What are the assumptions behind the t-test, and how do they affect its validity?

In my college statistics project, I had to analyze the test scores of two different teaching methods. Before applying the t-test, I first checked if the scores followed a normal distribution using a histogram and a Q-Q plot. This was crucial because if they were not normally distributed, the t-test results might be misleading. I found that the scores were approximately normal, allowing me to proceed with the t-test confidently. This experience taught me the importance of assumptions in ensuring the validity of statistical tests.

During my time volunteering at a local charity, we conducted a survey to evaluate the effectiveness of our fundraising methods. I was responsible for analyzing the responses. I ensured that the data collected was independent; each participant's response was separate. When I performed a t-test to compare the average donations from two different methods, I made sure to check the variances of the two groups. This attention to assumptions helped us present reliable results to the charity board, demonstrating which method was more effective.

In my first job as a junior analyst, I was tasked with comparing sales data from two different regions. I applied the t-test but first verified that the data met the necessary assumptions. I plotted the data to check for normality and used Levene's test to ensure equal variances. By validating these assumptions, I could confidently present my findings to the team, which highlighted key insights that informed our sales strategy. This experience reinforced how critical it is to understand the assumptions behind statistical tests for accurate analysis.