B is for Bimodal Distribution

Another one in my series of statistical terms for those who like words, this time with pictures:

LetterB

Credit for the camel picture is Flickr user Camel Droop. Graphs  and camel names were my addition. 

While human height is the typical example of a bimodal distribution, it actually isn’t one.  That’s why I went for dung heaps in my example sentence.

Pop Science and an Introduction

Hi everyone! After 10 weeks on basic internet science, I thought it might be fun to switch things up a bit.  For the next few weeks (more if we get inspired), I’ve invited a very special collaborator to help me put together a definitive guide to the good, the bad and the ugly of science/math references in popular music.

Say hi to Ben!

Ben is a childhood friend of mine who runs ten-four films, his own blog, is funny on Twitter, and he watches movies.  He grew up without a TV, so of course he rebelled and became a professional film maker.  He’s a font of knowledge on music in general and indie rock in particular, and is the kind of person that responds to emails like “what’s up with Rivers Cuomo?” with multi-page missives that are just a few citations short of being a media studies doctoral thesis. Since that kind of brilliant obsessiveness is one the traits I most value in others, Ben has always been one of my go tos for all things pop culture. If you want to get  a sense of where he’s coming from, check out his favorite albums, TV shows, songs, and movies of 2015.

Anything else you’d like to tell the nice people Ben?

Ben: Hello! And thanks for having me. As Bethany mentioned, this is the sort of thing I do when only vaguely prompted, or sometimes entirely unprompted, and for an audience that often consists of only myself. As Dante once noted, you have to follow your own star.*

*I’m mostly sure this is a Dante quote, but the Internet might be fooling me again.

I like appearing on this site, because it gives me a veneer of intellectual robustness, which is somewhat undercut by the fact that I had to use a thesaurus site right there because I couldn’t remember the word “robust.”

Okay, so what are the rules here?

Both Ben and I have a healthy dose of petty despot in us, so everything’s subject to change at our whim. However, here’s how we started:

  1. We kept the definition of “science songs” pretty broad. We decided to include things that referenced math, scientists and medicine, in addition to more general science stuff.
  2. We drew the line at “science”. Some people try to sneak what are basically “geek” references on to science lists. Dungeons and dragons, while geeky, is not actual science.
  3. The whole song didn’t have to be about science. I’m a pretty big fan of the one line reference, so sometimes that’s all it took to make the list.
  4. I classified how good the science was according to my own whims, Ben classified how good the song was according to his. Ben’s a filmmaker, my taste in music is terrible. It works better this way. Basically, if you don’t think the song should have made the list it did, complain to me. If you don’t like it’s order on the list, complain to Ben.

Wait, Ben, did I just make those rules up or is that how you did things too?

Ben: You made all those rules up. I just followed your lead. But I think we ended up contributing a roughly equal amount of songs to this endeavor, and I think it’s pretty telling we both had mental lists of songs in which we had either applauded or been irked by the science displayed.

Frankly, this is a pretty ideal setup, with you placing the ball on the tee for me here. I’m glad to be Waldorf to your Statler.

Now that you’re all up to speed, we’ll see you next Sunday for “Ten Songs that Got Science Right”.

Click here to read Part 1 of “Ten Songs that Got Science Right!”

 

More Sex, More Models, More Housework

Well hi! If you got here via Google, this is probably not the type of post you are looking for. This one has math, and the only pictures are graphs.  Sorry about that.

For everyone else, welcome to “From the Archives” where I revisit old posts  to see where the science (or my thinking) has gone since I put them up originally.

Back in 2013, a concerned reader had sent me a headline that warned men about a terrible scourge depriving them of all that was good in life. Oh yes, I’m talking about housework.  The life advice started from the headline “Want to Have More Sex? Men, stop helping with chores.”  The article covered at study that had devised a mathematical model of a couples sexual frequency vs the number of chores they did.  I couldn’t resist, and ended up writing a post called “Sex, Models and Housework“. It’s still one of my most viewed posts, though probably not the most read.

A few things to know about the original study (found here):

  1. That headline was pretty misleading. The study never said that men who didn’t do chores had more sex, the study said that men who did more traditionally female chores had less sex. Men who did more traditionally male chores actually had more sex.
  2. Despite being released in 2013, the data the study used was from 1992. The people in the study had an average age of early to mid 40s at that time, so this is a study looking at Baby Boomers and their relationships in the early 90s. With shifting culture, this is important to keep in mind.
  3. The model extrapolated out to men who do 100% of the traditionally female housework. One of my core concerns was how many data points they had in that range, or if they extrapolated beyond the scope of the model. Men reported doing an average of 25% of the “traditionally female chores” at baseline, with a standard deviation of .19.  It does not look likely they had many men in the 100% range, and those relationships may have had something else unusual going on.
  4. Given #3, you’ll excuse me if I doubt that this model really should have been perfectly linear:
    8fe80-sexandhousework

Those were my original thoughts, and rereading the paper I wanted to add a few more:

  1. One point I can’t believe I didn’t mention the first time around is the inherent selection bias in this data. You had to be a married couple to be included in the data. So a hypothetical couple who had an uneven distribution of housework and divorced was not counted. To be perfectly fair, they did take a bit of a look at this. These respondents were surveyed in 1988 and then again in 1992-1994. They did look at those who were married in 1988 but divorced by 1992 to see if the chore distribution/sexual frequency was different. It wasn’t.  However, given the ages of the respondents (born in the 40s-60s) many of them could have actually already been divorced before 1988 rolled around1. Additionally, those who are going through a divorce or in an otherwise rocky marriage likely didn’t take part in the survey. We don’t know if those numbers would have changed things, but I think we have reason to suspect that those most bothered by chore arrangements would be more likely to divorce.
  2. The women in the study worked an average of 15 hours fewer per week than men at paid labor. The women in the study spent 18 more hours per week than men at household chores. It’s worth noting that an “average” man in this study doing half of the chores would have actually been doing more labor for the house than the “average” woman. It would have been interesting to see a total on “labor for household” to see what the effect of an even vs uneven total workload was. This is important to rule out that it’s not the “gender” of the chores, but potential perceived unfairness that drives the decrease in sex.
  3. Child care hours were not included anywhere for either partner.

