Originally Posted by Para-Goomba
Good question, Wad, and a common one. In America, at least, people are generally trained in disciplines such as geometry and algebra that rarely arise in everyday life, while the more practically important fields of statistics and probability are ignored. I have two papers due today, so I can’t spend much time here right now, but as an example, I will calculate confidence intervals for the Israeli study, since it provides the requisite standard deviation and it is also the study with the smallest sample size (55 subjects).For the Israeli study, we can be 95% confident that the real population mean for BPEL falls between 5.17" and 5.54", and we can be 99% sure that the population mean falls between 5.11" and 5.60". Given the nature of this particular study, a reasonable "population" to generalize it to would be Israeli men suffering from erectile dysfunction.
To understand the relevant and uncontroversial inferential statistics I am using, this should be helpful, as should the first four sections here . To understand why population size (i.e., 65 million for American men whose average penis length you’re interested in) is irrelevant (as long as it’s at least 10 times larger than the sample size) to the statistics, see the central limit theorem , without which medical and psychological research — not to mention all of the social sciences — would be largely impossible.
Para,
I’ll defer to your experience in numerical probabilities and survey methodology as you are a researcher. However, I’m just not so sure that there has been a statistically large enough sampling of actual penises studied to formulate a reliable, accurate theorem - which will consistently hold up over larger & larger samplings of data/population, etc.
>>"To understand why population size (i.e., 65 million for American men whose average penis length you're interested in) is irrelevant (as long as it's at least 10 times larger than the sample size) to the statistics, see…."
Does this imply what I think it does? Let’s say there are 1,200 men in the NFL and I wanted to determine the average penis size of a modern NFL player, your statement seems to imply that I do not want to study a sampling of more than 120 men - for then the population (1,200 NFL players) would not be "at least 10 times larger than the sample size." So, in other words, I want to study less than 120 men to try to determine accurate size figures for the 1,200-member group.
What if I studied 1/2 that number - 60 men - and there just happened to be an unusually high percentage of larger dicked men in that study (let’s say the study was NBP and the linemen - the fattest of the samples - went last, before the thinner "skill position" players, so there happened to be a disproportionately small number of 320-lb men getting their NBP measured, that would clearly skew the numbers.
I understand that the science of statistically probability is quite complex (my cousin is and actuary and deals with this type of shit constantly for insurance companies), but often times our most beautiful and complex theorems begin to yield erroneous results as they are pressed into wider application. The old saying, "A lot of things look good on paper, but just don’t work in the real world" is not completely without merit.
I understand that if you flip a coin, the odds are always 50% for heads or tails - with each flip, whether you flip it twice or 10,000 times. But the human species is so varied, and human physiology is so complex - and the particular area of penis size has been so scarely studied - I just don’t believe that science has all of the needed data to formulate a reliable theory of probability regarding dick size.
">>…central limit theorem, without which medical and psychological research — not to mention all of the social sciences — would be largely impossible."
This was quite a grand statement; unfortunately, the comparisons between these subjects and "average penis size" are irrelevant. First of all, you are on extremely thin ice when you bring psychological research and the social sciences into the argument; both areas, of course, have long been the targets of the most scathing criticism by many highly respected academicians. Some have argued that the social "sciences" have led to some of our greatest societal failures. And psychology often boils down to a coin toss, there is so much subjectivity involved. When 20 psychiatrists can examine a patient and give 20 widely different reports - and then engage in heated arguments with each other over their findings…..need I say more.
And the allusion to cancer research does not find its parallel in the great penis size debate. Cancer research has, again, developed over so many millions of patients, their doctor’s reports, as well as intensive university research. Again, we’re saying that not even 1/60 of 1% of 65 million men have been studied. On the contrary, every cancer patient has had their treatment regimen and their responses charted by their doctors. These findings are discussed at gatherings, published in medical journals, etc., etc.
Using statistical probabilities in the hard sciences is one thing; trying to consistently apply these theorems in such a minisculely researched area (subject to wide variation) is bound to lead to erroneous conclusions. I’m not suggesting that these theories are "useless," however, I don’t believe they can offer us any satisfying level of certainty. And, their findings could be immediately shot down in the face of just 1 extensive study.