What are the potential consequences of violating the assumptions of a statistical test?

During my final year in college, I worked on a research project investigating the impact of study habits on exam scores. I initially used a t-test to analyze the results without checking if the data met the normality assumption. As a result, my findings suggested that certain study habits significantly improved scores, which seemed promising. However, after consulting with my professor, I learned that the data was skewed and did not meet the normality requirement. This was a crucial lesson; I realized that violating assumptions could lead to invalid conclusions, which could misguide future students. I corrected my approach by applying a non-parametric test, which better fit the data. This experience taught me the importance of thoroughly understanding the assumptions behind statistical tests.

While working part-time as a data assistant at a local non-profit, I was tasked with analyzing donor data to evaluate fundraising strategies. I initially used linear regression to model the relationship between donation amounts and various donor characteristics without verifying the assumptions of homoscedasticity and linearity. This oversight resulted in a misleading model that suggested a stronger relationship than truly existed. After discussing this with my supervisor, I learned that correcting these assumptions was essential for accurate reporting. I adjusted my analysis using robust regression techniques, which provided a clearer picture of the data and helped the organization make more informed decisions. This experience reinforced how crucial it is to respect statistical assumptions for reliable insights.

In my first job as a junior analyst at a marketing firm, I was involved in analyzing customer feedback data to improve our services. I performed an ANOVA test to compare satisfaction levels across different service categories without checking for independence and normality assumptions. This oversight led to inconclusive results, which raised concerns during team meetings. To rectify this, I took the initiative to educate myself on the assumptions and their implications. I re-ran the analysis using appropriate methods and communicated my findings clearly to the team. This experience taught me the importance of rigor in statistical analysis and how violating assumptions can mislead decisions. It also highlighted the need for continuous learning in my career.