5 Ways that Average Might Be Lying to You

One of the very first lessons every statistics students learns in class is how to use measures of central tendency to assess data. While in theory this means most people should have at least a passing familiarity with the terms “average” or “mean, median and mode”, the reality is often quite different. For whatever reason, when presented with a statement about your average we seem to forget the profound vulnerabilities of the “average”. Here’s some of the most common:

  1. Leaving a relevant confounder out of your calculations Okay, so maybe we can never get rid of all the confounders we should, but that doesn’t mean we can’t try at least a little. The most commonly quoted statistic I hear that leaves out relevant confounders is the “Women make 77 cents  for every dollar a man earns” claim.  Now this is a true statement IF you are comparing all men in the US to all women in the US, but it gets more complicated if you want to compare male/female pay by hours worked or within occupations. Of course “occupation and hours worked” are two things most people actually tend to assume are included in the original statistic, but they are not. The whole calculation can get really tricky (Politifact has a good breakdown here), but I have heard MANY people tag “for the exact same work” on to that sentence without missing a beat. Again, it’s not possible to control for every confounder, but your first thought when you hear a comparison of averages should be to make sure your assumptions about the conditions are accurate.
  2. A subset of the population could be influencing the value of the whole population. Most people are at least somewhat familiar with the idea of outlier type values and “if Bill Gates walks in to a bar, the average income goes way up” type issues. What we less often consider is how different groups being included/excluded from a calculation can influence things. For example, in the US we are legally required to educate all children through high school. The US often does not do well when it comes to international testing results. However in this review by the Economic Policy Institute, they note that in some of the countries (Germany and Poland for example) certain students are assigned to a “vocational track” quite early and may not end up getting tested at all. Since those children likely got put on that track because they weren’t good test takers, the average scores go up simply by removing the lowest performers. We saw a similar phenomena within the US when more kids started taking the SATs. While previous generations bemoaned the lower SAT scores of “kids these days” the truth was those were being influenced by expanding the pool of test takers to include a broader range of students. Is that the whole explanation? Maybe not, but it’s worth keeping in mind.
  3. The values could be bimodal (or another non-standard distribution) One of my first survey consulting gigs consisted of taking a look at some conference attendee survey data to try and figure out what the most popular sessions/speakers were. One of the conference organizers asked me if he could just get a list of the sessions with the highest average ranking. That sounded reasonable, but I wasn’t sure that was what they really wanted. You see, this organization actually kind of prided itself on challenging people and could be a little controversial. I was fairly sure that they’d feel very differently about a session that had been ranked mostly 1’s and 10’s, as opposed to a session that had gotten all 5’s and 6’s. To distill the data to a simple average would be to lose a tremendous amount of information about the actual distribution of the ratings. It’s like asking how tall the average human is…..you get some information, but lose a lot in the process. Neither the mean or median account for this.
  4. The standard deviations could be different Look, I get why people don’t always report on standard deviations….the phrase itself probably causes you to lose at least 10% of readers automatically. However, just because two data sets have the same average doesn’t mean the members of those groups look the same. In #3 I was referring to those groups that have two distinct peaks on either side of the average, but even less dramatic spreads can cause the reality to look very different than the average suggests.
  5. It could be statistically significant but not practically significant. This one comes up all the time when people report research findings. You find that one group does “more” of something than another. Group A is happier than Group B.  When you read these, it’s important to remember that given a sample size large enough ANY difference can become statistically significant. A good hint this may be an issue is when people don’t tell you the effect size up front. For example, in this widely reported study it was shown that men with attractive wives are more satisfied with their marriages in the first 4 years. The study absolutely found a correlation between attractiveness of the wife and the husband’s marital satisfaction….a gain of .36 in satisfaction (out of a possible 45 points) for every 1 point increase in attractiveness (on a scale of 1 to 10). That’s an interesting academic finding, but probably not something you want to knock yourself out worrying about.

Beware the average.

Pacifiers and baby boys

I’m a bit behind on this one, but this study was too interesting to pass up.

Apparently, research suggests that pacifier use by boys limits their social development.

So we’ll start with the bias alert.  I have a baby boy, and he does use a pacifier to help him go to sleep.  I didn’t have any particular feelings about this, I just gave it a whirl and liked the way it helped him calm down when he was tired.  Give it 5 minutes, and he tends to spit it out and go to sleep.  That seemed rational to me, I actually was unaware there was much controversy about this until I got reading this article (reiterating Dubbahdee’s point that I should never read parenting advice on the internet….oops).

