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On the marketplace Gypsy accepts bets on two dice throw (he throws two dice at the same time, not one after another). Gamblers come and say what numbers will be on each of the two dice (it is a bet on a pair). Which test should I use to check if the pair of numbers the people propose is a result of a single number preferences.

For example, suppose for some reason the people consider 3 as a magic lucky number and more often bet their money on that number. So most often they choose combination of double 3. Less often they choose 3 and any other number except 3. The least often they choose pairs that do not contain number 3 at all.

I have a feeling that the combination of 3 and 1 is rather rare. If that was true, it would mean that the people have preferences to the pairs, not numbers.

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You need to make your hypothesis more precise, then you can test it.

E.g. you could say "People will bet on double 3 more often than they ought to based on probability". If the dice are fair, double 3 ought to come up 1 in 36 times. So, you could do a one sample chi-square test to see if the actual bets were in the proportion 1 to 35 for "double 3" and "anything else" respectively.

If you have a different hypothesis, you might need a different one-sample chi-square or possibly another test altogether.

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  • $\begingroup$ In a 100 bets (in a 100 pairs) we had at least one 3 in 60 cases. And if we look at the pairs we have 10 pairs 3-1, 10 pairs 3-2, 20 pairs 3-3, 8 pairs 3-5 and 12 pairs 3-6 (the order does not matter). Please note that the probability of outcome has nothing to do with the test I need. $\endgroup$
    – Przemyslaw Remin
    Commented Oct 29, 2014 at 13:28
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    $\begingroup$ Then I don't understand what you are hypothesizing. $\endgroup$
    – Peter Flom
    Commented Oct 29, 2014 at 13:37
  • $\begingroup$ People put up the money for at least one three on dice in 60 cases out of 100. There were only 10 bets, such that at least one of the dice would be number 1. What is the expected number of pair three and one? Let's say there were 5 such pairs. How to test that the expected number is statistically the same as the empirical number? $\endgroup$
    – Przemyslaw Remin
    Commented Oct 29, 2014 at 13:52
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    $\begingroup$ Do you mean "Is the probability of picking both 1 and 3 independent of picking 1 and picking 3?" If picking 1 and picking 3 were independent then the probability would be 6/10 * 1/10 = 6/100. You got 5/100. You can test whether those two proportions are equal using, e.g. a t-test for proportions. $\endgroup$
    – Peter Flom
    Commented Oct 29, 2014 at 14:22
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    $\begingroup$ Yes, that is probably what I have been looking for. I must only make sure that this t-test takes into account number of observations. Maybe you already know that? Because 5/100 and 6/100 sounds the same if our sample is 100. But if it would be a 100 million that 1/100 would make a significant difference. Anyway, thank you for help! $\endgroup$
    – Przemyslaw Remin
    Commented Oct 29, 2014 at 16:24

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