Course Project Project Examples: t-Test Project 1. The 1-sample t-test Required elements: one population, one quantitative variable, a specific value for hypothesis Example scenario: Population: All 2-bedroom apartments in Lumpkin County Variable: monthly rent Research question: Is the average rent for a 2 bedroom apartment in Lumpkin County more than $600 per month? Hypothesis and rationale: \"I predicted that the average monthly rent for a two-bedroom apartment in Lumpkin County would be higher than $600. A college planning guide stated that students could probably share a 2-bedroom apartment off campus \"for about $600 a month.\" Based on casual observation, I believe that on average, this estimate is too low.\" 2. The matched pairs t-test Required elements: a) one quantitative variable and two populations in which individuals can be matched OR b) one population and two quantitative variable values for each individual For both (a) and (b) the hypothesis is about the computed difference between the two related values Example scenario for (a): Populations: All canned vegetables sold at Kroger; all canned vegetables sold at Wal-Mart Variable: price (*specifically, the difference in price charged for identical items at each store) Research question: On average, are canned vegetables cheaper at Wal-Mart than at Kroger? Hypothesis and rationale: \"We predicted that on average, Wal-Mart would charge less for the same canned vegetable item. This prediction is based on the general observation that things seem to cost less at Wal-Mart.\" Example scenario for (b): Population: All NGCSU students Variables: rating (1 - 10) of the taste of Coke; and rating (1-10) of the taste of Pepsi (*specifically, taste tests are conducted \"blind\" and the difference in ratings is computed for each participant) Research question: On average, do NGCSU students prefer Coke over Pepsi? Hypothesis and rationale: \" We predicted that on average NGCSU students would rate Coke better in taste than Pepsi. This prediction is based on the fact that in such close proximity to Atlanta, the Coca Cola capital, Coke is often the preferred soft drink.\" t-Test Project Examples Page 1 of 2 3. The 2-sample t-test (independent samples) Required elements: two populations, one variable Example scenario: Populations: 1) All current NFC football players; 2) All current AFC football players Variable: age Research question: Is there a significant difference between the average age of NFC players and AFC players? (by \"significant\" we mean statistically significant) Hypothesis and rationale: \"We predicted that there might be a difference between the average age of NFC and AFC players. In recent years, the AFC has been perceived as the stronger conference; one could theorize that on average, they have older players who are wiser and more experienced; OR one could theorize that on average, they have younger players who are in better shape and have more stamina. The purpose of this study is to determine if any such age discrepancy exists.\" t-Test Project Examples Page 2 of 2 Project Plan: t-Test Name: A. Type of statistical test you plan to conduct (check one, and give relevant details) 1-sample t-test a) Target population: b) Research variable: c) Research question: d) Expected result: matched pairs t-test a) Target population(s): b) The research variable will be the difference between and c) Research question: d) Expected result: 2-sample t-test a) Target populations (2): b) Research variable: c) Research question: d) Expected result: B. Data collection plan (check one, and give relevant details) I will use data from a file. Give name of file and details below. I will obtain data from a website(s). Give Name of website(s), full URLs and details below. Other data collection plan: Give specific details below. Project plan is: NOT Accepted Accepted Date Instructor Initials t-Test Project Resources Statistics ERAU - Worldwide With thanks to Brad Bailey, Sherry L. Hix, and Dianna Spence; North Georgia College & State University for the use of materials developed under NSF DUE-0633264 and NSF DUE-1021584 \"Where can I get data for my project?\" \"What would be a good research question?\" \"What projects have other students done?\" Sources of Data: 3 Categories Use data from a file that your instructor will provide The easiest and fastest way given course time constraints. Find data on the Internet Lots of good data available, but you have to find it. Physically go out and record data e.g., measure items, time events with a stopwatch, look at prices, look at nutrition labels You will learn morebut it will take more time! 1. Use Data from a File This will be the fastest but least rewarding way to get the data you need. Your instructor will tell you which files you can use and make the files available to you. Later modules will contain more detailed instructions on what you need to do to complete the project. 1. Use Data from a File Two files you can use are in the ERAU MATH 211/222 StatCrunch Group. They are: Delta Airline Data Southwest Airline Data You can also explore some of the other files in the ERAU MATH 211/222 StatCrunch Group. 