Inferential Statistics: Analyzing Gender Differences in Climbing Route Grades

Project Overview

This project analyzes whether females have an average climbing route grade lower than males, using a dataset of 1,000 climbers. It uses a variety of inferential statistical methods in R, including both traditional and non-traditional approaches.

The analysis follows the steps:

• Stating the null and alternative hypothesis
• Calculating point estimates and standard errors
• Performing hypothesis testing using both traditional t-test and non-traditional bootstrapping and permutation methods
• Visualizing results with boxplots, histograms, and distributions

We provide detailed commentary on the hypothesis testing process, supported by visual insights.

Key Components

• Hypothesis Testing: Comparison of the average climbing grades of males and females, testing the null hypothesis at a 0.05 significance level. As you see the p value is far from our distribution so we reject the null hypothesis.
• Bootstrap Method: Creating confidence intervals using resampling to assess the reliability of our estimates. We see that 0 is not contained in this confidence interval as a plausible value of the population parameter. This matches with our hypothesis test results of rejecting the null hypothesis. Since zero is a plausible value of the population parameter, we do not have evidence that female have an average grade equal or greater to the male. We are 95% confident the true grades mean for female and male is between -5.748401 to -3.654263.
• Permutation Test: A non-parametric method to observe if the difference in means is statistically significant.
• Visualizations: Boxplots, histograms, and distribution plots to visually assess data distributions and results.

How to Run the Project

1. Clone the repository.
2. Open the R markdown file inferential_statistics.Rmd in RStudio.
3. Ensure all required libraries (tidyverse, infer, readr) are installed.
4. Knit the markdown file to generate HTML or PDF output.

Conclusion

Based on our hypothesis tests and confidence intervals, we find statistically significant evidence suggesting that females have a lower average climbing route grade than males.