Can we, as a forum, please agree to learn some probability and statistics before continuing to have these threads? I don't even mean the hard stuff like tests, just things like the differences between population parameters and sample statistics, types of samples, how to formulate valid inferences (e.g. correlation vs. causation,) types of data, how to eliminate confounding variables, point estimates vs. confidence intervals, the mean average and how it relates to mean squared error, and at least some understanding of the Central Limit Theorem w.r.t. point estimates of a sample. I'm aware that basically all of the people I disagree with regularly have never formally learned any statistics or econonics, but sometimes it's hard to not attribute their comments to malice.
It would really help me out. TIA.
http://en.wikibooks.org/wiki/Statistics
The only way we can draw conclusions about the entire population of all welfare recipients is if the 2% who declined were forcibly tested, which would give us four groups of data (volunteered and passed, volunteered and failed, declined and passed, declined and failed) which we could analyze using two-way ANOVA, Pearson's chi-squared, or some other test. Without this data, the absolute most we could say about the population is that between 96.04% and 98.04% would have passed if everybody were tested, and that's by making an incredible (and frankly dishonest) assumption that an interaction exists between declining and failing. In real life a statistician would never say that. In real life a statistician would say they don't know and they would just exclude the categorical variables that are missing data.
Please, if you walk away from this thread having learned anything, please please please let it be that you can't say anything about a population if you haven't measured it.