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.
Josh: I think it would be of great benefit for you to work through your concerns. Either a therapist and/or a support group can be of great help. It helped me. I don’t like to see you in pain over these issues. You don’t have to suffer. I beleve that people can change, because I changed so many of my own negative thoughts and feelings over the years. You are young and it is OK to feel lost sometimes. You will find your way. If this thread really hurts you then do what you need to do. Stop reading this thread if that helps. You are the master and commander of the ship of your destiny. You can sail where you choose.
DCM, interesting that you think overt sexuality is the problem message within the community. I feel strongly that the balance (at least on the coasts – and this is a regional issue) has shifted in the other direction, that we’re too hung up on assimilationist “we’re just like you” “don’t rock the boat” image projection for political gains that we’ve alienated the genuinely (and I use this word now in a broad context) queer. People who are unabashedly interested in fetish communities or gender subversion or any non-normative sexual/gender expression are told to stop making “the normal gays” look bad. We’ve begun to fetishize “str8-acting” and “guy next door” behaviors to the exclusion and alienation of those who do not and cannot meet those expectations
That’s an interesting point, Jere, and I think there’s a balance somewhere that we haven’t yet struck. Mainly because our political and legal system hasn’t allowed us the freedom to define our own space in ways that are inclusive of everyone in our community. I think discussions like this are normal for any restricted minority, and are a symptom of what we have to change. The question becomes what’s the best way to gain that acceptance so that we *can* define ourselves in our own way. And I think I sometimes too quickly fall on the assimilationist side because of my own prejudices against behaviors that I can’t understand. I need to be more cognizant of your argument on a daily basis.
I got comment 100! No more complaining from Craig that we don’t comment.
Jere: that is a good point. In the coming out support group our facilitator made us aware of spectrum of the gay community. He was into the leather scene himself. Now that I am on the board of the Pride Center we always try to balance the concerns of all the different aspects of the GLBTIQ umbrella, including the fetish communities. It has helped to keep me open minded.
dcm, I believe you meant Anita Bryant. Anita Baker is a musician. but if you don’t make a big deal out of my spelling errors, I’ll not dwell on a momentarily celebrity misname.
I don’t really give a crap what the Anita Bryants and her ilk think about me and my life. I don’t think about her or her life at all. I’m not going to live my life so that I don’t upset someone’s impression of the way I, or anyone, should be.
I’m not meaning to be condescending here, but I don’t know how old you are, I imagine it’s younger than my (almost) 42 years. I remember being younger and concerned about things like what others thought of me. But as I’ve aged, I realized I shouldnt, and don’t give a flying fig. Life is too short for me to worry about what some religious wingnut thinks about me. It’s not as if every single gay man in the world suddenly became celebate, it would change thier minds, or how they feel about us, or how they feel about our rights. They’re against us, and going to be, no matter what we do simpy because we exist. I don’t feel the need to give them power over me.
But, look, we’ve upset Sassy josh, and brought this otherwise funny and entertaining post down to a morose level. Let’s just agree to disagree and get back to the Puntabufun!
And really, I meant no disrespect about the Puntabuschlong comment, cause really, that made me laugh out loud in my office when I read it, and it does even now.
HUGS…
Apparently Craig’s equipment just need to be mentioned and we all go nuts with the comments. This is quite an intersting thread. It went from very sexual to philosohpical and now mildly political.
I have that effect on people
Polt: I agree! Back to the fun (aka, why doesn’t anyone care that Craig and I finally compared?!)
Very sexual, philosophical and mildly political….man, if we could just condense all these comments into a man, I’d marry on the spot (if we were in three or so states here), cause that sounds like my dream guy.
Oh, and he should have longish hair too. 
HUGS…
Enrickyricardo: we don’t care cause we didn’t get to see the comparing taking place.
HUGS…
Seriously, enough politics, more dong comparing!
Amen Craiggers! Amen!
HUGS….
Anita Bryant! Whoops. :-p
I’m completely on the same page about the Puntabufun, but I think you’re misunderstanding something key about what I’m saying. I’m not concerned about what wingnuts or others think about me, personally. But I am concerned about how perceptions of the gay community dictate legal and institutional structures that keep us oppressed. There’s a big difference in saying “I make my own choices, fuck off,” and saying “I don’t care what you think of the community to which I belong.” I’ll shout the former from the rooftops, but we have to understand that judgments about our entire community are what they use to maintain our second-class citizenship. That was Harvey Milk’s whole argument about the need to come out — once we make it about personal decisions people join us much more forcefully. But if we stay in the shadows and leave the public discourse about us to stereotypes and corrupt moral judgments, we’re going to continue to get beaten down.
