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Monthly Archives: December 2012

Bootstrap: corrected

So, previously on this blog (here, and here) I was playing around with the bootstrap as a way of testing if two samples are drawn from a different underlying distribution, by simulating samples with known differences and throwing different tests at the samples. The problem was that I was using the wrong bootstrap test. Tim was kind enough to look at what I’d done and point out that I should have concatenated my two sets of numbers and the pulled two samples from that set, calculated the mean difference and then used that statistic to constructed a probability distribution function against which I could compare my measured statistic (ie the difference of means) to perform a hypothesis test (viz. ‘what are the chances that I could have got this difference of means if the two distributions are not different?’). For people who prefer to think in code, the corrected bootstrap is at the end of this post.

Using the correct bootstrap method, this is what you get:

So what you can see is that, basically, the bootstrap is little improvement over the t-test. Perhaps a marginal amount. As Cosma pointed out, the ex-gaussian / reaction time distributions I’m using look pretty normal at lower sample sizes, so it isn’t too surprising that the t-test is robust. Using the median rather than the mean damages the sensitivity of the bootstrap (contra my previous, erroneous, results). My intuition is that the mean, as a statistic, is influenced by the whole distribution in a way the median isn’t, so it a better summary statistic (statisticians, you can tell me if this makes sense). The mean test is far more sensitive, but, as discussed previously, this is because it has an unacceptably high false alarm rate which is insufficiently penalised by d-prime.

Update: Cosma’s notes on the bootstrap are here and recommened if you want the fundamentals and are already degree-level comfortable with statistical theory.

Corrected boostrap function:

function H=bootstrap(s1,s2,samples,alpha,method)

difference=mean(s2)-mean(s1);

for i=1:samples
    
    sstar=[s1 s2];
    
    boot1=sstar(ceil(rand(1,length(s1))*length(sstar)));
    boot2=sstar(ceil(rand(1,length(s2))*length(sstar)));
    
    if method==1
        a(i)=mean(boot1)-mean(boot2);
    else
        a(i)=median(boot1)-median(boot2);    
    end
    
end

CI=prctile(a,[100*alpha/2,100*(1-alpha/2)]);

H = CI(1)>difference | CI(2)
 
		   
    

More on Graeber’s Debt: The First 5,000 years

“The story of the origins of capitalism, then, is not the story of the gradual destruction of traditional communities by the impersonal power of the market. It is, rather, the story of how an economy of credit was converted into an economy of interest; of the gradual transformation of moral networks by the intrusion of the impersonal—and often vindictive—power of the state.” (p.332)

Our attitude to debt is a symptom of this erosion of social economies by currency economies. Mutually agreed, honour, credit is replaced by state-backed, economic credit. Loans which inexorably grow due to interest are enforced by brutal laws against debtors. This is the context for the rapacity of European colonialists – they were driven on by the tyranny of interest.

“All this helps explain why the church had been so uncompromising in its attitude toward usury. It was not just a philosophical question; it was a matter of moral rivalry. Money always has the potential to become a moral imperative unto itself. Allow it to expand and it can quickly become a morality so imperative that all others seem frivolous in comparison. For the debtor, the world is reduced to a collection of potential dangers, potential tools, and potential merchandise. Even human relations become a matter of cost-benefit calculation. Clearly, this is the way the conquistadors viewed the worlds they set out to conquer” (p. 319)

It is the secret scandal of capitalism that at no point has it been organized primarily around free labor. The conquest of the Americas began with mass enslavement, then gradually settled into various forms of debt peonage, African slavery, and “indentured service” (p.350)

This is a scandal not just because the system occasionally goes haywire, as it did in the Putumayo, but because it plays havoc with our most cherished assumptions about what capitalism really is—particularly that, in its basic nature, capitalism has something to do with freedom. For the capitalists, this means the freedom of the marketplace. For most workers, it means free labor. Marxists have questioned whether wage labor is ultimately free in any sense (since someone with nothing to sell but his or her body cannot in any sense be considered a genuinely free agent), but they still tend to assume that free wage labor is the basis of capitalism.

Our dominant image of the origins of capitalism continues to be the English workingman toiling in the factories of the industrial revolution, and this image can be traced forward to Silicon Valley, with a straight line in between. All those millions of slaves and serfs and coolies and debt peons disappear, or if we must speak of them, we write them off as temporary bumps along the road. Like sweatshops, this is assumed to be a stage that industrializing nations had to pass through, just as it is still assumed that all those millions of debt peons and contract laborers and sweatshop workers who still exist, often in the same places, will surely live to see their children become regular wage laborers with health insurance and pensions, and their children, doctors and lawyers and entrepreneurs.”(p351)

With this framing, Graeber repaints Adam Smith’s economic account – “It is not from the benevolence of the butcher, the brewer, or the baker that we expect our dinner, but from their regard to their own interest.” etc – as a purely moral account, a utopia utterly unlike the actual economic conditions Smith lived in.

To understand the history of capitalism, however, we have to begin by realizing that the picture we have in our heads, of workers who dutifully punch the clock at 8:00 a.m. and receive regular remuneration every Friday, on the basis of a temporary contract that either party is free to break off at any time, began as a utopian vision, was only gradually put into effect even in England and North America, and has never, at any point, been the main way of organising the production for the market, ever, anywhere.
This is actually why Smith’s work is so important. He created the vision of an imaginary world almost entirely free of debt and credit, and therefore, free of guilt and sin; a world where men and women were free to simply calculate their interests in full knowledge that everything had been prearranged by God to ensure that it will serve the greater good. (p.354).

For some critical commentary see here: http://onthespiral.com/review-reactions-debt-first-years, the Crooked Timber seminar (ht Alex)

Update 30/12/12. There’s an important point about rights being conceptualised as property, which Gemma summarises well:

Our freedom is defined as a right, which we own, as opposed to Graeber’s view that rights are actually obligations on others (e.g. our right to free speech is actually others obligations to allow my free speech). Rights have been defined in this way to justify debt-peonage or even slavery – if we own our rights, like property, then we are free to give them away or even sell them (p206).