Today I’m welcoming the handsome and talented David from Che Bello who is here to bring us another installment of Teach Me Something Tuesday:
Anybody who’s ever paid attention to a political race or any kind of opinion polling is familiar with a proportion. “100% of authors of today’s TMST think Kári is adorable,” a headline might read. Or “64% of Craig’s shoulder hairs have grown more than an inch in the past 12 hours.” These are both magnificent examples of proportions, one distinctly more horrifying than the other. But in political races, we’re often dealing with a population so large that we can’t ask everyone any given question. Even surveying all of Craig’s shoulder hairs would be a daunting proposition, imagine if you had to talk to every person in the country! So, how do we say anything about the population with any certainty at all? We construct the almighty CONFIDENCE INTERVAL!
Let’s say you’ve been hired by me to find out how many people agree with the ideas of nutjob Pat Buchanan. (For the latest vile nutjobbery, see here.) It should be 0%, but, sadly, we don’t often see extremes in public opinion. You go out and do a survey of a randomly sampled group of people that is representative and proportional to the population along demographics such as gender, ethnicity, education level, etc. (if you were to sample gun-brandishing veterans who can’t find manufacturing jobs anymore and don’t mind blaming it on immigrants, your sample would be pretty biased (and wouldn’t have the collective sense God promised a doorknob)), and what you come back with is that 42% of the population agree with his statements. So, are you ready to definitively say that that’s the true proportion that you would get if you asked everyone? Since you only took a sample, it can’t be. We use confidence intervals to say “Given the information that we’ve gathered, we think the true value we’re estimating is between x and y.”
So how do we do that? The basic form of any confidence interval is our estimate plus/minus a margin of error. This margin of error has two pieces: a critical value from what we call the z-table, and the standard deviation of our estimate. The z-distribution is familiar to you as a bell curve; it’s the normal distribution. We use the normal distribution here because of the central limit theorem. With repeated sampling, we know that the distribution of our proportions would be normal. That is to say if we took lots and lots of samples and made a histogram of the proportions of support for Buchanan for each one, it would eventually take the shape of a normal model. Or, if we took repeated samples of ten of Craig’s exes, eventually we could get a good estimate of how long the famed Puntabuschlong really is. This is true of all sampling distributions, even if the underlying population you’re sampling from is highly skewed. (The population, not the Puntabuschlong.) If you’re having trouble believing this, and that’s okay, as it’s a pretty earth-shattering revelation, check out the fun simulation here. Given that, we can use the normal model to set how wide our confidence interval should be. For a 95% confidence interval, the associated z-value is 1.96, because on the normal model 95% of the data fall within 1.96 standard deviations of the mean.
The second piece of our margin of error is the standard deviation of our estimate. We find this by taking the square root of [(our estimate)(1-our estimate)/N], with N being our sample size. It should be intuitive that dividing by our sample size is a good idea — the larger the number of people you’ve talked to, the more precise your estimate will be. That’s just another way of saying that its standard deviation (the average distance from each observation to the mean) will be smaller. Talking to more people means you can more closely pinpoint where the true proportion lies given the data you have.
So, putting those pieces together, we take our estimate (.42), and add/subtract 1.96(standard deviation). Let’s say that you sampled 2000 people. That means our standard deviation is sqrt[(.42)(.58)/2000], or 0.011. Multiplying this by 1.96 gives us .0216. If we subtract that from our estimate, we get .3984. And if we add that to our estimate, we get .4416. And now we’ve constructed a confidence interval for the true amount of support for Pat Buchanan in the population: .3984 to .4416. That means that we’re 95% certain that the true proportion of support, if we asked everyone in the country, for Pat Buchanan would fall between those two numbers. If this were true, I would stab myself in the eyes. The last polling data on Pat Buchanan comes from the 2000 election cycle, but none of them indicate much more than 20% support at that time, and I doubt it’s climbed much given his encouragement of John McCain to go to war on Iran for electoral benefits.
So the next time you’re looking at political polling data, you’ll now be able to think critically about it. Most firms don’t even publish confidence intervals, instead just giving news outlets their point estimates and saying the margin of error is 3 or 4 or whatever number of points. That leaves it up to the public to add and subtract the margins of error from both candidates and see if they overlap, meaning that the race would be too close to call. But with so few people being mathematically-minded or statistically educated, most people take estimates at face value. Stop doing this today and you’ll be well on your way to impressing someone in a political discussion (and winning your way into this cute statistician’s heart.) By the way, the confidence interval for proportion of the time shoulder hair turns me on? 0.00 to 0.01.