It’s all about power relationships. We’re required to think about what Anita Bryants and the like think of our community because we haven’t yet won our equality. We shouldn’t have to defend our individual actions to them, but until we move to a point where we’re treated equally in institutional spaces, we have to think about how we’re being characterized as a group.
Okay. No more from me on this topic. And yay that we can have serious discussions and all still be friends!
And Josh, we all love you! Nobody should be defined by prior choices, and if you run across people who do judge you based on them, you should know that they aren’t anywhere near being in your league. I don’t want to steal Polt’s signature HUGS… thing, so I’ll just give you a friendly ::snuggle:: instead.
I thought we all just assumed that Craig and Enrico were hung like hamsters and stuff their shorts with socks. Feel free to prove us wrong guys.
“if you run across people who do judge you based on them, you should know that they aren’t anywhere near being in your league.” Well said, dcm, very well said! you listening, Sassy josh?
I could go on with this dicussion (and I LOVE debating nearly any topic usually until the other person just gives up in frustration, but this clearly isn’t the forum for it), but since we’re discussing comparing organs, I’ve lost interest.
*shiny bauble, shiny bauble*
See, FDot and Jere, I told you guys that’s all it took.
HUGS….
Heh, way to turn all serious all of a sudden. Where here’s a perspective from way South. Brazilian society is very progressive unless you actually ask them what they think about something. There is a lot of silent progress around here, and in a big metropolis like São Paulo it’s easier to be out or talk about it, while at the same time there is a fringe element (neonazi and their ilk) who can be dangerous. Most I think couldn’t really care less about what others do in bed, as the main focus for “popular” conversation is neither cultural or politics – its the economy. Most people are intensely worried about jobs, money, security, etc and political participation is very low – which is why politicans here can get away with a lot, unfortunately, because only a small elite layer of the population keeps them in check. The media is very open and critical of power (no “Fox news” around these parts), but not everyone keeps themselves well-informed. Lastly, thank goodness, the religious aspect is kept reasonably at bay. There is a traditional and historic catholicism, which is not very politically involved or combative (rarely will you see some priest go out on TV or whatnot to rail against the evil “gays”), and an evangelical component, which I believe is more interested in extracting money and power from its “faithful followers” than anyth else.
Anyway I got lost. Where was I? oh yes. Peen comparisons. I want the next puntabulous meeting to have pictures and graphs!
ooh, it strikes me that I finally taught you guys something. Well about Brazil and about me.
Cliff notes version: the average Brazilian cares about a) how much money he has/makes and b) how he’s going to spend it. The culture wars afoot in America make no sense here, and the idea of an “oversexualized” gay community is silly to me. What makes us gay? The kind of sex we do. Therefore, sex is a big part of being gay. Plus, men are sex-addicted pigs. There ya have it. Deep insight!
David from Brazil: It’s not just the sex we have. Who you sleep with doesn’t define your sexual orientation. Sexual orientation is about both who you want to fuck and who you want to love.
Oh come on Ryan. You really think that you had to add that? That I didnt know what love is, only sex? I kid a lot here, and I *do* have a dirty, dirty mind, but I’m pretty sure I know what love is. I’m 29 and have been with the same person – monogamous and living together for almost 11 years. I barely went out before that, and had sex with a grand total of 3 people before my boyfriend. So yeah. Being gay is about sex AND love, of *course*.
Gee Craig and Enrico sure got quiet.
Well dang, I should have read this earlier today because CONFIDENCE INTERVALS! Hey, I taught that this morning! But now the conversation’s drifted off into different territory….
Still, I can contribute the observation that one of the more interesting articles I ever read about confidence intervals discussed (seriously) the difficulty of getting a good confidence interval for penis size. After pointing out the difficulty of self-reporting (and the observation that those concerned with penis size should make a concerted effort at getting people to self-report smaller-than-actual values, which will lead to a smaller “average” and allow more people can claim to be bigger than average) it went into detail about how the one group that really NEEDS a good confidence interval is condom manufacturers, and went on to discuss how they got a sample. I believe it involved spring break, Florida, and people drunk enough to allow someone else to measure them.
(I occasionally bring this up in teaching, but I have to talk fast and skip lots of words so that I reach the main point before I realize how embarrassed I am to be talking about it, though I think it’s one of the more interesting real-life examples.)
Sorry me and Enrico got all quite. I’ve been taking some “vitamins” and demanded a recount
Penises and Statistics reminds me…
A few summers ago, I was teaching a class in “How to teach AP Statistics”. My students were five returning adult students, working on a masters degree in math education. They were a hoot and a half, as (no doubt) someone’s great aunt used to say.
