TradeStation is excellent, but you need to open a trading account with them, otherwise you will have to pay about $100 a month to use the software ($200/month if you are a professional trader).
I can't remember their names, but I read that in a few books a long time ago. I am not sure but I believe it was in Perry Kaufman books (Trading Systems and Methods, perhaps). These statistical tests are not for the casual trader and do require some advanced mathematical knowledge.
It's free , with $500 account opening. if you don't trade, you just pay $50 inactivity fee end of year
Not yet for back-testing, i use Radarscreen and scanner ,,, This tools are different than most in the market. Testing simple ideas would be be easy (without money management), but still i'm learning easy-language and the platform, as i was with interactive brokers before, so can't say much. Nice thing you can just copy and past results from Radarscreen and scanner into Microsoft excel and analyze them, without having to export them. And it has a lot of advance order entry types and settings, you can also create orders macro and hotkeys