Obviously, I don’t yet know what his social development is going to turn out like (though at the moment he’s astoundingly unsympathetic to my lack of sleep), but I generally hope it’s okay.   End bias alert.

It took me a while to find the actual paper (why oh why do so many news sources not link to the actual paper????), but after scanning the whole thing I had a couple thoughts.

The headlines about this paper were stupid, of course.  The author actually had a pretty good theory based on actual science (babies learn emotions in part through mimicry, she wondered if a pacifier would make this harder for babies because their facial muscles were occupied), and of course it got over reported. Most headlines just mentioned “pacifier use” in general, but she clarifies pretty quickly that they only studied pacifier use during baby wake time….specifically excluding the type of pacifier use I described above (as a sleep aid).  This makes sense (the woman does have 3 boys herself after all) because you don’t have to spend very long around babies before you realize they’re probably not learning much when they’re trying to fall asleep.  They’re mostly just crying.

Anyway, the set up for the study was pretty good.  They assessed both 6 and 7 year olds and their emotional reactions vs pacifier use, and then later college students who were questioned about their history of pacifier usage to tie it to adult development.

For that second, I was curious about the length of pacifier use we were talking about, as this was based on the recollection of college students and their parents, and I was wondering how accurate that would be.  This graph sums it up nicely:

I’m not familiar with the emotional intelligence scale they’re using, so I’ll take their word for it that 4.7 to 4.4 is statistically significant….but wow, daytime use of a pacifier until 5 years of age?  That does seem like it should cause some concern.  Also, it seems as those the recollection bias here would be clustered at either end.  Parents would remember more accurately either remarkably short or remarkably long pacifier use…but that’s just a guess.

Overall, I thought it was annoying that “daytime use of pacifiers until kindergarten” got labeled as just “pacifier use”, but I thought the research was certainly intriguing.  I especially liked that they tested both younger children and adults to help prove their theory, as emotional development is most definitely a complex process that takes decades to work through.

What I actually liked about this study the most was Ann Althouse’s take on it.  She wondered if this meant you could stop overly emotional women from being overly emotional by giving them Botox so they couldn’t mimic those around them.  I’d say it’s worth a shot.

Workin’ for the Man

I’m headed back to work today.  It’s a bit early, but in exchange I get to work part time through Thanksgiving.

Given that, I thought this headline made for a good blog post today: “Is Opting Out the New American Dream for Working Women?“.  In a survey by ForbesWomen and TheBump.com, they found that:

84% of working women told ForbesWoman and TheBump that staying home to raise children is a financial luxury they aspire to.What’s more, more than one in three resent their partner for not earning enough to make that dream a reality.


Subsequently I saw several bloggers reference the fact that “84% of women want to be stay at home moms”, so I decided to do a little digging.  What did this survey really say?  Well, Forbes published more about the survey here.

Weirdly, in that recap, the only time the 84% number is mentioned is in reference to women believing staying at home is a financial luxury, leading me to be more than a little curious as to how they phrased the question.  Do 84% of women actively want to stay at home, or do 84% of women wish they had enough money that they got to make the choice?  This quote from the article lead me to believe perhaps we were really discussing something rather than prioritizing staying at home with the kids:

As one (working) mom of two told me, she may dream of leaving work to take care of her kids, but the (financial) reality of it is not so ideal. “Sure, if my husband made so much money that I could spend time with the kids, still afford great vacations and maybe the occasional baby sitter to take a class or go out with friends, I’d be the first to sign up,” she said. “So maybe while it’s a luxury I do think about, it’s not one I would want unless it was actually luxurious. I don’t want to be a stay at home mom who clips coupons or plans her weekly menu to make ends meet… If that’s the case, I’d gladly go on working to avoid that fate.”

So it sounds like at least some of the respondents were focused less on wanting to opt out of the workplace to raise their kids, and more on wanting to have enough money to keep their standard of living while not feeling pressured to work.  Two slightly but significantly different things IMHO.  I have rarely seen a stay at home mom who didn’t strive to make the household more financially efficient while at home, so this dream seemed a bit divorced from reality. This is backed up by the survey’s additional result that only half of working women think they’d be happier if they stayed home.  I’d also guess most of us would be happier if we had enough money to completely call the shots regarding where we worked.

Of course none of this addresses the totally skewed sample that comes from two websites joining up to do a survey like this.  Doubtless ForbesWomen/TheBump do not attract a random crowd.  Additionally, it should be concerning to our sense of family that 1/3 of women are resenting their husbands for not making more money….though to note the survey used the phrase “sometimes resent” while the article merely used “resent”.

