Introduction

This lab report is an individual assignment. While discussions about the data and R code with classmates are allowed, forming questions and answering them about the data should be done independently. Please follow the Report Guidelines available on the course helper webpage before starting the report.

Data Retrieval

Use the dataset women.csv for your analysis. You can load the data into your R session using the following code:

women <- read.csv("https://raw.githubusercontent.com/deepbas/stat120datasets/main/women.csv", 
                  sep = ",", header = FALSE, skip = 1)

colnames(women) <- c("No", "Country", "Level.of.development", "European.Union.Membership", 
                     "Currency", "Women.Entrepreneurship.Index", "Entrepreneurship.Index", 
                     "Inflation.rate", "Female.Labor.Force.Participation.Rate",
                     "Overall.Entrepreneurship")

Data Description

The dataset named women and titled Women Entrepreneurship and Labor Force, stored in women above serves as a rich compendium, capturing pivotal insights into the landscape of female participation in entrepreneurship across various countries, especially within the OECD. Sourced from the Women Entrepreneurship Index and Global Entrepreneurship Index report of 2015, this comprehensive dataset offers both categorical and quantitative variables.

Categorical Variables:

Country: Denotes the specific nation to which the data point belongs.
Level of Development: This variable categorizes countries based on their stage of economic growth - whether they are ‘Developed’ or ‘Developing’.
European Union Membership: It indicates whether a country is a member of the European Union or not.
Currency: Specifies the official currency used within the respective country.
Overall Entrepreneurship: A derived binary categorical variable indicating the relative level of entrepreneurship in a country. Countries with an Entrepreneurship Index above 42.7 are labeled as ‘High’, signifying a higher level of entrepreneurship activity, whereas those below this threshold are labeled as ‘Low’.

Quantitative Variables:

Women Entrepreneurship Index: This numerical value for the year 2015 mirrors the overall environment that facilitates or impedes women from launching businesses in their country.
Entrepreneurship Index: A numerical metric for the year 2015, reflecting the overall entrepreneurship ecosystem of a country.
Inflation Rate: It provides the inflation rate for the year 2015.
Female Labor Force Participation Rate: This metric from 2015 showcases the percentage of the female working-age population actively participating in the workforce.

The dataset spans a myriad of countries, from established economies like Austria, Belgium, France, and Germany to emerging economies such as Argentina, China, India, and Mexico. Each nation’s entry in the dataset sheds light on its respective entrepreneurial conditions, inflationary pressures, and the level of active participation of women in the labor force.

In essence, this dataset provides a robust foundation for in-depth analyses, especially for those keen on discerning patterns, trends, and disparities across economic, gender, and social dimensions, and leveraging this information to draw meaningful conclusions.

Required Analyses:

Address the following areas of statistical analysis in your report, ensuring correctness in your analysis and clarity in your written communication:

Categorical Variable Relationship:

Investigate the relationship between two categorical variables. Your analysis should include a two-way table and a stacked bar graph. Comment on any observed relationships and describe their nature.
Categorical-Quantitative Variable Relationship:

Examine the relationship between one categorical variables and a quantitative variable. Ensure you provide summary statistics and graphical comparisons of the quantitative variable across each level of your chosen categorical variable/s.
Quantitative Variable Relationship:

Explore the relationship between two quantitative variables. Your analysis should include summary statistics and graphical comparisons of the quantitative variable for each level of the categorical variables.
Randomized Hypothesis Test:

Conduct a randomized hypothesis test to assess the difference in the mean of a quantitative variable across two categorical levels. Ensure that you include relevant R code and summary outputs in an appendix.

Submission Details

Submit your report as a single PDF file to Gradescope. Ensure that your R-code is included only in the appendix and not in the main body of your report. While including plots and numerical summaries in the main content is acceptable, the R code that generates them should be hidden.

To hide the R code in your report:

Use the chunk option echo = FALSE to prevent the code from displaying but still execute it. This is ideal for hiding the code but showing the output (e.g., plots or summaries).
Alternatively, you can use include = FALSE to both hide the code and prevent its output from being shown in the document. This is useful if you want to execute some preparatory code without showing any results in the report.

In RStudio’s R Markdown, insert a new R chunk with Ctrl + Alt + I or Cmd + Option + I. Choose the appropriate chunk option based on your specific needs for each section of your report. For example, to hide code but execute it, use the chunk header {r echo=FALSE}.

Report Structure

In statistics, experts often share their work through articles in magazines (called journals) or books. The main type of article is called a ‘primary paper’. It’s like a story of what the researcher did, how they did it, and what they found out. Since working with data (or ‘data analysis’) is a big part of statistics, it’s important for students, even in beginner classes, to learn how to write in this style.