No Polt it was both hands and was cringeworthy I’m told.
Ryan: You are right, the deviation may even be higher. Occassionally it is referred to as “average” which is left to you imagination as to what average really is, but it gets a bit eye-roll worthy when every guy is the diameter of a beer can and 9 inches long. Yeah right. Where are these people (besides in Craig’s house)?
One Saturday afternoon the “penis show” was on the health channel. They asked women on the street what they thought a good size for a penis was and based on hand measurements (holding your hands X inches apart) the average size seemed to be 9-10 inches. I think there were a lot of disappointed ladies out there. So I guess it stands to reason that written fantasy would follow the pattern.
Ryan’s Law of Erotica Penis Conservation: In an erotic story with two or more men, any deficit in one of the men in terms of penis length will be compensated for by additional girth such that penis volume is equal for all men.
Cupcake: you are the only person i know who, when reading an erotic story, makes up mathematical properties, and laws and what have you.
I’m a bit concerned, cause I know intelligence is a turn on for some people, but not when someone is trying to get turned on by erotica.
HUGS…
Asimov’s Three Laws of Penis:
1. A penis may not injure a human being or, through inaction, allow a human being to come to harm.
2. A penis must obey any orders given to it by human beings, except where such orders would conflict with the First Law.
3. A penis must protect its own existence as long as such protection does not conflict with the First or Second Law.
Other than very big (nice to look at but not very practical) or very small, I *rlly* dont think size matters much. It’s what you do with it that counts (and of course, the rest of the package) -snicker-. Package.
Polt: The mathematical properties are derived after the main purpose of reading the story is finished.
I think I agree with the RLPCP. Usually if one is very long, one is very thick. Hmmm. There’s something to this.
You been watching I Robot again Craig?
David in B: Isn’t that what the under-endowed say to justify it? (I kid, I do honestly)
I resisted the urge to post the size. I dunno, it felt so.. crass. But it’s pretty decent in my opinion.
DinB: Crass? On Puntabulous? Never. Perhaps just a picture.
Or a third hand account from your BF.
Cupcake: When I’m reading erotica (and really, with high speed internet available, what’s the need to READ it anymore anyway?), I don’t think I very often got the story finished…before I was finished. And when I did, mathematical properties of what I just read were nowhere NEAR my thoughts. But then, I’m a political science major, what do I know about math anyways?
Tam: “Usually if one is very long, one is very thick.” I don’t know if this holds true…I can recall several….well, ‘pencils’ that I’ve seen on guys before. And I’ve seen a few…’fire hydrants’, short but thick. Always kinda felt sorry for the latter group…
HUGS….
DfB: two words my friend: “Prove” and “It.”
HUGS….
Well alright. According to my calculator (I had measured in centimeters after all) it is 7.0866 inches. Can’t prove it, but come on. If I was gonna lie i’d make up someth huge right?
I <3 my blog
DavidfB: I think you have more significant figures that can be justified.
Apparently, North Koreans are staying in the hotel next to my office.
Yeah see, now I feel silly and slightly embarassed
Anyway. I never asked or told that sort of thing to people I was flirting with through the Internet. Well. Once when I was just starting dating I specifically went out with one guy because he was famous for being well-endowed. It… ahm.. didn’t work out very well. But hey, learn something every day right?
DfB: Perfectly acceptable don’t be embarrassed. We’re all family here.
To be honest I’m not a huge fan of PwP (Porn without Plot). I need the characters to actually have a brain and some plot and characterization beyond being able to produce copious quantities of ejaculate in a 15 min. period. I have a couple of those books and after 100 pages, 6 of which are comprised of plot it’s burn-out and totally not sexy. Blah blah, who cares, fuck fuck fuck, literally. Next. Maybe it’s a girl thing but reading is for reading porn is for … well, other things.
Ryan: They are spying on you and reading your posts as we speak.
Tam: While recently reading a gay romance, I found myself skimming the final third of the couple’s first weekend of sexual exploration. By day three, I want more plot than sleep and breakfast.
Craig: If you really loved your blog, you would be taking pictures right now.
Exactly Ryan. When you are skimming the author has lost you. Yeah, I get it, they’re hot for each other. Now what? I’m curious who the author was. Maybe I’ve read it.