A side note about this survey….one of the last questions was about how much women spent on themselves per month.  Most (63% of working moms, 78% of stay at home mom’s) said they spent less than $100 a month on themselves.  Every time I see a question like this, I always wonder where people count cable TV and haircuts.  When I was getting my degree, they mentioned that during premarital counseling you should always ask the woman how much she thought a reasonable haircut cost.  Apparently that one expenditure can cause a lot of fights.  I definitely know women who believe a basic haircut costs $80 or more.

All that being said, I’m going to miss my little monkey today, but I’m happy to have a job I love to go back to, I don’t resent my husband, and I think a reasonable haircut for a woman costs $40.

Now THAT’s how you write a science headline

“Babies Shun Altruism, Prefer Bouncing”

Speaking of replication of results, this study failed to substantiate the idea that 10 month old babies had a moral code.  Turns out that the their preference for “helpful” robots was based less on the fact that the robots were helpful, and more on the fact that they bounced.

I’m sort of curious how many of the original study authors were parents.  I’ve only been a mom for 19 days and even I could tell you that babies like bouncy things more than discussions about man’s existential angst.  The 2 AM feeding helps you figure these things out pretty quickly.

For fun, I decided to conduct my own n=1 experiment and to present my son with a survey regarding his preference for robots in general and their morals in particular.  I thought it was a fairly well crafted survey.

I think my findings are best summarized with this picture:

I think that should be good enough for any number of social psychology journals.  

Growth charts and tiny babies

This is another post that reflects my current life situation, but it highlighted some pretty interesting issues with data tables.

This issue is particularly interesting to me because I delivered via unplanned/urgent c-section, in part because of some abnormal measurements found during a routine ultrasound.  We had to have quite a few follow up consults and testing (among other things, they actually had to assess for achondroplasia – better known as the major cause of dwarfism)*.

Given this, my mother thought I’d find this Wall Street Journal article on baby growth charts interesting.  Essentially, baby growth charts were set several decades ago based on a population that’s different from what we have now.  The CDC does not want to readjust the charts, as it would make obesity look more normal than they think it should, and this is causing a situation where a high number of children are measuring “off the charts”.

It’s an interesting situation when you realize that 95th percentile doesn’t actually mean “larger than 95% of children of the same age” but rather “larger than 95% of children the same age 40 years ago”.

Additionally, it also points out that the CDC growth chart is based largely on formula fed babies, who grow slightly differently from breast fed babies.  So at the same time Mayor Bloomberg is pushing breastfeeding, doctors are potentially telling parents their children need formula to speed their growth up to match a chart that only tracks where they would be if they had done formula to begin with (this is why state mandated health policy drives me nuts so often….you solve one aspect while leaving several causes unadressed).

As the availability of testing goes up, we have to be particularly vigilant to make sure our standards charts keep up as well.  Otherwise we routinize unnecessary testing and freak out new parents.  And from personal experience, I can say that’s just not nice.

*It was ruled unlikely, though apparently we can’t get a definitive no until he actually starts growing, or not as the case may be.  There’s no genetic history of it in my family or the husband’s, though we are both on the short side.  In this case, us being short is actually a positive….it means the abnormalities are more likely natural variations.  Our genetic consult doctor was hilariously terrible though….she suggested if we wanted more information about the condition we watch the reality TV show about it (Little People Big World).  Then she said it was unlikely, but maybe we should still watch the show.  She ended it all with a comment about how it was never good when genetics doctors had too much to say, so we should be happy she wasn’t talking too much.  I don’t think she was very self aware.  

Rich Mom Poor Mom

I have a sleeping baby in my lap, so you’ll forgive me if I have a one track mind.

Yesterday we met with a nurse who let us know that in Sweden, they have now set minimums for skin to skin contact between mom and babies during hospital stays.  If you don’t do the minimum, you pay the hospital bill.  This morning, in my first perusal around the internet in a few days, I see that Mayor Bloomberg is trying to find ways of encouraging new mother’s to breastfeed.

A note on research regarding babies and various practices in infancy:  Babies are a lot of work.  I realize I’m preaching to the choir on this, as many of my readers have successfully raised quite a few children, but it’s true.  Many of the practices that show lots of benefits for babies (skin to skin contact, breastfeeding, etc) take even more time than the alternatives.  While I believe these things are good for babies on their own, all data collected on these practices will be complicated by the fact that parents who engage in them tend to have more time, resources, and support than those who don’t.  Pushing these practices on those who are already particularly stressed may not have as profound an outcome as it did in the study, as the groups went from self selecting to random.

Something to think about for the policy makers.

Sorry, I’ve been reading over a lot of hospital literature and getting mildly annoyed.  I think that means the pain medication has worn off.  Nurse!

