Stats and Willies

A reader answers my earlier reader’s worry about the statistical validity of the large study that found that gay men have bigger willies than straight men:

As a stats nerd myself, I had to comment on your reader’s concerns about the differential sample size regarding the penis size. His concern is very likely unfounded. The differential sample size, per se, would have no effect on the relative differences between the two groups or on interpretation of the differences. Indeed, both of these samples are very large sample sizes and so sample size should not affect the characteristics of distributions. Generally, you only worry about it when you have sample sizes below 30 and that is not the case here. If there were differences in the shape of the distributions, your reader would be right and it would confound interpretation. However, it does not appear as though that is the case (see attached article).

Even if the distributions were skewed with a small proportion having very large penises (and more so than the proportion of those having very small penises), it would not really be a problem unless they were skewed in different directions. Because of the large sample sizes, the outliers (either very large or very small) would not have substantial effect in affecting the interpretation of the differences (or the mean in this case). Unfortunately, as a straight guy, I‚Äôd like to believe it‚Äôs not true!, however I don’t believe that there are statistical reasons to doubt the analyses …

I’ve had several expert emails on this and they all agree. Here’s the math:

According to Wikipedia, the population standard deviation in penis sizes is .8 inches.  Other surveys had a smaller SD, but for argument’s sake, we’ll use the larger one.  If we assume that gay and straight men have different average penis lengths but the same variance in lengths (i.e. Same standard deviation – this property is called homoscedasticty – no joke) we can use this .8 figure for our SD without issue. Our calculation is straight-forward:

Mean Difference in Penis Size: .33 inches
Gay Sample Size: 935
Standard Error (Gay Average): SD*Sqrt[N]/N = (.8)(Sqrt(935))/935 = .0262
Standard Error (Straight Average): (.8)(Sqrt(4187))/4187 = .0124
Standard Error (difference) = Sqrt(.0262^2 + .0124^2) = .028986
Z statistics = .33 / .028986 = 11.3847

With this very high z-statistic, the probability of Kinsey’s results happening by pure chance are extremely, extremely low – way less than .0001. Of course, this result depends upon accurate self-reporting and our assumption about having the same variance. If this result is not true, it is not because of the sample sizes.

Alas, stats was not my strong suit in grad school – but I did pass! The issue of self-reporting would only be salient if gay men were more boastful than straight men, but I don’t immediately see why this should be so. They’re probably all exaggerating a little.

Of course, if we are to agree that gay men have slightly bigger peepees than straight guys, the question is: why? Maybe hormone levels in the womb are a factor. I’ve long thought that the theory that homosexality is partly a function of abnormally high levels of testosterone n the womb was worth looking into. The stereotype is that gay men are somehow more feminine than straight men. But it could be that they are actually more masculine in the sense of having higher testosterone levels in fetal development. That might also shed light on the black-white-Asian penis differential. Are there any solid studies on that? (Apparently not.)

The Disgrace in Tehran

It is easy to become numb to an outrage. But what just happened in Tehran – the Holocaust denial conference – really requires us not to give in to numbness. Anyone who seriously wants to question the fact of one of the greatest crimes in human history is a monster. Period. That such a person now controls a country that is trying to seek nuclear weapons should concentrate the mind. Anne Applebaum gets it right, as she often does:

Iran is serious ‚Äî or at least Iran’s president, Mahmoud Ahmadinejad, is deadly serious. Holocaust denial is his personal passion, not just a way of taunting Israel, and it’s based in his personal interpretation of history. Earlier this year, in a distinctly eerie open letter to German Chancellor Angela Merkel, he lauded the great achievements of German culture and assaulted "the propaganda machinery after World War II that has been so colossal that [it] has caused some people to believe that they are the guilty party." Such views hearken back to the 1930s, when the then-Shah of Iran was an admirer of Hitler’s notion of the "Aryan master race," to which Persians were meant to belong. Ahmadinejad himself counts as a mentor an early revolutionary who was heavily influenced by wartime Nazi propaganda. It shows.

The London Times has also recognized this new low.

