# Why does increasing the number of bootstrapped cases make PLS coefficients significant?

I am running a PLS model with a low number of observations ($n=50$). While several pieces of academic work argue that this sample size is appropriate to run this type of model, I am quite confused when it comes to the number of cases I take in my bootstrapping procedure.

I get some very strong path estimates for certain paths without a significant t-statistic (50 cases, 500 samples). However, when I put the number of cases above n (lets say 100 cases, 500 samples), the t-values are more in line with the path estimates.

• That seems like a logical result to me. If you arbitrarily increase the bootstrap re-sample size, the estimates will be less variable. I presume such an arbitrary increasing of the bootstrap re-sample size is totally inappropriate, so what is your motivation for doing it at all? – Andy W May 29 '13 at 12:16

As @Andy notes, you can arbitrarily increase your bootstrapped sample size (lets call it $b$). As $b$ approaches $\infty$ the standard error of your estimator will tend towards zero. All non-zero coefficients will by definition be statistically significantly different from zero. I remember reading a journal article where an author artificially inflated their sample size using bootstrapping and reported the resulting p-values. This is very wrong! It also may help to explain some people's naive mistrust in the concept of bootstrapping.