# Thread: Is TTEST valid for statistical diff between systems when 1 sytem has known distrib?

1. ## Is TTEST valid for statistical diff between systems when 1 sytem has known distrib?

What statistics tests would you need to detect if there is statistically significant difference between the following two systems?
The first system generates 7 numbers each time it is run. Each number can range from 0 to 7. The probability of appearance of each number is known. The probabilities for each number are shown below:
7 1.214 out of 1 million
6 5.1 out of 100 thousand
5 9.18 out of 10 thousand
4 9.18 out of 1 thousand
3 5.508 out of 1 hundred
2 9.914 out of 50
1 19.828 out of 50
0 16.996 out of 50

The second system also produces 7 numbers which also range from 0 to 7. How many tests of this system would have to be run to determine that difference between systems is statistically significant? Do you disregard the probability of occurrence of each number and simply run a T-Test on the values produced by both systems after 30 runs of each system?

2. ## Re: Is TTEST valid for statistical diff between systems when 1 sytem has known distri

I just got a recommendation from a friend to use Kullback-Leibler Divergence to test for difference between two probability distributions. I will try this.

3. ## Re: Is TTEST valid for statistical diff between systems when 1 sytem has known distri

I have one last question. I can use R to simulate 10 million runs of the system with known probability distribution. How many runs of the system with unknown probability distribution are required to obtain 95% confidence that a empirical distribution function obtained from the test sample is the system's probability distribution?

4. ## Re: Is TTEST valid for statistical diff between systems when 1 sytem has known distri

Would the solution for the following scenario be the same statistical test I could use?

A casino has slot machines which when operating according to expectations produce the following 8 outcomes

\$500 payout 1.214 out of 1 million
\$100 payout 5.1 out of 100 thousand
\$ 10 payout 9.18 out of 10 thousand
\$ 5 payout 9.18 out of 1 thousand
3 game tokens 5.508 out of 1 hundred
2 game tokens 9.914 out of 50
1 game token 19.828 out of 50
no award 16.996 out of 50

The casino operator would like to know with 95% confidence which slot machines need to be sent to service department if they are not performing according to expectations. What statistical test could the casino operator run to identify which slot machines need to be sent to service department?

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