I just got a crap load of yaoi yesterday from the Book Depository but I got The Fathom’s Five – The Cross of Sins by Geoffrey Knight. It’s supposed to be a really good adventure story.
Tam: Caught Running ~ Abigail Roux & Madeleine Urban
I’m a Pisces and am too sensitive too even existerskatez. Penises lead to relationshitz (at least for me) and therefore are frustrating and make me sad. Booo. I’ma be celibate forevaz.
Oh my, that’s a classic. I’ve read it. Hmmm. Have you read Josh Lanyon? Less sex, more murder. The Ghost Wore Yellow Socks is really good and Somebody Killed His Editor is really funny. Not usually Josh’s style but it’s the start of a series. I think I laughed out loud literally in the first two pages.
If you like horror/mystery Jordan Castillo Price writes some good ones, the Psycop series is great (I binged one weekend and read 4 in a row) or the Channeling Morpheus/Sweet Oblivion series with Wild Bill and Michael is pretty spooky and bloody (vampires).
I can’t add much to this discussion. But, I can say that when The Argyle Deity wears tight pants his package is prominantly distracting at times.
I have never been obsessed with size. Perhaps that is due to certain activities I have not experianced. I always found shape and perkiness to be more of a turn-on for me. The first and thus far only guy I have been with was very well shaped.
Despite my aesthetic sense, I would rather fall in love with a good guy with an OK cock than a bad guy with an amazing appendage. I know I need much more than physicality.
Hang in there Josh. Someday your prince will come. Or so they tell me.
@Josh: I think you’re on to something, there. I can think of a lot of times I wished I had remained a little more priestly (ha…that’s a big assumption, a celibate priest). And being sensitive isn’t a bad thing — at least not to the good guys like me.
Sassy josh: Penises (penii?) don’t HAVE to lead to realationships, AND I’m pretty sure you won’t be celebate forever, AND if you want proof of BOTH those statements…just let me know. I’m only a trainride away.
Cupcake and Tam: See when we were talking about erotica, I immediately thought porn, not romance. I myself have enjoyed a gay romance-ish novel or two in my time. And then, plot is all important. However, in porn, plot’s not necessary. Hell, in visual porn, words aren’t even necessary. And sometimes, they’re not necessary in real life sex either……just sayin’….
HUGS….
dcm: oooh, sensitive good guys are fun. Especidally depending on where they’re sensitive. Bah-da-BUM! Thanks folks, I’m here all night.
HUGS….
Polt: Definitely a difference between the two, but for me visual porn without words is BORING. And subtitles don’t cut it.
I think we’re nearing a discussion of the ways in which the overt sexuality of the gay community marginalizes and alienates some members.
I agree with Tam: porn without plot tends to be boring. It doesn’t need much plot, but it needs something to distinguish it from all the other porn out there.
Although, it isn’t boring if I find the participants hot from previous work. I guess then I can make my own plot.
Tam: I wonder if that is a male/female difference. I don’t need dialog in porn, and bad dialog can actually be a big turnoff.
Not necessarily dialogue Chris but total silence is weird. At least let me know you’re liking it. When all is silent you expect speech bubbles to pop up and some guy on an old timey piano to chime in with some background music. And it’s very likely a girl thing.
DCM: the level of overt sexuality in the gay community was a BIG turn off for me for a long time. I attended a coming out support group and had to work through a lot of my hangups. I am not promiscuous. I can’t have intimacy with strangers, and that is what I desire. However I want to avoid being sexophobic. It is a normal part of life, and I do belive that it is a part of building a relationship. When I meet the right guy I will want to be intimate with him, but for me it would be a part of deeper path. I do not hookup, I have been tested, and held to my values. Now, I try to be more open minded about the people in the gay community who are more permiscuous. To each his own. I am only the master and commander of the ship of my own destiny. (on iPhone sorry if spelling suxers)
well said Chris D. And the spelling on your iPhone is better than the spelling from my laptop…with a spellcheck.
HUGS…
M. Nico: LOL! Exactly. “Song.”
I think size does matter in a way. If it’s too small, they’ll probably be self-conscious and then act insecure. Confidence is the number one thing I look for. And often, that correlates to da p33n.
I’ve only seen cuatro p33ns in real life (whore?) and the smallest one was siete.