2. Use Internet Data Sources There is a LOT of data available on the internet. The following five slides suggest some internet sources you might want to explore if you choose to use data from the internet for your project. Later modules will contain more detailed instructions on what you need to do to complete the project. 2. Use Internet Data Sources I. Government/Community Websites Census Bureau: http://www.census.gov/ Bureau of Justice Statistics: http://bjs.ojp.usdoj.gov/index.cfm?ty=daa City Data Site: http://www.city-data.com/ State and county statistics sites State and national Dept.'s of Education County tax assessment records 2. Internet Data Sources II. Restaurants: Nutrition Info Applebees: http://www.applebees.com/downloads/nutritional_info.html Arby's: http://www.arbys.com/nutrition/Arbys_Nutrition_Website.pdf Burger King: http://www.bk.com/cms/en/us/cms_out/digital_assets/files/pages/Nutritio nInformation.pdf McDonalds: http://nutrition.mcdonalds.com/nutritionexchange/nutritionfacts.pdf Ruby Tuesday's: http://www.rubytuesday.com/assets/menu/pdf/informational/nutrition.pdf Your favorite place to eat? 2. Internet Data Sources III. Sports Data Sports Statistics Data Resources (Gateway) http://www.amstat.org/sections/SIS/Sports Data Resources/ General Sports Reference Site www.sports-reference.com NFL Historical Stats: http://www.nfl.com/history Individual team sites 2. Internet Data Sources IV. Retail/Consumer (General) Cost/Prices e.g., Kelley Blue Book: http://www.kbb.com/ Consumer Report ratings . http://www.consumerreports.org/cro/index.htm Product Specifications e.g., size measurements, time/speed measurements, MPG for cars 2. Internet Data Sources V. Aviation Data Bureau of Transportation Statistics: http://www.transtats.bts.gov/databases.asp?Mode_ID=1&Mode_De sc=Aviation&Subject_ID2=0 Federal Aviation Agency. http://www.faa.gov 3. Collect Data Yourself This would be the most beneficial way to complete the project in terms of actually learning statistics! It will also be the most time-consuming. The slides that follow give some ideas you might use. If you have an idea, ask your instructor! Sample Student Projects Matched Pairs t-Test: 2-tailed: Ha predicting that on average, students' rating of Coke and Pepsi would be different. t statistic =2.62 P value= 0.0116 (2-tailed) Conclusion: Evidence that on average, students rated the two drinks differently (Coke was rated higher) Participant Coke #1 8 #2 7 Pepsi 9 5 Sample Student Projects t-Test for 2 independent samples: 1-tailed: Ha predicting that on average fruit drinks have higher sugar content per ounce than fruit juices t statistic = -0.14 P value= 0.5555 Conclusion: Sample data did not support Ha. No evidence that on average, fruit drinks have more sugar than fruit juices. Sample Student Projects One Sample t-Test : 1-tailed: Ha predicting that the average purebred Boston Terrier puppy in the U.S. costs more than $500 Stratified sample representing different regions of the country t statistic = 1.73 P value= 0.0449 Conclusion: Evidence at 0.05 significance level that on average, purebred Boston Terrier puppies are priced higher than $500.00 in the U.S. Sample Student Projects t-Test for 2 independent samples: 1-tailed: Ha predicting that in local state parks, oak trees have greater circumference than pine trees on average t statistic = 4.78 P value= 7.91 x 10 -6 Conclusion: Strong evidence that in local state parks oak trees are bigger than pine trees on average. Lurking variable identified and discussed: age of trees (and possible reasons that oak trees were older) Sample Student Projects Matched Pairs t-Test: 1-tailed: Ha predicting on average, Wal-Mart prices would be lower than Target prices for identical items t statistic =.4429 P value= 0.3294 Conclusion: Mean price difference not significant; insufficient evidence that Wal-Mart prices are lower. Item 64-oz. Mott's Juice 12-oz LeSeur Peas WalMart Target 2.79 2.89 1.19 1.08 Look at resources for collecting data Look at sample projects Think about your own interests t-Test Project Resources Statistics ERAU - Worldwide With thanks to Brad Bailey, Sherry L. Hix, and Dianna Spence; North Georgia College & State University for the use of materials developed under NSF DUE-0633264 and NSF DUE-1021584 t-Test Project Instructions and Rubric Project Overview 1. Choose a research question: a) that can be addressed using a t-test b) for which you can collect data to analyze 2. Devise a plan to collect your data 3. Submit a project plan form to the instructor and obtain approval 4. Once your research question and data collection plan are approved, carry out your research: a) Collect data b) Conduct t-test analysis, using guidelines below c) Write your results in a report, using the outline given below 5. Turn in your written report using the link in Module 9 of the course Blackboard site. Data Collection Options: The following are suggestions on where you can collect data. 1. Reliable/reputable websites (e.g., sponsored by the census bureau, professional sports leagues, universities, real estate agencies, car manufacturers, consumer groups, financial institutions, well- known product manufacturers, restaurants/fast food companies, weather tracking agencies, county/city/state/federal government organizations, etc.) 2. Visit to one or more locations where item(s) you are researching can be found (e.g., stores to write down prices, rivers to