Does anyone know of any packages or source code that does simple statistical analysis, e.g., confidence intervals or ANOVA, inside a SQL Server stored procedure?
In more recent versions of SQL Server you can use .net objects natively. So any .net package will do. Other than that there's always external proc calls...
Unless you have to do it within the stored proc I'd retrieve the data and do it outside SQL Server. That way you can choose from any of the open source or commercial stats routines and it would probably be faster too.
The reason you probably don't want to do that is because these calculations are CPU-intensive. SQL Server is usually licensed by the CPU socket (roughly $5k/cpu for Standard, $20k/cpu for Enterprise) so DBAs are very sensitive to any applications that want to burn a lot of CPU power on the SQL Server itself. If you started doing statistics calculations and suddenly the server needs another CPU, that's an expensive licensing proposition.
Instead, it makes sense to do these statistical calculations on a separate application server. Query the data over the wire to your app server, do the number-crunching there, and then send the results back via an update statement or stored proc. Yes, it's more work, but as your application grows, you won't be facing an expensive licensing bill.