It’s worth noting that hypothesis testing as it’s normally taught is a messy, confused hybrid of two approaches (Fischer and Neyman/Pearson), each of which is individually somewhat more elegant (but still doesn’t make philosophical sense):
http://ftp.isds.duke.edu/WorkingPapers/03-26.pdf
http://marketing.wharton.upenn.edu/ideas/pdf/Armstrong/StatisticalSignificance.pdf
It’s worth noting that hypothesis testing as it’s normally taught is a messy, confused hybrid of two approaches (Fischer and Neyman/Pearson), each of which is individually somewhat more elegant (but still doesn’t make philosophical sense):
http://ftp.isds.duke.edu/WorkingPapers/03-26.pdf
http://marketing.wharton.upenn.edu/ideas/pdf/Armstrong/StatisticalSignificance.pdf