count turtles, car dealers to write down data about cars, etc.) 3. Other resource by permission (if you have an idea, ask your instructor). Important Note: ERAU and all other universities have strict policies and approval procedures for any research projects that involve collecting data from human subjects. There is not time in this course for you to go through that approval process. Therefore, your project in this course cannot involve directly collecting data from human subjects. This includes conducting surveys. Project Design There are 3 project design options for the t-test project, listed below. To see components and examples for each type of project design, consult the t-test Project Examples Word document or the t-test Project Resources PowerPoint file. A. The 1-sample t-test (Sample size must be at least n = 40.) B. The matched pairs t-test (Sample size must be at least n = 40.) C. The 2-sample t-test (independent samples) (Sample size must be at least n = 50. You may split this across your two samples; for example, you may have two independent samples of size 25, or one of 27 and another of 23, etc. Although your independent samples are not required to be identical in size, it is better if the sample sizes are similar.) t-Test Project Instructions and Rubric Page 2 of 7 Project Plan Form Download a copy of the project plan Word document, t-Test Project Plan, save a copy for your records, and then complete the form. Upload the completed form using the link provided in the module assignment item. If the form is not completed satisfactorily, it will be returned to you for revision. NOTE: Your project plan must be approved by the instructor before you may begin your project! Project Report Layout and Grading Rubric Your final report should be written in paragraph form and should include the following 10 sections: Introduction, Population(s), Variable(s), Data Collection, Study Design, Results - Descriptive Statistics, Results - Confidence interval(s), Results - Hypothesis Test(s), Findings, and Discussion. An explanation of what should be addressed in each section is described below. Read this entire paper prior to beginning your project and use it when writing your project. All portions of the rubric that will be used to grade your paper are included in the discussion below. There are 20 items in the grading rubric. Each is worth a maximum of 5 points for a total or 100 points. The layout of the rubric is as follows: Item Name Performance necessary to achieve 5 points. Performance necessary to achieve 4 points. Performance necessary to achieve 0 to 3 points. Introduction. State the topic of your study as a research question AND as a specific hypothesis that you tested; your specific hypothesis should note a statistically significant result that you expected to find AND the practical reason that you expected this result (your rationale). Overview of Research Stated clearly: (1) Research question, (2) Expected findings, (3) Rationale Two of the three criteria at left are satisfied. Research question and expected findings not stated clearly. Rationale not explained. Population(s). Define clearly the population(s) that you intend for your study to represent. (Examples: all NFL football players, all cars manufactured this year, all biology majors at NGCSU, all small towns in the Southeastern U.S., all shoppers at the Daytona Beach Wal-Mart, all houses for sale in Metro Atlanta, etc.) Research Population Specified Revised 6/10/13 Targeted population(s) welldefined and appropriate. Reasonable target population(s) defined, but not fully appropriate Target population(s) of research project not defined, poorly defined, or incorrect. t-Test Project Instructions and Rubric Page 3 of 7 Variable(s). Define clearly the variable(s) that you will obtain during your data collection (e.g., gender, age, salary, price, miles per gallon, score on a particular personality test, miles commuted one-way to school daily, major, etc.) This must be specific: \"time spent watching TV\" is too vague; \"number of hours spent watching TV in the last 3 days\" would be specific enough. If your variable is a measurement (e.g., height) give units (e.g., inches). If your variable is a score (e.g., on a personality quiz), give the range of possible scores (e.g., 0 to 15). Definition of Variables Research variable named; measurement and possible values of variable are clearly defined. Research variable named, but details are lacking on how variable is measured or quantified. Research variable not adequately defined. Data Collection. Describe your data collection process and sampling strategy. If you located data on a website, provide the URL and tell how you selected individuals from that website to include in your sample. If you obtained data from an agency, office, store, or other similar source, explain where you went and how you selected items to include in your sample. If you collected measurements, describe the device you used (e.g., tape measure, odometer, scale, stopwatch, etc.) No matter what data collection process you used, address: a) what steps you took to avoid bias in your sample; and b) whether you believe the sample(s) you obtained were representative of the population. Tell why or why not. Include a table with your raw sample (not