# RES600 INTRODUCTORY TO DATA ANALYSIS MODULE 3

**Module 3 – Home**

**MORE ADVANCED STATISTICAL MEASURES**

**Modular Learning Outcomes**

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

- Case
- Understand differences between parameters, statistics, population and samples; and how such differences influence the way we estimate parameters in the population.
- Understand sampling distributions, and how we use them in the estimation process.
- Understand Type I and Type II errors in research.

- SLP
- Understand and be able to construct confidence intervals for the mean, and be able to interpret such estimates.
- Be able to find the sample size needed for a desired interval.

- Discussion
- Understand and be able to construct confidence intervals for the mean, and its interpretation and uses. Develop critical thinking regarding confidence intervals.

**Module Overview**

In this module we will continue developing our understanding of statistical measures and their applications, beyond what was covered in module 2. We will start by discussing the role of statistical models in research, and continue to learn more about sample characteristics, variables, and parameters. We will talk about an important concept called sum of squared errors, and its importance in regards to model fit. Next we will understand what sampling variation is and how it helps us in estimating the true population mean. We will conclude with learning about confidence intervals, why and when we use them, and how to calculate them.

**Module 3 – Background**

**MORE ADVANCED STATISTICAL MEASURES**

**Required Reading**

On parameters and statistics and populations and samples:

*http://statistics.about.com/od/Glossary/a/What-Is-The-Difference-Between-A-Parameter-And-A-Statistic.htm**https://www.youtube.com/watch?v=M-L8C2aOf7E*

On differences between sample and sampling distribution:

On confidence intervals:

*http://www.youtube.com/watch?v=R2vhjC5qCQk**http://onlinestatbook.com/lms/estimation/confidence.html**http://onlinestatbook.com/lms/estimation/mean.html**http://onlinestatbook.com/lms/estimation/confidenceM.html**http://onlinestatbook.com/lms/estimation/proportion_ci.html**http://onlinestatbook.com/lms/estimation/proportion_ciM.html*

On Type I and Type II errors:

**Optional Reading**

*http://www.unc.edu/~nielsen/soci708/mod5/soci708mod5.pdf*

*http://www.itl.nist.gov/div898/handbook/prc/section1/prc14.htm*

**Module 3 – Case**

**MORE ADVANCED STATISTICAL MEASURES**

**Assignment Overview**

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

Venkatesh, F. & Davis, F. (2000). A theoretical extension of the technology acceptance model: Four longitudinal field studies. *Management Science, 36*(2), 186-204. Retrieved from the Trident Online Library.

**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.
- What is the sample used in this study? What is the population targeted by this study? Can we generalize from the sample to the population?
- Describe key statistics in this study. Does the study describe parameters? Explain.
- Explain the process for validating the survey instrument.

Please organize your paper in a scholarly way. Add section titles when necessary. Explain your logic, and when appropriate, use external sources and use 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 understands the key research questions in this paper.
- Student is able to understand and identify the following research-related concepts: samples, populations, parameters and statistics; confidence intervals and types of error in inference.
- 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 3 – SLP**

**MORE ADVANCED STATISTICAL MEASURES**

The hypothetical data file *debt.xlsx* was shows the level of debt in 100 American households. Use these data in SPSS:

- Calculate the mean and standard deviation for the sample.
- Can you infer that the calculated mean is the mean debt in the population? Why?
- Develop a 95% confidence interval for the average level of debt per household in the United States.
- Interpret the results.
- If you’d like the accuracy of your estimation to be within -/+$1,000 from the true mean, what size of a sample would you need?
- What steps can you take, when you design your study, to make sure the sample represents the population?

**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 3 – Outcomes**

**MORE ADVANCED STATISTICAL MEASURES**

- Module
- Identify and understand differences between parameters, statistics, population and samples.
- Understand the concept of sampling distributions and its implications for statistical inference.
- Understand and be able to construct confidence intervals for the mean and proportions, and their interpretations and uses.

- Case
- Understand differences between parameters, statistics, population and samples; and how such differences influence the way we estimate parameters in the population.
- Understand sampling distributions, and how we use them in the estimation process.
- Understand Type I and Type II errors in research.

- SLP
- Understand and be able to construct confidence intervals for the mean, and be able to interpret such estimates.
- Be able to find the sample size needed for a desired interval.

- Discussion
- Understand and be able to construct confidence intervals for the mean, and its interpretation and uses. Develop critical thinking regarding confidence intervals.

Discussion: Understanding Polls—Confidence Interval

Many newspapers, when reporting results of political polls, say that “with 95% confidence, the results are in error by no more than +/- 3 percentage points.” The typical sample size is about 1,500. This allowance for error is intended to cover both sampling variability and the effect of small biases.

- Assume that the poll (sample) indicates that just about 50% of likely voters favor a particular candidate. How large a +/- term is required for a 95% confidence interval for the population proportion?
- Would the +/- term be much different if 40% of likely voters in the sample favored the candidate?
- Why is the quoted +/- 0.03 larger than the +/- term you calculated in Question 1?