# RES600 INTRODUCTORY TO DATA ANALYSIS MODULE 2

**Module 2 – Home**

**BASIC STATISTICAL MEASURES**

**Modular Learning Outcomes**

Upon successful completion of this module, the student will be able to satisfy the following outcomes:

- Case
- Understand the various attributes of variable distributions, and the implications of these attributes for research.
- Understand the selection of measures and the basic concepts associated with the normal distribution.

- SLP
- Understand key concepts related to and measures of central tendency and dispersion, measure selection, and the normal distribution.

- Discussion
- Develop critical thinking regarding variables and their distributions.

**Module Overview**

In this module we use the language and knowledge we acquired in the previous module and start talking about basic statistical measures, which allow us to understand the data we collect. Before we run inferential analyses, we need to be able to describe the data and understand its qualities. For these purposes, we will discuss the concepts and applications of frequency distribution, shapes of distributions, skewness and kurtosis measures, and measures of central tendency (mean, mode, median), measures of dispersion (standard deviation, variance and range). We will then discuss when to use which measure and emphasize the advantages of using well-validated existing scales when they exist. Finally, we will discuss one of the most important distributions in management research, namely the normal distribution which is the basis for most statistical techniques we will in this course and beyond. In this context, we will also discuss z-scores, probability distribution and percentiles.

**Module 2 – Background**

**BASIC STATISTICAL MEASURES**

**Required Reading**

**On measures of central tendency:**

- Dietz, D., Barr, C. D., & Çetinkaya-Rundel, M. (2016). OpenIntro statistics, 3rd ed.

(The textbook is available under a Creative Commons license. Visit openintro.org for a free PDF, to download the textbook’s sources, or for more information about the license.)

*https://www.openintro.org/stat/textbook.php?stat_book=os*

Chapters 2, 3, and 4. *http://onlinestatbook.com/2/summarizing_distributions/measures.html*- Watch:
*http://www.youtube.com/watch?v=E4HAYd0QnRc* - Watch:
*http://www.youtube.com/watch?v=RAekTsenqPI*

**On the Normal distribution**

*https://www3.nd.edu/~rwilliam/stats1/x21.pdf**http://www.youtube.com/watch?v=mai23vW8uFM**http://www.dummies.com/how-to/content/understanding-the-statistical-properties-of-the-no.html**http://www.dummies.com/how-to/content/how-to-find-a-percentile-for-a-normal-distribution.html*

**Optional Reading**

*http://www.youtube.com/watch?v=uanvaJCYY_8*

**Module 2 – Case**

**BASIC STATISTICAL MEASURES**

**Assignment Overview**

Please read the following research paper (available in Trident’s e-library):

Turel, O., and Zhang, J. (2010) *Does virtual team composition matter? Trait and problem-solving configuration effects on team performance.* *Behaviour & Information Technology, 29*(14), 363–375.

**Case Assignment**

Based on the above information, write a paper, addressing the following issues:

- What are the key research questions in this study? Summarize the key findings in this paper.
- Describe the measures used, their level (interval, ratio, ordinal, etc.), and the their descriptive statics (of central tendency and spread).
- Why does the “standard performance” have a mean of zero? A standard deviation of one?
- Were the provided descriptive statics appropriate for the types data? Why?
- What was a key issue the authors faced in their analysis? Why is it an issue? And how did they deal with it?

Please organize your paper in a scholarly way. Add section titles when necessary. Explain your logic and when appropriate, use external sources with proper citations. Conclude your report with a paragraph or so evaluating the entire exercise in terms of what you have learned and your reflections on the topic.

The paper is usually between 5 and 12 pages long.

**Assignment Expectations**

- Student is able to understand the key research questions in this paper.
- Student is able to identify and interpret descriptive statistics in the paper; as well as issues and solutions related to normality.
- Student answers the questions with clarity, depth and critical thinking.
- Completeness and coherence: Chain of thought is easy to follow.
- Student uses relevant evidence and additional papers/resources to support the propositions.
- Paper is clearly written with appropriate format. Reference list is complete. Citation is properly done.

Your assignment will be graded using the following criteria:

- Assignment-Driven Criteria: Student demonstrates mastery covering all key elements of the assignment.
- Critical Thinking: Student demonstrates mastery conceptualizing the problem. Viewpoints and assumptions of experts are analyzed, synthesized, and evaluated. Conclusions are logically presented with appropriate rationale.
- Scholarly Writing: Student demonstrates mastery and proficiency in scholarly writing following required structure and organization of the assignment, using relevant and quality sources to support ideas, using in-text citations of sources and properly formatting references (bibliography).
- Professionalism and Timeliness: Student demonstrates excellence in taking responsibility for learning, adhering to course requirement policies and expectations. Assignment submitted on time or with professor’s pre-approved assignment extension.

**Module 2 – SLP**

**BASIC STATISTICAL MEASURES**

- The following data were collected from 10 individuals:

Age |
Number of past jobs |
Current job status |
Income |

25 | 1 | employed | 30,000 |

34 | 2 | unemployed | 40,000 |

29 | 2 | employed | 40,200 |

38 | 2 | unemployed | 45,000 |

44 | 1 | employed | 52,000 |

49 | 4 | unemployed | 25,000 |

55 | 4 | employed | 80,000 |

23 | 3 | unemployed | 120,000 |

44 | 2 | employed | 120,000 |

44 | 3 | unemployed | 38,000 |

- Calculate the mean, median, and mode for “Age” (with SPSS).
- Calculate measures of dispersion for “Age” (with SPSS).
- Calculate Skewness and Kurtosis for “Income” (with SPSS). Is this variable skewed? If so, what kind of skew?
- Prepare a frequency distribution for the data of “number of past jobs.” Plot it (bar chart).
- Given the provided income distribution (and assuming normality), what would be the z-score for someone who earns $40,000/year? $100,000/year?

**SLP Assignment Expectations**

- Answer all questions with clarity and depth. Show your critical thinking ability.
- Show necessary reasoning.
- You do not need to write an essay for SLP assignment; answering the questions is sufficient.

Your assignment will be graded using the following criteria:

- Assignment-Driven Criteria: Expressing quantitative analysis of data to support the discussion showing what evidence is used and how it is contextualized.
- Interpretation: Explaining information presented in mathematical terms (e.g., equations, graphs, diagrams, tables, words).
- Presentation: Ability to convert relevant information into various mathematical terms (e.g., equations, graphs, diagrams, tables, words).
- Conclusions: Drawing appropriate conclusions based on the analysis of data.
- Timeliness and Professionalism: Student demonstrates excellence in taking responsibility for learning, adhering to course requirement policies and expectations. Assignment submitted on time or collaborated with professor for an approved extension on due date.

**Module 2 – Outcomes**

**BASIC STATISTICAL MEASURES**

- Module
- Identify and understand measures related to variable distributions.
- Identify basic measures of central tendency and variability in data and choose appropriate summary statistics depending on the nature of the data.
- Understand the normal distribution and its uses.

- Case
- Understand the various attributes of variable distributions, and the implications of these attributes for research.
- Understand the selection of measures and the basic concepts associated with the normal distribution.

- SLP
- Understand key concepts related to and measures of central tendency and dispersion, measure selection, and the normal distribution.

- Discussion
- Develop critical thinking regarding variables and their distributions.

# Module 2 Discussion

Reflect on your research intentions and a variable which may be potentially of interest to you. Please describe this variable and how you may measure it (e.g., which sample will you approach). Then explain whether you expect it to be normally distributed and the logic for your assumption. If you expect a deviation from normality, please explain how you may deal with it. You may search external sources for addressing the last point.