summarized) data as an appendix at the end of the report. Data Collection: Data Sources, Instruments, Measurement Data Collection: Sampling Data Representation: Raw Data Revised 6/10/13 Data collection procedure explained fully, including (1) Source of data identified clearly (website address, etc.), (2) Sound measures taken to ensure accuracy of data, (3) Copy of survey, description of measurement procedures, or other specific data collection details provided. Two of the three criteria at left are satisfied. Ineffective data collection procedures OR poor description of data collection procedures. (1) Sampling strategy explained fully, (2) Sound measures taken to avoid bias explained, (3) Representative sample addressed adequately. Two of the three criteria at left are satisfied. Ineffective sampling procedures OR poor description of sampling strategy. Raw sample data (not summary data) are included in the study in a complete and organized manner. Raw sample data (not summary data) are given, but presentation is incomplete or disorganized. Raw sample data used in the study are not provided. t-Test Project Instructions and Rubric Page 4 of 7 Study Design. Identify the statistical test you conducted to analyze your data. Also tell which type of design you used (one-sample, matched pairs, etc.) Give other design details (e.g., was it1-sided or 2-sided? Left-tailed or right-tailed?) State your null and alternative hypotheses, both in words and in appropriate mathematical symbols. If you used a matched pairs design, explain clearly how the pairs of values were matched and how the difference was computed (e.g., by subtracting before - after, left - right, etc.) Statistical Test and Hypotheses Statement Correct statistical test and type of design used. Null and alternative hypotheses stated correctly in words AND in mathematical terms. Some errors in statement of statistical test and type design. Null and alternative hypotheses stated correctly in mathematical terms but not in words or vice versa. Type of statistical test and/or type design stated incorrectly. Null and alternative hypotheses not stated in mathematical terms or stated incorrectly. Results: Descriptive Statistics. Give descriptive statistics (sample size, mean, standard deviation, and 5-number summary) for each data set. Note that t-tests for 2 independent samples will require statistics for 2 sets of data-- one for each of the two separate samples. Matched pairs ttests will require statistics for 3 sets of data-- one for each of the 2 related values (e.g., before and after) and another one for the difference between each pair of numbers. Report each set of descriptive statistics using an appropriate table and chart. All tables and charts should be placed directly in your report. Discuss the implications of the descriptive statistics in terms of your research problem. Discuss whether the conditions necessary for the confidence intervals and hypothesis tests you used are satisfied and support your discussion with appropriate charts/graphs. Descriptive Statistics: Research Variable For each data set, research variable is described fully, using mean, standard deviation, 5number summary and appropriate charts and/or graphs. A summary of the research variable is given for each data set, but at least one summary is incomplete. Charts and/or graphs are used but some are inappropriate. Descriptive statistics for research variables omitted or not given clearly for each data set. Charts and graphs not included. Conclusion and Discussion of Descriptive Statistics Discussion of results of descriptive statistics including summary statistics and chart and graphs is insightful; adds meaning and significance to the report; no unwarranted conclusions. Adequate discussion of results of descriptive statistics including summary statistics and chart and graphs and their practical implications; reasonable explanation of findings offered; no unwarranted conclusions. Implications of results of descriptive statistics including summary statistics and chart and graphs not discussed; no attempt to explain findings. Report draws unwarranted conclusions or uses inappropriately certain language. Revised 6/10/13 t-Test Project Instructions and Rubric Data Representation: Charts/Graphs Conditions necessary for the inferential statistics used in the report to be valid are discussed and verified with appropriate charts, graphs, or tables, or note is made that the confidence intervals or tests may not be valid due to those conditions not being satisfied. Page 5 of 7 Conditions necessary for the inferential statistics used in the report to be valid are mentioned with an inadequate attempt to verify them or some but not all are verified. Conditions necessary for the inferential statistics used in the report to be valid are either not mentioned or no attempt is made to verify them. Results: Confidence Interval. Report an appropriate confidence interval for your study; include the end points of the confidence interval, margin of error, and description of the meaning. Statistical Analysis - Confidence Intervals Correct confidence interval(s) used and (1) explanation of all details is thorough, articulate, and precise, (2) accurate end points reported, (3) accurate margin of error reported. Correct confidence