week 1 reflection: What did you find that was really useful, or that challenged your thinking?
Focus on what you learned that made an impression, what may have surprised you, and what you found particularly beneficial and why. Specifically:
What did you find that was really useful, or that challenged your thinking?
What are you still mulling over?
Was there anything that you may take back to your classroom?
Is there anything you would like to have clarified?
ANSWER THE ABOVE BASED ON THE DOCUMENTS BELOW
Welcome to Statistics – the study of data! In this module we explore the GAISE report and what is involved in the process of statistical inquiry. We will look at study design and sampling. We will review the measures of center (mean, median and mode) in the context of sampling design and inquiry. By the end of this week’s investigations, you will be prepared to begin thinking about your own comparative study for the final project in the course.
Weekly Goals
Become acquainted and reacquainted with colleagues
Review basic statistics – measures of center
Look over the GAISE report and the process of statistics
Distinguish between Categorical and Quantitative Data and their representations
For Quantitative Data distinguish between continuous and discrete data and their representations
Distinguish between an observational study and an experiment
Identify design characteristics of a good study
Identify different types of sampling and the strengths and weaknesses of each type
Identify sources of bias in a study Define and identify lurking variables
Ice-Breaker and Personal Reflection [Wiki]
Part One: Meyer-Briggs
Take the Meyer-Briggs quiz.
We will get to know each other by creating a personal Wiki profile page.
To access the Wiki, please click on the Wiki link on the left side of the navigation bar.
Post your Meyers Briggs type, along with a photo of yourself, to your Wiki page.
Respond to the following questions:
Do you agree or disagree with your Meyer’s Briggs profile? Why?
How does your profile correctly reflect your role when you work with others or in a group?
Part Two: Personal Reflection
In the Personal Reflection section of your wiki profile, reflect on what statistics means to you. Some questions to consider (you need not address them all nor limit yourself to these):
What do you think of when you hear the word “statistics”?
How do you use or interact with statistics in your personal life?
How do you approach or incorporate statistics (if at all) into your classes?
How do you use or interact with statistics in your personal life?
What do your students understand about statistics?
How do you use statistics (if at all) to inform your teaching?
What do you know about the Statistics and Probability section of the Common Core State Standards for Mathematics for your grade band? How is this affecting your classes?
Please complete this reflection BEFORE completing any other investigations for this week. It should be a snapshot of you “before this course”; something we may return to at the end of this course to see how your thoughts and understandings may have changed.
Please post your introduction by Tuesday, 11:59 pm. Review the Wikis pages of your class. Identify at least two classmates with two Meyer-Briggs characteristics in common with you.
Please follow up with your classmates by Friday, 11:59 pm by posting comments to their Wiki pages.
DoW #1 aka Data of the Week
DoW stands for "Data of the Week".
Each week, you will be presented with data that relates to the week’s investigations. The form of the data will vary from week to week. Sometimes, it will involve gathering data yourself; other times the data will be presented to you in one form or another. It is important for you to become familiar with the Data of the Week at the start of each week; this data will be referred to during the investigations & will be central to the activities and discussions.
“Become familiar with the data” has many meanings. Some things you should do:
View the data in ways that are meaningful to you. You might organize it, graph it, or use some technology to help you do these things.
In your journal, write down interesting things you see in the data
In your journal, write down questions that you have about the data
Spending 15 minutes with the DoW at the start of the week will prepare you to engage with the data during the week’s investigations.
This Week’s DoW examines the question: Are the conclusions about the health affects of passive smoking associated with the affiliation of the author(s) of the article?
Bias in Smoking Article for Week One
A study1 of 106 reviews about the health effects of passive smoke looked at the association between the conclusion of the review and the affiliation of the author(s). A summary of the study is provided below:
Why Review Articles on the Health Effects of Passive Smoking Reach Different Conclusions
Deborah E. Barnes, MPH; Lisa A. Bero, PhD
Objective: To determine whether the conclusions of review articles on the health effects of passive smoking are associated with article quality, the affiliations of their authors, or other article characteristics.
Data Sources: Review articles published from 1980 to 1995 were identified through electronic searches of MEDLINE and EMBASE and from a database of symposium proceedings on passive smoking.
Article Selection: An article was included if its stated or implied purpose was to review the scientific evidence that passive smoking is associated with 1 or more health outcomes. Articles were excluded if they did not focus specifically on the health effects of passive smoking or if they were not written in English.
Data Extraction: Review article quality was evaluated by 2 independent assessors who were trained, followed a written protocol, had no disclosed conflicts of interest, and were blinded to all study hypotheses and identifying characteristics of articles. Article conclusions were categorized by the 2 assessors and by one of the authors. Author affiliation was classified as either tobacco industry affiliated or not, based on whether the authors were known to have received funding from or participated in activities sponsored by the tobacco industry. Other article characteristics were classified by one of the authors using predefined criteria.
Data Synthesis: A total of 106 reviews were identified. Overall, 37% (39/106) of reviews concluded that passive smoking is not harmful to health; 74% (29/39) of these were written by authors with tobacco industry affiliations. In multiple logistic regression analyses controlling for article quality, peer review status, article topic, and year of publication, the only factor associated with concluding that passive smoking is not harmful was whether an author was affiliated with the tobacco industry (odds ratio, 88.4; 95% confidence interval, 16.4-476.5; P,.001).
Conclusions: The conclusions of review articles are strongly associated with the affiliations of their authors. Authors of review articles should disclose potential financial conflicts of interest, and readers of review articles should consider authors’ affiliations when deciding how to judge an article’s conclusions. JAMA. 1998;279:1566-1570
1Barnes, Deborah E. 1998 Why review articles on the health effects of passive smoking reach different conclusions. JAMA. 279(19): 1566-1570.
