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I have a model that predicts the probability of an event occurring, and then based on a given return if the event occurs, calculates the expected value. If the expected value is positive, a wager is placed. If the event occurs, the outcome is the return, and if it does not occur the wager is lost. I have tested the model on historical data, and the results are positive, but not so positive that I feel confident that my average outcome is statistically different from 0.

How can I conduct a hypothesis test on my results from testing on the historical data? Below is the distribution of my results, with -1 being a lost wager, 0 being an event where no wager was placed due to a negative expected value, and anything greater than 0 being the return from a successful wager.

All Outcomes

Successful Wagers

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Assuming the outcomes from each of the trials are independent, you could use a one-sample t-test to test whether the mean return when you wagered is significantly different from zero. You should not include the times where you did not wager in this test.

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  • $\begingroup$ I had forgotten how robust this test is due to the central limit theorem, and had dismissed it due to the odd shape and discontinuity of my distribution. Thank you for your response and the reminder. $\endgroup$
    – user62117
    Commented Apr 26, 2014 at 2:43

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