interval(s) used AND two of the three criteria at left are met. Inappropriate confidence intervals used OR no confidence interval(s) used, reported, or explained correctly. Results: Hypothesis Test. Report the results of your hypothesis test; include the test statistic, degrees of freedom, and the p value of the significance test. Statistical Analysis - Hypothesis Test Interpretation of Hypothesis Test and p-Value Results Revised 6/10/13 Correct hypothesis test is conducted and (1) explanation of all details of test is thorough, articulate, and precise, (2) accurate t statistic reported, (3) accurate p-value reported. Correct hypothesis test is conducted AND two of the three criteria at left are met. Inappropriate hypothesis test conducted OR hypothesis test not conducted, reported, or explained correctly. Includes correct interpretation of the p-value in terms of the specific problem being studied and is correct and consistent with respect to (1) Level of Significance, (2) Rejection of the Null Hypothesis, (3) Real-world conclusion about subject being studied. Results are interpreted correctly and consistently with respect to: (1) significance, (2) rejection of null hypothesis, (3) real world conclusion about subject being studied. p-values not interpreted correctly or consistently t-Test Project Instructions and Rubric Page 6 of 7 Findings. Interpret the results in the context of your original research question. Do your analyses support your expected findings? Explain. Interpret p-values and discuss significance levels. Compare the results of your confidence intervals and hypothesis test. Conclusion and Discussion of Inferential Statistics Discussion of results of inferential statistics in terms of the problem studied including results of confidence interval(s) and hypothesis test(s) is insightful; adds meaning and significance to the report; no unwarranted conclusions. Adequate discussion of results of inferential statistics in terms of the problem studied and their practical implications; reasonable explanation of findings offered; no unwarranted conclusions. Implications of results of inferential statistics not discussed; no attempt to explain findings. Report draws unwarranted conclusions or uses inappropriately certain language (such as the hypothesis test proves the hypothesis). Relationship between Hypothesis Tests and Confidence Intervals Explanation of the relationship between the hypothesis test and confidence intervals is included and correctly explains how conclusions from both techniques are the same. Explanation of the relationship between the hypothesis test and confidence intervals is attempted, but with some minor errors. No attempt is made to explain the relationship between the hypothesis test and confidence intervals, or an attempt is made, but is inaccurate. Discussion. What conclusions, if any, do you believe you can draw as a result of your study? If the results were not what you expected, what factors might explain your results? What did you learn from the project about the population(s) you studied? What did you learn about the research variable? What did you learn about the specific statistical test you conducted? Summary Discussion of Project Revised 6/10/13 Good discussion of what the student learned from the project, the research variable, the statistical test conducted, and results that can be drawn from the study. Discussion shows insight and thoughtfulness. Adequate discussion of what the student learned from the project, the research variable, the statistical test conducted, and results that can be drawn from the study. Shows that some thought was given to the implications of the study. No discussion of what the student learned from the project, the research variable, the statistical test conducted or the discussion is superficial with little thought or insight. t-Test Project Instructions and Rubric Page 7 of 7 The last four items from the grading rubric shown below apply to the report overall, not to a specific section. Project Plan Approved project plan form, signed by instructor, is attached to project report. Approval obtained on project plan, but approval sheet missing from submitted report. Incomplete or missing project plan or approval not obtained. Report Format Project report is submitted as a formal paper in paragraph form with full sentences, and is typed and well formatted. Project report is submitted as a formal paper, but with minor issues (e.g., poor or inconsistent formatting, not typed. Project report is not submitted as a formal paper OR Final report is written in Excel or other program with no paragraph formatting. Originality and Initiative An original research topic was selected AND report demonstrates initiative in carrying the project out. An original research topic was selected for this project. Topic selected is not original; it has been studied frequently by other students. Writing and Readability Report is exceptionally well organized and well written, with all charts and tables embedded in report. Report is reasonably organized and readable with few writing errors; all charts and tables are embedded in report. Report is poorly organized and hard to follow; charts and tables not embedded in report; many writing errors, awkward sentences. Revised 6/10/13