Robust statistical methods were used to analyze data on stock returns and factors from 1963 to 2015. The study found that outliers in the data can distort results, leading to misleading conclusions about the relationship between risk factors and stock prices. By using robust regression, the researchers confirmed a positive link between average equity returns and firm size, as well as a significant relationship between returns and the book-to-market ratio, especially for small stocks. They also discovered a negative relationship between returns and beta for most U.S. equities when outliers were removed. Additionally, the study revealed a strong interaction between size and beta in explaining stock returns, and highlighted the importance of total earnings-to-price factor in predicting returns for small to moderately-sized stocks.