Math 101a Projects

Math Autobiography
Project 1: Reading the News
Project 2: Public Opinion Poll
Project 3: Numerical and Graphical Summaries of Data
Project 4: Is the Relationship Statistically Significant?

Talk about your previous experiences with math classes. What classes have you taken in the past? Do you like math? Love math? Hate math? What events and/or past traumas have transpired to shape your feelings regarding math? Talk about your previous math teachers. What is the most positive memory or experience you've had with math? Least positive? What exactly do you like or dislike about math? In what kind of environment do you learn best? Why are you taking this class? Do you have any preconceived notions about statistics coming into this class? What do you expect to learn in this class? What have you heard from other students regarding this class? Do you plan to take additional math classes in the future or is this it for you? Give at least one example of how you have had to use math recently outside of school.

The above questions are guidelines to get you started. In general, reflect upon your past experiences in math, as one who does mathematics, one who "consumes" mathematics in daily life, and one who must communicate mathematics, as well as your associated level of confidence. Be sure to mention your intended major and possible career choices. This assignment should be about 2 pages typed.

Find a newspaper or web article that discusses a recent study involving statistical methods.
You are not allowed to use opinion polls or magazine advertisements.

• Begin by providing a brief summary of the study and results as described in the news article.
• Identify the type of study conducted, i.e., an observational study, a randomized experiment, or some other type.
• Comment on how well the simple concepts of Chapter 1 were applied in the study.
• Identify all of the seven critical components (discussed in Chapter 2) and be sure to address those that are missing.
• Consider at least one of the missing components and give an example of a hypothetical report that could lead to a different conclusion about the applicability of the results of the study.
• Discuss whether any other information is missing from the news article that would have helped you answer the previous questions.
• Comment on whether the news article, including the headline, accurately reports the conclusions that can legitimately be made from the study. Determine if the results are meaningful enough to encourage you (or your family members) to make a change in lifestyle, attitudes, or beliefs on the basis of the research.

To the best of your ability, design a survey with three unbiased questions to measure attitudes toward something of interest to you. Then design a second version by changing just a few words in each question make it deliberately biased. The goal is to compare the results of the two surveys. In other words, are you able to sway public opinion by crafting a deliberately biased survey? Therefore, you need to ensure that your biased questions are designed to create a consistent bias in the same direction.

Bring 4 (typed) copies of your survey for both sets of questions to class on Tuesday, January 30. Your group will exchange surveys with another group in order to critique each other's questions. Based upon their critique you may need to alter the wording of your biased and/or unbiased questions

You will need a sample of at least 40 people. Administer the unbiased survey to 20 people and the biased version to a different group of 20 people. You may need to select more than 40 people to survey since some people may be unavailable or unwilling to participate.

The paper should be written according to the following format guidelines:

• Part I: Introduction
  What is it about this topic that is interesting to you? Have similar polls been done elsewhere? If so, what were the results? Before giving the survey try to predict the results of the answers provided by the two samples: the group with biased questions vs. the group with unbiased questions. Describe the population of interest for your survey.
• Part II: The Questionnaire
  Be sure to provide a list of the exact questions that were asked for each version of the survey. Discuss whether or not you altered your questions based upon the critique by your classmates.
• Part III: Methods
  What sampling method did you choose? Why? Explain exactly how you chose your samples. This should include some mention of who comprises your sample for each survey. Describe, in detail, the methods used to collect the data. Be sure to include a description of the setting in which the questions were asked.
• Part IV: Description of Results & Statistical Summaries
  Report your results, including a margin of error. Include appropriate numerical and/or graphical summaries of your data. The results should be self-contained within the main body of the paper without needing to refer to the appendix.
• Part V: Conclusions
  What kind of conclusions can you draw? Did the data behave as you expected? Can your results be used to make generalizations about public opinion for your population of interest? Explain. Discuss whether or not your unbiased survey falls victim to any of the seven pitfalls often encountered when asking questions in a survey. For example: you might remark on whether your survey is confidential or anonymous and how that might affect the results of your survey. (By design, the biased set of questions should be examples of questions with deliberate bias. Does bias enter into this second set of questions in any other fashion?) Are your measures valid? Reliable? Critique the methods used to collect the data. Could the sampling method have produced biased results? Is there anything you would do differently next time? How might this affect the conclusions of the study? What similar questions might someone chose to investigate in the future to build on your results?
• Part VI: Appendix
  Include the following: the original list of questions (biased and unbiased) from before they were altered, the critiques of your questions by three of your classmates, and the individually signed copies by each group member of the personal Statement of Academic Honesty.

