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Using Basic Data Analysis Techniques to Summarize and Analyze Statistical Questions

Research Questions and Sub-questions

For this project, which in total is worth 15% of your final course mark, you will be using some of the basic data analysis techniques learned in this course to summarize and analyze a statistical question. You will be asking a statistical question that can be answered with the statistics we learn throughout this course, then collecting data from reliable sources for analysis. This data will be summarized using charts and graphs, descriptive summary statistics like mean, median, or mode, and will include analytical statistics such as standard deviation, z-scores, or linear regression analysis. You will then use the results of this analysis to draw conclusions about your findings, discuss the limitations of the data and analyses, and propose future analyses to better understand the data. 


The research questions you can ask will be somewhat limited by the scope of this course, since we are only covering a fraction of the full set of statistical tools available, given that MDM4U would typically have 110 instructional hours in a high school setting, and we are limited to about 17.5 hours over our course. Most of the analysis can be done using techniques covered in our course, but you may want to read some additional material from our textbook if you wanted to include stronger statistical analytical tools. An additional look into hypothesis testing in Chapters 9 and 10 in particular may be useful. If you are choosing to use additional analytical tools, you can feel free to book an appointment with me for some additional help as these tools will be useful for any future statistical analysis you may need to do. 


This proposal will include a brief summary of your proposed research topic (around 200 – 300 words), your proposed research question or questions, your proposed hypotheses, and at least 2 data sources that have already been collected containing data that will be used for your analysis in APA format. This will be used to make sure you will have enough material to complete the project by the end of the course and will be worth 3% of your final course mark. This will be a brief summary of the data collected so far, the analyses you plan to perform on the data, and an outline of your plan to finish the project by the final due date. More information will be given later on what is required for this update. 
 
 You will be submitting your findings in the form of a report which will be handed in in place of a final exam on December 13th by 11:59 PM. This report will briefly introduce your topic, summarize your research questions and hypotheses, present the data and analysis, draw conclusions from the analysis and discuss the results. Any outside data sources will be cited using APA format and must be included in in-text citations and in a Works Cited page at the end of your report. The report will be organized into the following sections: 

Hypotheses


• Abstract: This is a summary of your research topic and questions, the data and analytical methods used, and the main findings from your report. This should only be written after you finish your report and should summarize all the important findings made in 300 – 400 words. 
• Introduction: Briefly introduce your topic and any relevant background knowledge needed to understand where your research question came from. This should give enough information to indicate why you are asking the question, and to get people interested in your data. It should also describe where you gathered your data from, and why you chose these sources. This should 

be no more than 400 – 500 words in length and should include citations for any sources used. 


• Research Questions and Sub-questions: Clearly state your main research question (such as a question about the overall relationship between two variables) and any smaller sub-questions that you may look at to get a better understanding of your main question.

• Hypotheses: Clearly state your hypotheses for the main research question and any sub-questions listed. Here you state what you believe the data will show, such as a positive linear relationship between two variables or a significant difference between two populations. 
• Summary of Data: This should include any tables of raw data, any graphs such as histograms or bar graphs showing the data, and should include measures of central tendency (mean, median, and mode if possible) and measures of dispersion (variance or standard deviation).  
• Analysis of Data: This should include any statistical analyses done on the data, including any hypothesis testing (if you read the appropriate chapters), any tests of significant differences between a data point and a sample or population (such as z-scores), or differences between two populations. This could also include tests of correlation such as a linear regression, which we will cover in a bit more detail when we look at using Excel for statistics. 


• Conclusions: Here you are interpreting your data. What conclusions can you draw from your study? Does the data and analyses done support or refute the hypotheses you made? What are the limitations of the data or analytical techniques used? What could be done in the future to overcome these limitations or to get a better understanding of the data involved? What are some actions that could be taken as a result of your conclusions? For example, if you found that cold weather does seem to correlate with COVID-19 cases, are there future studies that could be done to look at the specific cause of this correlation? Could policies be implemented to try to limit the spread of the virus as a result of these findings? About 400 – 600 words. 


• Is there a relationship between the average temperature and number of new COVID-19 cases in Toronto? 
• Would the average number of new COVID-19 cases be significantly different in North American cities with a higher mean temperature compared to cities with a lower mean temperature? 
• Did the average GPA of students in a particular program significantly change as a result of the switch to online learning? 
Examples of Research Hypotheses: 
• I believe that the number of COVID-19 cases in Toronto would increase as the temperature drops as a result of more people staying indoors in heated buildings to avoid the cold. This would lead to an increase in the spread of the virus, and the number of new cases of COVID-19 should correlate with the daily temperature highs from 10 days previous. 
• I believe that cities with the top 10 highest mean annual high temperatures would show a significantly lower number of COVID-19 cases per capita than the cities within the lowest 10 mean temperatures group. 
• I believe that comparing the average GPA of students graduating from a program that was taught entirely online as a result of the pandemic with the average GPA of that program prior to the pandemic when taught face-to-face would show a significantly higher GPA. 


Examples of Statistics Used: 
• One-Variable Descriptive Statistics 
o Measures of Central Tendency (Mean, Median, Mode, Weighted Mean) 
o Measures of Dispersion (Variance, Standard Deviation) 
o Visual Representation (Histogram, Bar Graphs, Frequency Tables, Etc.) 
o z-scores to indicate where a data point is located within a data set 
• One-Variable Inferential Statistics 
o z-scores to determine if a data point is significantly different from a mean 
• Two-Variable Descriptive Statistics 
o Visual Representation (Scatter Plot) 
• Two-Variable Inferential Statistics 
o Student’s t-Test Between Two Populations and Two Data Sets 
o Linear Regression Analysis and Correlation Coefficients.

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