What are the assumptions behind conducting a t-test, and why are they important?

During my final semester in college, I worked on a project analyzing survey data for my statistics class. We aimed to compare the average study hours of students who scored above and below the class average. Before applying the t-test, I ensured our data met the necessary assumptions: checking for normal distribution using histograms and conducting a Levene's test for equal variances. This preparation helped us confidently interpret our results, which showed a significant difference in study habits. By understanding these assumptions, I learned how vital they are to ensure our findings were valid and could inform our recommendations on improving study practices.

I volunteered at a local non-profit that focused on health education. We collected data on community members' health habits before and after a workshop. To assess the effectiveness of our workshop, I proposed using a t-test to compare the health scores before and after. I made sure to verify the assumptions: our data was normally distributed, and we had independent observations since participants did not influence each other. By confirming these assumptions, we presented credible findings to the board, showing a significant improvement in health scores. This experience taught me the importance of solid statistical foundations in making impactful decisions.

In my first job as a quality control analyst, I frequently worked with performance data to analyze product defects. During one analysis, I needed to compare defects between two production methods. I applied a t-test but first checked the assumptions: I verified the data's normality and ensured equal variances with an F-test. These steps were crucial because they gave us confidence in our analysis and allowed us to recommend one production method over another. This experience solidified my understanding of how assumptions affect the validity of statistical tests in real-world applications.