I completely agree, Chris. Everybody is looking for different things at different points in their life, and who am I to try to restrict someone else from fulfilling a bodily desire. But there’s a difference between fulfilling those desires and openly advertising with every form of communication that you’re available and willing for random hook-ups. I know that it’s intended as a joke around here, and I’ve participated in my own way, but it gets tiresome for someone who would like to believe that there are guys out there who are looking for the kind of true intimacy you’re talking about. Other than me, lol. I just spend a lot of time thinking about the stereotypes with which gay people get labeled (and coming from the South I’ve heard the worst of them), and am very conscious when we actively reinforce them — like by proclaiming to the world that we’re totally okay with lots and lots of meaningless sex.
Tam: I agree, I am not a fan of silence in porn. I find some music in porn interesting. I that well done porn with powerfull music can be a very expressive art form. I often thought it would be cool to have a sexual soundtrack when I meet the right guy. Perhaps that would seem to choreographed. Good sex needs to be responsive and can’t always be timed to songs. I do however have what I think is a really good mid-orgasmic mantra in my mind to share with just the right person at the right moment. I hope I get to use it one day.
Chris: You’re talking about “Keep Singing My Song” right!?
And while I don’t have sex (unless David is the one defining my vida de sexo), I talk a lot when kissing! I’ll start kissing someone, then be like, “Oh yeah, in class today, blah blah blah.” I do it all the time. My friends are like “That would be annoying” but no one’s ever complained!
Speaking only for myself, I can say that I take everything said here as a joke and for fun. I mean, that’s what Puntabulous is all about, after all. But if someone would be “toally okay with lots and lots of meaningless sex” then how does that affect someone else’s life at all, unless that someone else is being forced into meaningless sex. If we’re going to worry about reinforcing negative stereotypes, perhaps we should avoid the one where gays only care about large phalluses. Coining the term Puntabuschlong, while funny, could also play into negative stereotypes and labeling someone.
Frankly, in my opinon (for what it’s worth) people need to lighten up and enjoy life instead of worrying about what other people think of them. Enrico had it right, confidence is majorly attractive, not obsessive concern with what others think of you or what you do.
HUGS…
Enrico: You measured them all?
This conversation is making me feel worse and worse about myself. I don’t want my sexual preference to even need such long discussions. I’m fucked up enough dealing with my own issues and then to have there be these stereotypes and pseudo-expectations put on how I am supposed to act is utterly frustrating. I constantly am in fear of having my past sexual experiences define who I am as a person, by others, but more specifically by myself, which hurts ten times more. Fuck.
[this has to be the most serial post I have ever written, anywhere, ever.]
Enrico: I like guys who are confident enough not to need to brag about how big their dick is. Sometimes too much confidence can make some one cocky. I like a guy who is confident, but also not afraid to be vulnrable at times. Sharing insecurities can be a part of real intimacy.
Yes, yes, very true Polt. Just because you don’t personally believe in something, doesn’t mean you should talk bad about it (unless it’s Lady GaGa!)
You all know that no, oh, oh, I do not hook uh, uh, up (I fall deep), but while I don’t personally identify with Polt’s sexual choices, I still respect that it is a POSSIBLE choice and isn’t ‘better’ than any other. And Polt’s right; if both parties aren’t looking for meaningful sex, then who is being harmed?
But Polt, Puntabuschlong doesn’t enforce stereotypes… it’s just a nod to the awesomeness that is Craig.
And now that Craig and I have compared (remember when everyone was paying for karaoke and Craig and I disappeared?) I think it’s time all the attention is on ME. Thanks!
Ryan: Since I was actually WITH each person, I saw each one on several occasions and we talked about size. Doesn’t everybody?
Speaking of gays: LOL!!!!!!
Ah, Enrickyricardo….what’s that saying, the wisdom that comes out of the mouths of babes? (and there was no sexual innuendo meant anywhere in that statement).
HUGS…
I would never presume to judge anyone else’s choices, nor would I condone anyone doing so. (Hello, atheism.) But when we make a message so pervasive as to give people the impression that it’s the only valid choice, that’s when red flags start getting raised for me. It’s the “pseudo-expectations,” as Josh put it, that we’re reinforcing. And I think there’s a distinction to be made between the size queen stereotype, which acts within our own community, and the stereotype of meaningless promiscuity, which has been perverted by conservatives over and over again to paint us as threats to the stability of society. You don’t see Anita Baker running around saying “Gays can’t teach in our public schools because they only sleep with people with huge cocks!”
OMG! That album cover is awful!
Almost as awful as losing Enrico and I’s contest
Chris D.: Cockiness is often a sign of insecurity. Confidence doesn’t need the reassurance of bravado.