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Tomas, for some values the formula IMHO gives bogus results.
Instead I would suggest to use the following:
pWinRate = (NbrOfWinTrades + NbrOfEvenTrades / 2) / NbrOfTotalTrades
Of course the inverse is the pLossRate = 1 - pWinRate
The result is between 0..1 (multiply by 100 to get percent result).
UM
----- Original Message -----
From: "Thomas Ludwig" <Thomas.Ludwig@xxxxxx>
To: <amibroker@xxxxxxxxxxxxxxx>
Sent: Monday, November 03, 2003 9:49 PM
Subject: [amibroker] Backtesting and statistics
> Hi all!
> The performance summary in the backtesting report window contains a
> lot of figures. But as useful as these figures are - they do not
> really tell us if the backtesting results are statistically
> significant.
>
> Therefore I suggest to add a new figure proposed by Arthur Merrill in
> Stocks & Commodities some years ago (Bonus Issue 1993). It's called
> the "chi squared with one degree of freedom, with the Yates
> correction". It's calculated using the following simple formula:
>
> X^2 = ( |R-W| -1)^2 / (R+W)
> where: R = number of times right
> W = number of times wrong
>
> Interpetation:
> Below 3.84: Significance doubtful.
> Above 3.84: Probably significant. Probability of one in 20 that the
> result was by chance.
> Above 6.64: Significant. Probability of one in 100 that the result was
> by chance.
> Above 10.83: Highly significant. Probability of one in 1,000 that the
> result was by chance.
>
> Let`s apply this formula to a simple example. Let's assume that the
> backtest gives 10 signals with 7 of them profitable; let's also assume
> that the other figures in the backtest report are okay. So the results
> look good at the first glance. However, the chi squared figure is just
> 0.9 - very insignificant!
> On the other hand, if the backtest gives 100 signals with 70 of them
> profitable the chi squared figure is a whopping 15.21 - highly
> significant!
>
> Of course, these are very simple examples and the difference between
> them is rather obvious. But that might not be the case in other
> examples. And I'm afraid that even obvious things are often
> overlooked, especially if the other figures in the backtest report
> look good. Therefore in my opinion the chi squared figure would be a
> valuable addition for the correct interpretation of the backtest
> results.
>
> Tomasz - any chance to add this?
>
> Regards, Thomas
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