A Question for Romney

A reader writes:

You can’t really argue that Romney hasn’t explained why he’s changed his position on ENDA. He did give a reason to the NRO:

"My experience over the past several years as governor has convinced me that ENDA would be an overly broad law that would open a litigation floodgate and unfairly penalize employers at the hands of activist judges."

Here’s where the real follow-up question to Romney should focus:

"You say your experience as a governor changed your mind on ENDA. Well, it happens that you‚Äôve been governor of a state that has had a law on the books since 1989 prohibiting discrimination based on sexual orientation. Has Massachusetts in fact seen a litigation floodgate? Can you cite any examples of employers who’ve been unfairly penalized at the hands of activist judges?  During your term as Massachusetts governor, did employers come to you complaining about how the non-discrimination law was harming then?   

And if not, then how can you claim your experience as governor leads you to believe that a federal version of your own state’s law would have all these harmful consequences?"

C’mon, K-Lo. Ask him.

Frum Again

He asks:

[I]f Andrew has not recanted his opposition to ENDA, why does he berate and abuse Mitt Romney for the offense of agreeing with him?

Er, I didn’t. Go read the post to see for yourself. The entire point was Romney’s flip-flopping. I merely pointed out that Romney had reversed himself on the ENDA question and I was interested in why. My anti-ENDA position is unchanged (I was trashing it on HRC’s satellite radio show just the other week), but I’ve largely given up on the matter, because support – gay and straight – is so overwhelming. David asks me to substantiate this. Here’s opinion poll data from 2001. A Gallup poll found 85 percent support for equal rights for gays in employment. A Harris poll found more explicitly on ENDA that

61 percent of Americans favored a federal law prohibiting job discrimination based on sexual orientation. Additionally, the survey found that 42 percent of adults surveyed believe that such a law currently exists.

The following states already have such a law: California, Connecticut, the District of Columbia, Hawaii, Illinois, Maine, Maryland, Massachusetts, Minnesota, Nevada, New Hampshire, New Jersey, New Mexico, New York, Rhode Island, Vermont, Washington and Wisconsin. Hence my quixotic libertarianism being a lost cause. Frum has another post on the subject here, where he plainly concedes that Romney once

"declared himself in favor of a federal antidiscrimination law against gays and civil unions – while staying cautiously mute on the issue of marriage."

No one can dispute this 180 degree turn on both ENDA and civil unions. Not even Frum. I’ve watched some brazen say-anything-to-get-elected maneuvers in my time, but this one is pretty out there, don’t you think?

Gondry – Yrdnog?

Was that YouTube a fake? A reader suggests it was filmed backwards, with artful passers-by walking backwards to convey the impression of it being in real time. What about his words at the beginning?

There’s an obvious cut between it and the shot showing him solving it. With the addition of some background ambient noise, the whole thing is made to appear genuine. I personally think realising how it’s done improves it; makes it more Gondry-esque.

Watching it again, it’s clear my reader is right. Gondry has used reverse filming before. Here’s the link.

Another Reader Review

A reader writes:

I have been reading your blog for upwards of 3 years now and was reluctant to buy your Tcscover_32 book thinking it would have little new for me. 

How wrong I was. After one of your many plugs for the book, I broke down and bought it. You have written an interesting, important book. It is not only a great and convincing argument for conservatism, but a solid rebuke of the "conservative" Republicans and fundamentalism.

2 comments I wanted to make: 1) It is striking how utterly arrogant the ideology of fundamentalism and by extension the Republican party is. At its essence these people think they know all, what is best for me, how I should live my life, what is right. 

2) It seems another term needs to be created to replace "conservative". Republicans of  the last decade have taken the term conservative and not only bastardized it, but made it almost completely meaningless. When people say "George Bush is very conservative," What does that mean? It has lost all connection to what it once meant.

The right-wing media have done their best to rubbish the book and distort its message. They’ve done this because they realize the power of its case. But it’s surviving because of one thing: people who have read it. I’m grateful. You can buy what some don’t want you to read here.