Other than that, how has this research fared?

Well, as you can imagine, it caused a stir in academic circles. There was a New York Times Magazine cover story about it provocatively asking “Do More Equal Marriages Mean Less Sex?” based heavily on the study. Many people walked away concerned about the age of the data, and how applicable it was to  people over 20 years later.  Researchers from Georgia State University were able to (somewhat) replicate the study (pre-published copy) using data from 2006. A few things about that study:

  1. The study population was younger by about a decade and less wealthy than the original study population, and they had more sex overall
  2. Cohabiting but not married couples were included, but couples without children were not.
  3. They tossed 10 respondents who said they had sex 50 times a month
  4. This study ended up with three categories of couples: traditional, egalitarian, and counter-conventional. Of those
    1. Egalitarian: Divided housework approximately evenly, with anywhere from a 35%-65% split. This group  was 30% of the sample size had the most sex and highest satisfaction.
    2. Traditional: The woman did more than 65% of the housework. This was about 63% of the sample, and had slightly less sex and women had slightly less satisfaction than the egalitarian couples.
    3. Counter-cultural: The man did more than 65% of the housework. This was only 5% of the sample size, and did not work out well. These couples had a lower sexual frequency than either of the first two groups, and were less satisfied overall.
  5. I felt thoroughly vindicated by this line “No research, however, has considered the possibility that the observed effect of men’s shares of domestic labor on sexual frequency and satisfaction could be non-linear.”

So I was at least correct in my concerns. Presuming that this data holds, the line is likely fairly straight until it hits the extreme on one end, then plummets.  Interestingly, this study still didn’t compare total labor, and the women in this study worked 20 hours fewer at paid labor than the men, and about 15 hours more per week in housework. Again, child care was not included in the work totals. Since this group was younger, it’s likely at least some of that discrepancy is child care.

So where does this leave us?

Well, it looks like my concerns about assuming a linear model are valid, and that assuming relationships haven’t changed between Baby Boomers and Gen Xers is not a great idea. While some changes to marital set ups can have a negative effect (say a wife working longer hours) they are frequently immediately offset by a positive effect (increased income). This paper here has some interesting examples of these sorts of trade offs. I’m increasingly convinced that the details of the division of labor matter much less than sufficient and equally divided labor.

I would love to see a break down of just the couples on the “man doing all the housework” end. In the second study that was only 24 couples, and we don’t know if the arrangement was through conscious choice or because of circumstances such as unemployment. In fact, I think further research should ask people “how much does your current relationship reflect your expectations prior to the relationship?”. That might catch some of the effect of cultural script changes better than just asking people what they are doing.

Regardless, I have to go do some dishes.

1. According to this the median age at first marriage in 1975 was 21. If you got married in 1975, your chance of being divorced 13 years later was about 30%. This is not a negligible amount of people

What I’m Reading: March 2016

The Unbearable Asymmetry of Bullshit. Alas, we are outnumbered.

It won’t help with the asymmetry thing much, but I love this site. I plan on using it early and often.

Oh wait, here’s some more on bullshit and academic infighting, along with a proposal to call the study of bullshit “Taurascatics“. I’m in.

And one more thing about bullshit and rage….for anyone who is overwhelmed or perplexed by the current state of politics, I read this blog post once a month to keep myself grounded: The Toxoplasma of Rage.  It’s a great reminder that your ingroup is persecuting my ingroup, and that you really need to stop. My ingroup is far too busy enumerating the faults of your ingroup to have time to deal with this crap.

On a lighter note, did you know James Garfield came up with his own proof of the Pythagorean theorem during a discussion with congress? I am wondering how many current members of Congress could actually define the Pythagorean theorem.

My book for the month (well, one of them) is Guesstimation: Solving the World’s Problems on the Back of a Cocktail Napkin. Basically it’s about how to estimate complicated problems. A little repetitious, but an interesting mental exercise book so far.

These are some interesting numbers on growing American commute times.  Apparently I spend 20.8 days a year commuting. I resent the “wasted life” part though. Between the train and the bus I get a lot of reading and thinking done. That’s pretty much what I would have done with that time if I had my druthers anyway.

This was an interesting piece about how to make science fairs better. I like the idea of a myth busters style fair. That could get fun.

There’s an interesting Vox piece about health/science journalism and how it’s a good way of losing friends. I liked the piece, but I think she left out the issue of policy recommendations. It’s one thing to talk about evidence for a problem, and it’s another thing to talk about policy recommendations. Very often we see people start with the former, end with the latter, then claim all criticism is because people “don’t like evidence”.  At work when this happens, we have one doctor who will immediately announce “you realize we just all wandered in to an evidence free zone right?”. I like him.  Anyway, describing a problem and prescribing solutions are two different things, and if you mix them up you are DEFINITELY going to lose some folks.

And speaking of evidence and policy, here’s an interesting one on weird statistical methodology in a nutrition paper.

Finally, here’s an interesting deep dive in to social psychology’s replication problem, what it means, and how seriously we should take it.