## Men, women, lying and Golden Balls

It got me thinking. Here’s what I found; first from wikipedia:
“The biggest amount won in the first series was £61,060 on 6 August 2007 when contestant Helen stole all the cash from her opponent Sam”
“The highest potential jackpot so far was £168,100 (…) The actual jackpot, £93,250, was stolen by contestant Klara.”
“The largest jackpot so far was (…) £100,150 and the entire jackpot was stolen by contestant Sarah
No mention of any big jackpots stolen by a man. Do you notice a pattern here? I think I do :)

Also, I found a document with lots of statistics but I admit not having the patience to figure out what all of them meant in laymans terms – here’s one interesting table though:

GB stats

The highlighted part shows that if the players have agreed to split the money, women turned out to be lying considerably more often than men.

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### 6 Responses to Men, women, lying and Golden Balls

1. Thanks for linking to my balls. Much appreciated.

2. Karl Campbell says:

Just a quick comment, in this case, the sample size is not large enough to support a generalized conclusion.
While it is true that more women than men lied in these particular trials, one cannot generalize and say that men are more trustworthy than women, or that women are more greedy than men. One can’t even say that more women than men would choose to steal the jackpot.
The sample size is far too small, as shown by the fact that if one person changed their actions, the results would change by a percentage point or more.

3. Artem says:

Karl, since you seem to be an expert on statistics, could you please explain this table to the public, and also tell us what the probability is that the true relationship is reversed?

You can find some clues here:
http://en.wikipedia.org/wiki/Standard_error_(statistics)
http://en.wikipedia.org/wiki/Confidence_interval

This sample size is quite sufficient to make the hypothesis that women are greedier and more cunning than men to be highly probable. A much, much greater potential flaw in this statistics is selection bias, be it selection by the show producers or self-selection by candidates. It might very well be that women applying to participate in this show are a little greedier than the overall population.

If that was a random selection study, the results would be statistically significant.

4. Artem says:

BTW, you can find the scientifically sound interpretation in the original study.

For example,
“The hypothesis of no difference between men and women who initially plan to steal (split) and then split (steal) cannot be rejected, p=0.590 (p=0.237).”

Also:
“The null hypothesis of no di erence between the overall cooperation rate of men and women cannot be rejected (p=0.435) as well as the one for the mutual cooperation rate (p=0.503).”

But:
“Players above the age of 40 cooperate signi cantly more than players below 40 (p=0.001).”

And:
“We nd that women are more likely to vote against men and vice versa. In round 1, males cast a vote against females in 65% and females against males in even 75%.44 In round 2 we nd that only females are more likely to cast a vote against males (52%, p = 0; 096), but that males are signi cantly more likely to vote against their same sex (54%, p = 0; 064).”

I haven’t read the study in detail, but it seems like there’s significant probability (although <50%) that there's no difference between rates of cooperation and deceit between men and women.

5. Artem says:

A little more on the interpretation:

“The hypothesis of no difference between men and women who initially plan to steal (split) and then split (steal) cannot be rejected, p=0.590 (p=0.237).”

That means that there’s only ~24% probability that there’s no difference between men and women who first plan to split but then switch to steal (the scenario in the posted video). So, there’s ~76% probability that women are making this choice more often, i.e. con their partners this way in this game more than men do.

Of course, as I mentioned before, it does not address the selection bias.

6. Shawn says:

That’s not what it means, it means that given that there actually is no difference in stealing/splitting rates the probability we would get these results by chance is 24%. It doesn’t tell you what the actual chance of there being a difference is, that requires a prior probability for the chance of there being a difference along with use of Bayes’s theorem.