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    <p>The boot function is "expecting" to get a function that has two arguments: the first being a data.frame and the second being an "indices" vector (possibly with duplicate entries and probably not using all the indices) to use in selecting rows and probably having some duplicate or triplicates.) It then samples with replacement determined by the pattern of duplicates and triplicates from the original dataframe (multiple times determined by "R" with different "choice sets"), passes those to the indices argument in the boot.function, and then collects the results of the R number of function applications.</p> <p>Regarding what is reported by the <code>print</code> method for boot objects, take a look at this (done after examining the returned object with str()</p> <pre><code>&gt; duncan.boot$t0 [1] 5.003310e+00 1.053184e-05 &gt; apply(duncan.boot$t, 2, mean) [1] 5.342895220 0.002607943 &gt; apply(duncan.boot$t, 2, mean) - duncan.boot$t0 [1] 0.339585441 0.002597411 </code></pre> <p>It becomes more obvious that the <code>T0</code> value is from the original data while the bias is the difference between the mean of the boot()-ed values and the <code>T0</code> values. I don't think it makes a lot of sense to be asking why p-values based on parametric considerations are increasing in association with an increase in estimated t-statistics. You are really in two disparate regions of statistical thought when you do that. I would have interpreted the increase in p-values as an effect of the sampling process, which does not take into account the Normal distribution assumptions. It is simply saying something about the sampling distribution of the p-value (which is really just another sample statistic).</p> <p>(Comment: The sourcebook used at the time of R development was Davison and Hinkley's "Bootstrap Methods and their Applications". I'm no claiming any support for my answer above, but I thought to put it in as a reference after Hagen Brenner asked about sampling with two indices in the comments below. There are many unexpected aspects of bootstrapping that arise after one goes beyond the simple parametric estimation and I would first turn to that reference if I were tackling more complex sampling situations.)</p>
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    1. POHow to get bootstrapped p-values and bootstrapped t-values and how does the function boot() work?
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    1. POHow to get bootstrapped p-values and bootstrapped t-values and how does the function boot() work?
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    1. COI would be curious what the folks at stats.stackexchange.com have to say about the statistical aspect of this question. I would have said that the "effect of the sampling process" you mention is that bootstrapped bias estimators tend to exhibit increased variance and so may be imprecisely estimated (at least, that's my foggy recollection).
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    2. COI wasn't actually calculating any variances, although I will admit that I think the bootstrapped p-values will generally have higher variance than Normal theory might lead one to expect.
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    3. COWhen you look at the summary, you get t-values as well as p-vaules. these two values are related to each other. If you give me the t-value, i can calculate you the p- value and vice versa. If the t-value increases, than obviously the p-value decreases. I think you agree, right? So if you agree, I don't understand why this is not the case in the bootstrapped case. I would disagree with the sentence: "R does not take into account the normal distribution assumption when computing p values". I thought this is exactly what R does.
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      1. USHagen Brenner
 

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