Abstract

This short section (about 5% of your paper’s length) should quickly summarize your work. It should cover the reason for your analysis, the main question you’re addressing, the statistical methods you used, your findings, and what you believe these findings mean. Essentially, by reading just the abstract, someone should grasp the essence of your entire paper.

Introduction

Start by setting the scene for your analysis: provide some background and mention previous related studies, if available. Clearly state the main focus or objective of your data analysis. Explain why this focus is important or interesting. Briefly outline the methods or approaches you took, highlighting if you conducted an experimental or observational study.

Methods

Detail the techniques you used both to gather and analyze your data. The description should be clear enough that someone else could replicate your analysis. Specify how the data was collected, the statistical tests performed, and any relevant setups. While you can reference the manual for in-depth statistical test details, avoid including complex mathematical formulas. Write in the past tense, describing the entire analysis approach as though you conducted it independently. The aim is to provide a concise overview of your analysis method, not a step-by-step breakdown.

Results

This section should present the main findings from your data analysis. Describe the key patterns, trends, and notable differences you observed. While visuals like charts and graphs will illustrate your results, it’s essential to explain them verbally too. State the primary data trends and support them with statistical outcomes in brackets. Direct the reader to any relevant figures or tables. Remember, this section is for presenting findings only; interpretations and broader implications should be reserved for the following Discussion section.

Discussion and Conclusion

Start by recapping your main findings and linking them to your initial questions and hypotheses. Examine your results in the context of existing knowledge and research. Delve into broader implications, and consider how your results fit into a larger landscape. Address potential issues in your analysis like violation of assumptions, outliers, bias, and other errors that could impact the validity of your conclusions. Reflect on any ethical constraints tied to your study and their potential influence.

Grading Rubric

Aspect	Excellent: 10	Satisfactory: 7	Needs work: 5
Introduction	Introduction captivates with original insights and creative angle, setting a compelling stage for the analysis.	Introduction shows some original elements and creativity but lacks a captivating edge.	Introduction is generic, with no original insights or creative elements.
—	—	—	—
EDA & Data Description	Comprehensive exploration and succinct description of data. Insightful initial analyses that enhance understanding of the dataset.	Basic exploration and description of data. Some relevant analyses but lacks depth.	Minimal or incorrect data exploration. Descriptions are vague or missing.
—	—	—	—
Properly Labeled and Captioned Figures	Figures are well-crafted with clear, informative labels and captions. Visuals enhance the narrative and data understanding.	Figures are adequately labeled and captioned, but visuals do not significantly aid comprehension.	Figures are poorly labeled or not captioned, providing little to no informational value.
—	—	—	—
Numerical Summaries Table	Tables are well-organized, offering clear, comprehensive statistical summaries that enhance the analysis.	Tables present essential data but lack clarity or detail, making them less effective.	Tables are poorly organized, lacking critical data or are confusing.
—	—	—	—
Statistical Methodology	Methodology is robust, well-justified, and appropriately complex, showing deep understanding of statistical tools.	Methodology is sound but lacks sophistication or full justification, showing only moderate understanding.	Methodology is flawed or overly simplistic, indicating a poor grasp of statistical principles.
—	—	—	—
Results Section	Results are detailed, clearly expressed, and supported by the data and statistical analysis, demonstrating thorough analysis.	Results are reported with basic details and support but lack depth or clarity in places.	Results are incomplete, unclear, or not supported by the data or analysis.
—	—	—	—
Conclusion	Conclusion draws powerful, well-supported inferences from the results, offering meaningful implications and future directions.	Conclusion summarizes the results adequately but with limited implications or future insight.	Conclusion is cursory or fails to adequately tie results to broader implications or suggestions.
—	—	—	—
Statistical Jargon & Application	Employs a rich vocabulary of statistical jargon correctly, enhancing the academic rigor of the analysis.	Adequate use of statistical terms, though sometimes imprecise or sparingly used.	Limited or incorrect use of statistical jargon, detracting from analytical depth.
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Submission Promptness	Both the proposal and final report are submitted on time or ahead of schedule, demonstrating good time management and commitment.	The proposal or final report is slightly late, indicating room for improvement in time management, but does not necessitate resubmission.	The proposal or final report is late, suggesting significant issues with time management and may require resubmission.
—	—	—	—
R-code Organization (in Appendix)	R-code is meticulously organized and selectively commented, demonstrating efficiency and clarity.	R-code is organized with functional comments but lacks the precision and clarity of top submissions.	R-code is disorganized or missing critical elements, indicating a need for further refinement.