The data from the study is summarized in the table & graphs below:
Investigation 1: The Process of Statistics
One way to think about statistics is as a problem-solving tool. The following four-step approach to statistics is taken from the Annenburg Learning Math program, Data Analysis, Statistics, and Probability. We will refer to sections of this program throughout the course. (It will be referred to as “The Annenburg Series”.)
Four components make a problem statistical: the way in which you ask the question, the role and nature of the data, the particular ways in which you examine the data, and the types of interpretations you make from the investigation. The table below summarizes the four steps of statistical problem solving:
Four Steps of Statistical Problem Solving:
1. Ask A Question
Asking a question gets the process started. It's important to ask a question carefully, with an understanding of the data you will use to find your answer. In framing your question, you need to specify:
The Observational Units: the “things” or “people” that you observe in the study. These are the members of the population and the sample.
The Variable(s): the characteristic(s) of the observational units that you would like to gather data on. Variables can be quantitative (numerical) or categorical (non-numerical).
2. Collect Approriate Data
Collecting data to help answer the question is an important step in the process. You obtain data by measuring something, so your measurement methods must be carefully selected and defined. There are many methods of gathering data, such as
Survey/Census
Experiment
Observation
Sampling: selecting a subgroup of your entire population to gather data on.
3. Analyze the Data
The original data collected is called raw data: it has not been organized, summarized, or represented in any new way. Data analysis is the process of organizing, summarizing, and representing data.
We analyze data using:
Tables
Graphs
Calculations that summarize the data (e.g, mean, median, range…)
4. Interpret the Results
After you analyze your data, you must interpret it in order to attempt to answer the original question. This includes explaining unexpected findings and discussing sources of bias (error) in the process. Interpretations should be supported by the analysis and often include probabilities that indicate the strength of the results.
Similarly, the GAISE Report (A Curriculum Framework for PreK-12 Statistics Education. 2005 Franklin, Christine, Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M., Schaeffer, R.) says:
The Investigative Process includes:
1. Formulate the Question
Teachers help pose questions (Questions in contexts of interest to the student)
Students distinguish between statistical solution and fixed answer
2. Collect Data to Answer the Question
Students conduct a census of the Classroom
Students understand individual-to-individual variability
Students conduct simple experiments with non-random assignment of treatment
Students understand variability attributable to an experimental condition
Students should understand what constitutes good practice in conducting a sample survey
Students should understand what constitutes good practice in conducting an experiment
Students should understand what constitutes good practice in conducting an observational study
Students should be able to design and implement a data collection plan for statistical studies, including observational studies, sample surveys, and simple comparative experiments
3. Analyze the Data
Students should be able to summarize numerical and categorical data using tables, graphical displays, and numerical summary statistics such as the mean and standard deviation
Students should understand how sampling distributions (developed through simulation) are used to describe sample-to-sample variability
Students should be able to recognize association between two categorical variables
Students should be able to describe relationships between two numerical variables using linear regression and the correlation coefficient
Students observe association between two variables
Students use tools for exploring distributions and association, including:
Bar Graph
Dotplot
Stem and Leaf Plot
Scatterplot Tables (using counts)
Mean, Median, …, Range
Modal Category
Histograms
The IQR (Interquartile Range)
MAD (Mean Absolute Deviation)
Five-Number Summaries and Boxplots
Students acknowledge sampling error
Students quantify the strength of association between two variables, develop simple models for association between two numerical variables, and use expanded tools for exploring association including:
Contingency Tables for two categorical variables
Time Series Plots
Simple lines for modeling association between two numerical variables
4. Interpret Results
Students describe differences between two or more groups with respect to center, spread, and shape
Students acknowledge that a sample may not be representative of a larger population
Students understand basic interpretations of measures of association
Students begin to distinguish between an observational study and a designed experiment
Students begin to distinguish between “association” and “cause and effect"
Students recognize sampling variability in summary measures such as the sample mean and the sample proportion
Students should understand the meaning of statistical significance and the difference between statistical significance and practical significance
Students should understand the role of P-values in determining statistical significance
Students should be able to interpret the margin of error associated with an estimate of a population characteristic
You may download the entire report from the ASA website.
I, Activity B: Sampling, Bias, and the Lurking Variable
A solid statistical study requires quality data to ensure a meaningful interpretation. This may sound simple, but it is no simple task to ensure that the data gathered represents what you believe it represents. Each decision you make, from the initial framing of the question to the selection of the sample to the actual collection of the data, can influence the quality of the data. Bias refers to systematic issues in the design of a study that affect the quality of the data.
In this activity, we look at sampling and bias.
View the presentation on Bias Week One - Understanding Bias. This presentation provides an overview of the issue of bias in statistics. It reviews some points brought up in Activity A, and previews some of the information in the following reading.
Read this chapter from CK-12 on Study Design. As you read, let the following questions guide you. Reflect on them in your journal.
What is the difference between a survey and a census?
What is a sample? Why do we use them?
What is a representative sample? What is a random sample?
Why is a random sampling method desirable?
What is Random Sampling? Stratified Sampling?
Sampling Biases Undercoverage (incorrect frame)
Convenience Sampling
Size Bias
Non-Response Bias
How can you reduce sample bias?
A Lurking Variable is a variable that directly affects both variables under consideration, making them appear to be related when they may not actually be related. The presence of possible Lurking Variables can influence the quality of a study. The YouTube video, The Lurking Variable, Part 1 discusses a hypothetical study on the relationship between depression and cancer diagnoses, highlighting the relevance of considering lurking variables in your study design and interpretation.
After watching the video, reflect on the following in your journal:
What is the lurking variable in the study?
What makes it a lurking variable?
How does the presence of this lurking variable influence the interpretation of the data?
Optional: You can watch the second part of this video, The Lurking Variable, Part 2.
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