Anyways, in the midst of some discussion or other, one of the ladies in the class mentioned the topic of the typical measurement of male reproductive anatomy. (I think we were talking about sources of bias in surveys, and the problems of self-reported data came up. I think I mentioned the Kinsey report and its claims re: the frequency of sexual activity, which led to…)
Anyways, when they all went off for a break, I did a google search to see what I could find out about how scientists determine the typical length of male genitalia. One of the more promising links was to a site that was gathering data using the internet, and offered to show graphs of all sorts of statistics (length vs girth, length vs ethnicity, etc…).
I was considering the idea of showing the site to my class, when I got to the bottom of the webpage: “Methodology”. Naturally, for such measurements to be meaningful, it is important for everyone to do their measurements the same way. So the page gave detailed instructions on how to measure penis length and girth.
What kept me from using this page in class: the instructions were illustrated with vivid, life-size photographs. And at that point, I had the sense that the page existed merely to serve as a forum for the guy in the photos. (I wonder if he ever sold a tea kettle on ebay?)
MORAL: If you’re using the internet as part of a presentation in front of an audience, NEVER do a google search or navigate to a page unless you’ve checked it out in advance.
SECOND MORAL: You can’t trust what a dude says about his thang unless he posts life-size photos of it on the internet.
TwoPi: And even then it can be photo-shopped.
We got quiet cause you guys weren’t talking about us enough.
TwoPi: I love when my teachers click on inappropriate links by accident! My teacher once clicked on a link IN HIS SYLLABUS, that accidentally led to porn. Oops.
Wow, I go out for dinner with the ladies and what happens, you guys get all political and serious on me. Can’t leave you boys alone for a minute.
Obviously as a straight girl I can’t comment on a gay lifestyle or sexual practices. As a Canadian I can comment on things like yes, everyone in Canada can get married to whomever you like (not counting your dog or your sister – we let Alabama have that one), we have hate crime legislation that clearly states based on sexual orientation, we have the charter of rights and freedoms which doesn’t allow for discrimination based on sexual orientation. We’re not perfect, yes gay bashing happens sometimes, but I hope we’re getting there. Most Canadians likely don’t care what/who people sleep with, but don’t want to see it either. They prefer not to think about it most often.
I work in a pretty progressive government department and probably bureau. My colleague in the next office is gay and told me about his partner my first day in the division, there is another guy who is gay and I finally figured out why Mary Beth looked familiar, it’s because I knew her as Murray last year. I don’t think there will ever be acceptance by 100% of the population, there’s always someone who hates someone for something be it color or gender or sexual orientation, which I think seems to be and ugly side of human nature.
Congrats on being 100 Ryan.
130 comments! We must be talking about penis!
Not just any penis, Michelle, the famed Puntabuschlong! Which, according to the latest rumors, ain’t nuthin’ once you’ve seen the elusive Enrico-meat.
Yay, Michelle is back. Hope your move went smoothly Michelle and you love your new home.
Thanks Tam! Now that I have internet and tv, everything’s swell.
134 comments and none of them from Kari, Object of My Devotion. ::sigh::
Enrico: I’d laugh, but I don’t want to tempt the Fates. But it is hard to imagine how such a “mistake” creeps into your syllabus.
I can just see the student evaluations at the end of the term: “He should show porn in class more often…”, or “My favorite part of the class was when we read the syllabus…”
i read and enjoy you, but never comment–seeing as how my particular brand of neurotic darkness is so completely incompatible with all the lighthearted dorkiness that generally goes on here, i figure, why spoil things?
tonight (prolly because i’m a little shitfaced), i’m gonna make an exception, because here’s the thing about buchanan: yeah, he’s ultra-conservative; and yeah, he’s probably a nazi sympathizer; and yeah, he’d undoubtedly love to throw all us homogays into concentration camps and fill our every orifice with concrete–believe me, i understand all that.
what i also understand–and what most liberals either don’t, or won’t–is, he’s also a very shrewd, observant student of history, and has drawn some very compelling parallels between the fall of past so-called eternal empires, and what’s now happening to ours.
in other words: yeah, he can be an asshole, but he can also be (and quite often is) right.
[excuse me now while i crawl back into my bunker at ruby ridge, adjust my tinfoil hat and await the invasion of the black helicopters]
Tam: And your extended comment is just ONE reason why Canada ROCKS and why I want to live there.
Michelle M.: Yay, you made it!
HUGS…
Damn! I get busy at work and miss all the debates, I am sad now. And Josh, remember that for every a-hole that pre-judges you based on rando past hook-ups there are at least a dozen Puntapeople here who love you for being the Sassy Josh you are. Let me see, Polt has HUGS, dcm took ::snuggle::… how about I give you a friendly *goose*