our statistical tests.

**Selection of appropriate statistical tests**

Over the last few weeks we discussed many statistical tests. During week one we went over descriptive and inferential statistics as well as mean median, and mode. We went over range; max(range)-min(range), variance, and standard deviation; stdev.s(range). Week two goes into the F-test and T-test. F-test was used to compare “variances to determine if the differences noted could be from simple sampling error.” (Week 2, Lecture 2, n.d, page 3). Then there is the T-test which is used to test mean equality testing. During week three we went over multiple testing such as variance test, chi square distribution, and ANOVA; analyzes variance. Week four consisted of linear regression and multiple regression. Lastly, week five discussed confidence interval and effect size measure. Ultimately determining the appropriate statistical tests lies upon the nature of study.

**Evaluating statistical results**

Confidence level and effect size measure is used to evaluate data results. “A confidence interval is a range of values that, based upon the sample results, most likely contains the actual population parameter.” (Week 5, Lecture 1, n.d, page 1). Effect size measure is calculated for different statistical tests and consists of values such as “large”, “moderate” or “small”. With large effects would cause the rejection of the null hypothesis. A moderate outcome would need to be redone because it is less clear in results. Small effect would cause the rejection of the null hypothesis as well but with little or no practical significance.

**Conclusion**

At the beginning of this course my assumptions of statistics were vague and not very accurate. After completing this course, I can say that I have a much more appreciation of the what statistics provides. Though there are many kinds of statistical testing as well as different ways to analyze them, answers will be found. Combining statistics like descriptive and inferential statistics, and hypothesis development and testing, has provided me with enough knowledge to continue using these statistical formulas to help me make decisions based solely on data.

References

Explore. (n.d.). Retrieved October 6, 2019, from https://www.stat.uci.edu/what-is-statistics/.

Sethuraman2, D. K., & Mourougan, S. (n.d.). Hypothesis Development and Testing. Hypothesis Development and Testing, 19(5), 1–7. Retrieved from https://pdfs.semanticscholar.org/9bd0/d555e809ac52142271fd04489e7d5e97e2ec.pdf

Week 1 Lecture 1. (n.d.). 2019c Canvas Lecture Week 1 – 1a. Retrieved from https://ashford.instructure.com

Week 1 Lecture 2. (n.d.). 2019c Canvas Lecture Week 1 – 1a. Retrieved from https://ashford.instructure.com

Week 2 Lecture 1. (n.d.). 2019c Canvas Lecture Week 2 – 1a. Retrieved from https://ashford.instructure.com

Week 2 Lecture 2. (n.d.). 2019c Canvas Lecture Week 2 – 1a. Retrieved from https://ashford.instructure.com

Week 3 Lecture 1. (n.d.). 2018c Canvas Lecture Week 3 – 1a. Retrieved from https://ashford.instructure.com

What is the difference between descriptive and inferential statistics? (2019, April 5). Retrieved October 6, 2019, from https://businessdegrees.uab.edu/blog/descriptive-statistics-vs-inferential-statistics/.