Recruiting participants for study I am planning to recruit participants in a college by advertising through posters, fliers, and the College Facebook. Is this method of recruitment considered clustered sampling, which is a type of probability sampling? I am afraid that if I make use of a convenience sampling, it will not be considered "probability sampling" and hence I will not be able to apply some statistical tests like regression analysis, factor analysis or ANOVA.
Any thoughts would be appreciated.
Thank you
 A: First, I address your question about whether what you are doing could be cluster sampling.
The answer is, "No." From Bayesian Data Analysis 3rd ed., chapter 8, pg. 210, final paragraph under Cluster sampling header:

In cluster sampling, $N$ units are divided into $K$ clusters, and
  sampling proceeds in two stages. First, a sample of $J$ clusters is drawn, and second, a sample of $n_j$ units is drawn from the $N_j$ units within each sampled cluster $j = 1,\ldots,J$.

You are not dividing the units up into discrete clusters, and you are not sampling the two stages described above. Therefore, you are not using cluster sampling.
Second, I address your more general question about whether this is probability sampling.
The answer again is, "Probably not."
From the Wikipedia entry on probability and nonprobability sampling:

A probability sampling is one in which every unit in the population
  has a chance (greater than zero) of being selected in the sample, and
  this probability can be accurately determined.

The college students in your sample will be selected from those who saw the ads, decided to do the study, and actually completed it. You will likely not have any information to build a probability model describing that process, in which case this is nonprobability sampling, in which there is no accurate method for estimating the probability of selection.
As @whuber said, "The sampling method imposes no limits whatsoever on the analysis, but it places severe restrictions on what the analysis means." In addition to this, I suggest that you record how your subjects heard about the study and include it as a covariate in your analysis. It doesn't matter if the recruitment effect is not "statistically significant". You should include those covariates because it is an adequate summary of how the data was collected, and will make the missing data within the recruitment type strata ignorable. See BDA3 chapter 8 for details.