I will be looking for clear and concise writing. I will expect an organized, polished product. I will pay particular attention to the type of sampling method used. The main body of the paper need not exceed 4 pages (if single spaced), but you may write more if necessary.

Each group must turn in one copy of the typed paper for the project. However, each student is expected to submit a CONFIDENTIAL STATEMENT describing their individual contribution to the project, the extent to which the other group members contributed to the project, and remarks regarding how well the group worked together. An email soliciting the confidential statement will be sent out before the project is due. The confidential statement should be submitted via email no later than noon on 2/8/07.

All members of the group will receive the same grade unless special circumstances suggest otherwise. For instance, the letter grades for individuals who do not turn in the confidential statement will be 1/2 of a letter grade lower than the group grade. In addition, 5% of each individuals project grade will be based upon your critique of another group's questions—this critique will be completed in class on 1/30.

PART I - Summarize Your Data

Project preparation assigned on the first day of class: Measure your pulse rate 72 times over the next 5 weeks, but do not take more than one measurement in any 10-minute period or more than 7 measurements in one day. Be sure to record the associated activities at the time the measurements are taken, e.g., during exercise, after meditating, upon waking up, etc. Please record the number of hours you sleep each night (including naps) as well as the number of hours you study each day.

By now you should have measurements for 72 pulse rates as well as a daily record of the number of hours spent studying since the beginning of the semester.

• Before summarizing your data, predict the shape of the data. Do you expect it to be uniform, bimodal, bell-shaped, left or right-skewed, etc.? Why?
• Find the mean, median, and mode(s). Which measure of center seems most appropriate to describe your data? Explain.
• Find the interquartile range.
• Create a five number summary. Identify any potential outliers.
  Be sure to show your work involved in identifying outliers using the IQR.
• Use Minitab to construct a boxplot (adjusted for outliers) for your data. How does the shape of the boxplot compare to the shape you predicted above? For example, if you predicted that the data would be left-skewed is that reflected in your boxplot? Explain.

• Before summarizing your data, predict the shape of the data. Do you expect it to be uniform, bimodal, bell-shaped, left or right-skewed, etc.? Why?
• Find the mean, median, and mode(s). Which measure of center seems most appropriate to describe your data? Explain.
• Find the range and interquartile range.
• Use Minitab to find the standard deviation.
• Which measure of variation (range, IQR, or standard deviation) seems most appropriate to describe your data? Explain.
• Use Minitab to construct a histogram for your data. How does the shape of the histogram compare to the shape you predicted above? In other words, give a written assessment of the shape of the data for pulse rates based upon your record of events while taking measurements.
• Regardless of the shape of your data, assume that it is bell-shaped in order to answer the following questions. (You will need Table 8.1 or your calculator.)
  • What percentage of your data actually falls within one standard deviation of the mean? How does this compare with the 68% estimated by the Empirical Rule?
  • Find the pulse rate that divides the top 10% of rates from the bottom 90%.

Part I Appendix - include a typed copy of the data spreadsheets for pulse rates and hours of study. Be sure that all observations are accompanied by the record of events and/or associated comments. An Excel spreadsheet template for tables will be provided.

PART II - Critique a Graphical Summary

Read the provided article: Hefling, Kimberly, Associated Press. "Small Towns. Big Sacrifice." Lewiston Sun Journal 20 Feb. 2007, A1 & A7. Printed from: www.sunjournal.com.

Begin by summarizing the article and the information that the graph is attempting to portray. Write an in-depth discussion of all features of the graph that are misleading. Refer to the checklist for statistical pictures found on page 173 of your text, discuss what (if any) features you think should have been added or changed to make it a better picture. Discuss any/all of the appropriate disasters and difficulties for graphs when analyzing your examples. If information is missing, discuss at least one different interpretation that might exist provided that information was included.

For each example, do your best to construct a more accurate graph of the information that the original graph was trying to depict. Be sure that the new picture that you create is well constructed-use the checklist to make sure your picture does not fall victim to the pitfalls.

This project should be typed. All visual displays of data for Part I should be constructed using Minitab. The graph for Part II may be constructed by hand. Contact Grace if you need additional assistance with Minitab beyond the instructions provided in class. As usual, I will expect an organized and polished product. In particular, you should copy the visual displays of data from Minitab and paste them into the body of your word processing document.

Contact Grace for extra copies of the article and associated graph.

