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Save or Die: Yea or Nay?
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<blockquote data-quote="Ainamacar" data-source="post: 5274742" data-attributes="member: 70709"><p>I have some lies, damned lies, and (internet) statistics for you, because I'm actually kind of curious. I will apply a classic test of proportions, with null hypothesis that the proportion of anonymous voters from each group should be equal.</p><p></p><p>At the time I carefully counted, there were 75 pro votes with 30 anonymous, and 101 anti votes with 22 anonymous. I'm only looking at the DM votes, incidentally.</p><p></p><p>Let n=75 and x=30. Similarly, let m=101 and y=22.</p><p>So the sample proportion of anonymous voters for each group is p_pro = x/n = 0.4, and p_anti = y/m = 0.218.</p><p></p><p>The pooled probability estimate (OK since I'm testing the evidence that the proportions are equal) that a vote comes from an anonymous voter is p_pool = (x+y)/(n+m) = 0.295</p><p></p><p>The z-statistic for this test is (p_pro - p_anti)/sqrt(p_pool*(1-p_pool)*(1/n+1/m)) = 2.62, and associated p-value = 2*normal_distribution_CDF(-|z|) = 0.0088. As with most hypothesis testing the level of significance is up to the investigator, but a p-value this small is strongly suggestive that the null hypothesis is implausible. Likewise, a two-sided confidence interval with 99% confidence for (p_pro - p_anti) is (.002, .362). The result consistent with the null hypothesis is just outside this range. Anyway, if all the assumptions of the method hold the evidence we have suggests there is less than a 1% chance that the true proportion of DMs who are pro-save-or-die and vote anonymously is the same as the proportion of DMs who are anti-save-or-die and vote anonymously.</p><p></p><p>What assumptions are made? The basic ones are that the sample we have is representative of all DMs (or possibly all DMs at Enworld, or all DMs reading this particular thread, etc.) if they were required to vote (and implicitly the assumption of no vote stuffing), and that the distribution of these proportions is normally distributed. The latter is probably decent given the sampling size and observed proportions, and the former is laughable because, well, internet poll.</p><p></p><p>Still, taken seriously, what alternate explanations might be plausible? It isn't necessarily that vote stuffing occurred:</p><p>1) Enworld does not attract the pro and anti people equally strongly (correlated with "old-school" vs. "new-school"?), but those who are attracted more strongly are more likely to sign up.</p><p>2) The proportions for non-voters (e.g. people such as myself who both play and DM enough not to have cast a vote in either category but might have if the questions were asked more carefully) is different for some reason, even if the overall proportion if we had to vote is basically equal.</p><p>3) Any of a bajillion other forms of self-selection related to signing up for a hobby board, and then voting on a particular poll.</p><p></p><p>So, it isn't ridiculous to think vote-stuffing occurred given the numbers, but it isn't exactly a foregone conclusion either. It is what it is.</p><p></p><p>On topic, I prefer save-or-die to be used sparingly, without losing it entirely. Dying like a chump sucks, but save or die can be awesome if foreshadowed or hinted at. The threat's the thing. Creeping in the tunnels where Medusa lurks, knowing she lurks there? Every corner could mean death, but we must press on! Running into her at the gas station because the wife sent you out to get some milk? Chump death. Your wife is also a medusa, and you forgot her sister was in town? OK, you might have deserved it. Demonstrating save-or-die vs. hapless NPC, just in time for the boss fight? The fight might be like waiting for the dragon to breathe, and hoping you can make it -- totally nerve-wracking. But springing a slow-burn kill on the PCs by surprise gives 'em time for the dread, and time to do what it takes to overcome.</p><p></p><p>But if you have to use them, hopefully even the rattiest rat-bastard DM remembers he should be screwing the PCs, and not his buddies. Genre matters. Verisimilitude matters. The table matters most.</p></blockquote><p></p>
[QUOTE="Ainamacar, post: 5274742, member: 70709"] I have some lies, damned lies, and (internet) statistics for you, because I'm actually kind of curious. I will apply a classic test of proportions, with null hypothesis that the proportion of anonymous voters from each group should be equal. At the time I carefully counted, there were 75 pro votes with 30 anonymous, and 101 anti votes with 22 anonymous. I'm only looking at the DM votes, incidentally. Let n=75 and x=30. Similarly, let m=101 and y=22. So the sample proportion of anonymous voters for each group is p_pro = x/n = 0.4, and p_anti = y/m = 0.218. The pooled probability estimate (OK since I'm testing the evidence that the proportions are equal) that a vote comes from an anonymous voter is p_pool = (x+y)/(n+m) = 0.295 The z-statistic for this test is (p_pro - p_anti)/sqrt(p_pool*(1-p_pool)*(1/n+1/m)) = 2.62, and associated p-value = 2*normal_distribution_CDF(-|z|) = 0.0088. As with most hypothesis testing the level of significance is up to the investigator, but a p-value this small is strongly suggestive that the null hypothesis is implausible. Likewise, a two-sided confidence interval with 99% confidence for (p_pro - p_anti) is (.002, .362). The result consistent with the null hypothesis is just outside this range. Anyway, if all the assumptions of the method hold the evidence we have suggests there is less than a 1% chance that the true proportion of DMs who are pro-save-or-die and vote anonymously is the same as the proportion of DMs who are anti-save-or-die and vote anonymously. What assumptions are made? The basic ones are that the sample we have is representative of all DMs (or possibly all DMs at Enworld, or all DMs reading this particular thread, etc.) if they were required to vote (and implicitly the assumption of no vote stuffing), and that the distribution of these proportions is normally distributed. The latter is probably decent given the sampling size and observed proportions, and the former is laughable because, well, internet poll. Still, taken seriously, what alternate explanations might be plausible? It isn't necessarily that vote stuffing occurred: 1) Enworld does not attract the pro and anti people equally strongly (correlated with "old-school" vs. "new-school"?), but those who are attracted more strongly are more likely to sign up. 2) The proportions for non-voters (e.g. people such as myself who both play and DM enough not to have cast a vote in either category but might have if the questions were asked more carefully) is different for some reason, even if the overall proportion if we had to vote is basically equal. 3) Any of a bajillion other forms of self-selection related to signing up for a hobby board, and then voting on a particular poll. So, it isn't ridiculous to think vote-stuffing occurred given the numbers, but it isn't exactly a foregone conclusion either. It is what it is. On topic, I prefer save-or-die to be used sparingly, without losing it entirely. Dying like a chump sucks, but save or die can be awesome if foreshadowed or hinted at. The threat's the thing. Creeping in the tunnels where Medusa lurks, knowing she lurks there? Every corner could mean death, but we must press on! Running into her at the gas station because the wife sent you out to get some milk? Chump death. Your wife is also a medusa, and you forgot her sister was in town? OK, you might have deserved it. Demonstrating save-or-die vs. hapless NPC, just in time for the boss fight? The fight might be like waiting for the dragon to breathe, and hoping you can make it -- totally nerve-wracking. But springing a slow-burn kill on the PCs by surprise gives 'em time for the dread, and time to do what it takes to overcome. But if you have to use them, hopefully even the rattiest rat-bastard DM remembers he should be screwing the PCs, and not his buddies. Genre matters. Verisimilitude matters. The table matters most. [/QUOTE]
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