Probability, Sampling Distributions, and Confidence Intervals
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Probabilitywk4.docxProbability, Sampling Distributions, and Confidence Intervals
Life is filled with uncertainty.
—Thomas Dietz, Professor, Author
—Linda Kalof, Professor, Author
Our daily lives revolve around things that we cannot control. Before we step out the front door we ask, will it rain today? What is the chance of getting stuck in traffic? Or better yet, will my class be cancelled? Even though Dietz and Kalof (2009) suggest that life is uncontrollable, we still try to feel a small sense of control through a smart use of statistics. Probability helps us to understand and cope with the seemingly uncertain decisions of life.
Uncertainty is also present in our samples since we rarely have the ability to measure the entire population. Understanding probability also assists us in obtaining accurate, representative samples. From probability-based samples we can construct confidence intervals to obtain a range of values in which our population value may lie.
In this week, you will explore probability as it relates to an observed occurrence. You also will explore the concept of the sampling distribution as well as confidence intervals of specific data. Finally, you explore the results of data to determine implications for social change.
Learning Objectives
Students will:
· Evaluate various distributions
· Evaluate confidence intervals
· Create visual displays of data
· Analyze data from datasets
· Analyze implications for social change
Learning Resources
Required Readings
Frankfort-Nachmias, C., & Leon-Guerrero, A. (2018). Social statistics for a diverse society (8th ed.). Thousand Oaks, CA: Sage Publications.
· Chapter 5, “The Normal Distribution” (pp. 128-150)
· Chapter 6, “Sampling and Sampling Distributions” (pp. 151-178)
· Chapter 7, “Estimation” (pp. 179-201)
Wagner, W. E. (2016). Using IBM® SPSS® statistics for research methods and social science statistics (6th ed.). Thousand Oaks, CA: Sage Publications.
· Chapter 3, “Selecting and Sampling Cases”
· Chapter 5, “Charts and Graphs”
· Chapter 11, “Editing Output”
Magnusson, K. (n.d.). Welcome to Kristoffer Magnusson’s blog about R, Statistics, Psychology, Open Science, Data Visualization [blog]. Retrieved from http://rpsychologist.com/index.html
As you review this web blog, select the Interpreting Confidence Intervals – new d3.js visualization link, once you select the link, follow the instructions to view the interactive for confidence intervals. This interactive will help you to visualize and understand confidence intervals.
Note: This is Kristoffer Magnusson’s personal blog and his views may not necessarily reflect the views of Walden University faculty.
Walden University Library. (n.d.). Course Guide and Assignment Help for RSCH 8210. Retrieved from http://academicguides.waldenu.edu/rsch8210
For help with this week’s research, see this Course Guide and related weekly assignment resources.
Datasets
Document: Data Set 2014 General Social Survey (dataset file)
Use this dataset to complete this week’s Discussion.
Note: You will need the SPSS software to open this dataset.
Document: Data Set Afrobarometer (dataset file)
Use this dataset to complete this week’s Assignment.
Note: You will need the SPSS software to open this dataset.
Document: High School Longitudinal Study 2009 Dataset (dataset file)
Use this dataset to complete this week’s Assignment.
Note: You will need the SPSS software to open this dataset.
Optional Resources
Rice University, University of Houston Clear Lake, and Tufts University. (n.d.). Online Statistics Education: An Interactive Multimedia Course of Study. Retrieved from http://onlinestatbook.com/2/estimation/ci_sim.html
Use this website for your practice as you consider confidence intervals and how the width changes. Also, consider why the width might be important.
Skill Builders:
· Confidence Intervals
· Sampling Distributions
To access these Skill Builders, navigate back to your Blackboard Course Home page, and locate “Skill Builders” in the left navigation pane. From there, click on the relevant Skill Builder link for this week.
You are encouraged to click through these and all Skill Builders to gain additional practice with these concepts. Doing so will bolster your knowledge of the concepts you’re learning this week and throughout the course.
Discussion: The Importance of Relationships
As its name implies, confidence intervals provide a range of values, along with a level of confidence, to serve as an estimate of some unknown population value. Since it is rare to have access to the entire population, you must frequently rely on the confidence interval of the sample to make some inference about the population of interest. Before making accurate inferences to the population, we need to fully understand how the three key components of the interval—variability in the data, sample size, and confidence level—impact the width of the interval.
For this Discussion, you will explore the relationship between these components and understand the trade-off between reducing risk in our confidence of estimates and increasing precision.
To prepare for this Discussion:
· Review Chapters 6 and 7 of the Frankfort-Nachmias & Leon-Guerrero text and in Chapter 7, p. 188, consider Hispanic migration and earnings and focus on how different levels of confidence and sample size work together.
· Review Magnusson’s web blog found in the Learning Resources to further your visualization and understanding of confidence intervals.
· Use the Course Guide and Assignment Help found in this week’s Learning Resources to search for a quantitative article related to confidence intervals.
· Using the SPSS software, General Social Survey dataset and choose a quantitative variable that interests you.
By Day 3
Using SPSS:
1. Take a random sample of 100.
2. Calculate the 95% confidence interval for the variable.
3. Calculate a 90% confidence interval.
4. Take another random sample of 400.
5. Calculate the 95% confidence interval for the variable.
6. Calculate a 90% confidence interval.
Post your results and an explanation of how different levels of confidence and sample size affect the width of the confidence interval. Next, consider the statement, “Confidence intervals are underutilized” and explain what the implications might be of using or not using confidence intervals. Provide examples based on the results of your data. Also, use your research to support your findings.
Be sure to support your Main Post and Response Post with reference to the week’s Learning Resources and other scholarly evidence in APA Style.
Assignment: Introduction to Quantitative Analysis: Confidence Intervals
To prepare for this Assignment:
· Review the Learning Resources related to probability, sampling distributions, and confidence intervals.
· For additional support, review the Skill Builder: Confidence Intervals and the Skill Builder: Sampling Distributions, which you can find by navigating back to your Blackboard Course Home Page. From there, locate the Skill Builder link in the left navigation pane.
· Using the SPSS software, open the Afrobarometer dataset or the High School Longitudinal Study dataset (whichever you chose) from Week 2.
· Choose an appropriate variable from Weeks 2 and 3 and calculate a confidence interval in SPSS.
· Once you perform your confidence interval, review Chapter 5 and 11 of the Wagner text to understand how to copy and paste your output into your Word document.
For this Assignment:
Write a 2- to 3-paragraph analysis of your results and include a copy and paste of the appropriate visual display of the data into your document.
Based on the results of your data in this confidence interval Assignment, provide a brief explanation of what the implications for social change might be.