In addition to the paper copy of the project, the Excel spreadsheet of data must also be submitted via email to Grace no later than noon on 3/15/07.

Your job is to test for an association between two qualitative variables using a contingency table and a Chi-square test for independence to determine statistical significance.

Select two qualitative (categorical) variables for which you are interested in determining if there is a relationship. You are not allowed to get the data from a website, book, or journal. Carefully collect the data for the desired variables. Be sure to get counts of at least 5 in each cell of your contingency table. Ideally, you should try to ensure that the individuals you use are not related to each other in ways that would influence the data.

Your data may be collected using either a survey or by conducting an ethical experiment. In either case, be sure to follow the guidelines for the design of a good study as discussed in Part 1 of the text. Your sample should include at least 30 people. Your population of interest should consist of all Bates students or the entire Bates College community—this includes students, faculty, and staff.

The paper should be written according to the following format guidelines:

• Part I: Introduction
  State the research question of interest. Why is this question of importance? What is it about this topic that is interesting to you? Have similar studies been done elsewhere? State any hypotheses you have about the relationship you expect to find and why.
• Part II: Methods
  Include a description of the survey or experiment used to obtain the data. Describe how the survey or experiment was designed and how the data was collected. Explain your choice of sampling method, why you chose that particular method, and exactly how the sample was selected.
• Part III: Describing the Data
  Explain what each variable measures. Be sure to include a copy of the data set in your appendix.
• Part IV: Description of Statistical Analysis & Results
  Provide a description of the statistical methods used to summarize and analyze the data. Be sure to include a contingency table, as well as any appropriate numerical and graphical summaries of your data within the body of the paper. Compute and discuss the risks and relative risks. Discuss whether those terms are appropriate for your study. (It may be that "risk" is not an appropriate term, in which case you should compute proportions and relative proportions.) What did you learn? Did the data behave as you expected? Use a Chi-square test to determine if there is a statistically significant relationship between the two variables. Report the results of the test (test statistic and significance level). Interpret the result of the analysis. In particular, what do the results mean statistically in terms of the research. Discuss the role of sample size in making the determination of statistical significance. The main results should self-contained within the main body of the paper without needing to refer to the appendix.
• Part V: Conclusions
  In essence, this is the time for the discussion summarizing what has been learned from the data. What are your findings? What kind of conclusions can you draw? Can your results be used to make generalizations about the relationship between the two variables for your population of interest? If you observed a relationship, discuss whether a cause-and-effect conclusion be drawn. Critique the methods used to collect the data. Could the sampling method have produced biased results? It is possible that the participants were related to each other in a way that might have influenced the data? Are there confounding variables that might affect the data? Critique your methods including issues pertaining to the reliability of your data as well as the validity of your conclusions. Is there anything you would do differently next time? How might changes in the way the study is conducted affect the conclusions of the study? What similar questions might someone chose to investigate in the future to build on your results?
• Part VI: Appendix
  The appendix should include a copy of the data set with labeled variables in a spreadsheet format, i.e., the data set before it is organized into the contingency table. If you use a survey then a copy should be included in the appendix. Include any other pertinent information that was not included in the previous sections of the paper.

I will be looking for clear and concise writing. I will expect an organized, polished product. I will pay particular attention to the type of sampling method used. The main body of the paper need not exceed 5 pages, but you may write more if necessary. The length of the appendix will depend upon the material included.

Each group must turn in one copy of the typed paper for the project. However, each student is expected to submit a CONFIDENTIAL STATEMENT describing their individual contribution to the project, the extent to which the other group members contributed to the project, and remarks regarding how well the group worked together. I will send out an email soliciting the confidential statement before the project is due. The confidential statement should be submitted via email no later than noon on 4/3/07.

All members of the group will receive the same grade unless special circumstances suggest otherwise. For instance, the letter grades for individuals who do not turn in the confidential statement will be 1/2 of a letter grade lower than the group grade. In addition, 10% of each group's grade will be based upon a class presentation to be made on either April 3rd or 5th. Likewise, 5% of each individual's project grade will be based upon individual critiques of class presentations for 2-3 other groups.

I will be available to provide assistance regarding the use of either TI-83 and TI-84 calculators or Minitab for those wishing to use technology for statistical analysis and construction of graphs where necessary. Note: Minitab can be used to perform the statistical analysis of the Chi-square test for independence, but it is easier to use a TI-83 calculator.

Copyright ©2007 Bates College. All rights reserved.

Last modified 3/15/07 by glc.