Tracking the wild bad data

As someone who spent 3 years studying family dynamics in grad school, I was pretty interested in the NYT piece that ran last week on class divides in single vs married households.  The article generated a lot of buzz, and if you haven’t read it, I would recommend it.

People seemed to either love or hate this article, and it’s stirred up a whole lot of discussion online.  One of the more interesting points that got brought up though, was a discussion about why the focus was on single moms as opposed to deadbeat dads.

This led to some quoting of an interesting statistic regarding custodial parents and child support.  When I first read this statistic, it was from Amanda Marcotte over at Slate who put it this way:

…. in a substantial number of cases, the men just quit their families. That’s why only 41 percent of custodial parents receive child support.

Now, I’ve perused internet comment boards enough to know that there are a LOT of men out there griping about how much they pay in child support.  I was a little shocked to read that apparently 59% don’t give anything.  I clicked on the closest link she had provided…..which took me over to the NYT Economix blog and an item by Nancy Folbre. There was the stat again, except with a few more qualifiers:

In 2009, the latest year for which data are available, only about 41 percent of custodial parents (predominantly women) received the child support they were owed. Some biological dads were deadbeats. 

So that frames it a little differently.  It’s still a little unclear from that statement, but it started to occur to me that this probably meant only 41% were up to date on their support payments…not that only 41% of non-custodial parents were paying.

I clicked on the link provided by Folbre, and got to the Census Bureau website, which put it all this way:

 In 2009, 41.2 percent of custodial parents received the full amount of child support owed them, down from 46.8 percent in 2007, according to a report released today by the U.S. Census Bureau. The proportion of these parents who were owed child support payments and who received any amount at all — either full or partial — declined from 76.3 percent to 70.8 percent over the period.

Now that’s still a lot of deadbeats, but it is a slightly different picture from the one we originally started with.  When I clicked on the link from the Census Bureau snapshot to the report it originally came from, I noticed something else interesting….only about half of all custodial parents have court ordered support, and the non-payment stats above appear to reflect only what is happening in the court ordered cases.  The non court ordered cases are certainly hazy….30% of custodial parents said they never went to court because they knew the other person couldn’t pay….but it is interesting that the quoted stats only apply to half of the custodial parent cases.

Overall, I must say I kind of enjoyed attempting tracking the evolution of a stat (in reverse).  It’s not often you get to actually see how things evolve from the primary source to several steps out….and it was an interesting mental exercise.  Thanks for taking the journey with me.

Spanking and Mental Trauma

The headline reads “Spanking Linked to Mental Illness“, and I was immediately intrigued.  Spanking, generally, is a very hard thing to study, as it is so often correlated with other things.  Physical punishment of children is often linked to frustrated and under resourced parents, cultural norms that can be positive or negative, and even immigration status.

Curious how the study authors controlled for such things, but assured by the article that they had, I flipped over to the study itself.  It didn’t take long for me to realize this was yet another example of bad journalism mucking about with a half decent study.

The article starts like this:

Although the American Academy of Pediatrics (AAP) strongly discourages spanking, at leasthalf of parents admit to physically punishing their children. Some research suggests that as many as 70-90 percent of mothers have resorted to spanking at one time or another. Anew study published in the journal Pediatrics may cause parents to think more carefully before laying a hand on their little ones.

However, the study states:

Physical punishment was assessed with the question, “As a child how often were you ever pushed, grabbed, shoved, slapped or hit by your parents or any adult living in your house?” Respondents who reported an answer of“sometimes” or greater to this event were considered as having experienced harsh physical punishment. The term harsh physicalpunishment was used for this study because the measure includes acts of physical force beyond slapping, which some may consider more severe than “customary” physical punishment (ie, spanking).

 So the study specifically excluded “customary” physical punishment when it assessed the effects on future mental illness….which pretty much completely contradicts the headline.   I also doubt this is what 70-90% of mother’s are admitting to when they spank “at one time or another”.  


It’s all (culturally) relative

Last week I put up a post regarding a study on sexism levels in men whose wives stay at home.  I argued that due to the diversity of that group of men, and the variety of reasons a woman might stay home, this study was essentially meaningless.

Another issue came up in the comments section that I wanted to touch on: cultural relevance of data.

Most studies that get press here in the US are from the US, performed on American subjects.  This is sketchy business.

In the study about stay at home moms, mothers who worked part time were lumped in with the stay at home mothers.  Interestingly, in the Netherlands, this would actually be 90% of the women.  Does that mean that nearly every Dutch man married to a woman is more likely to be sexist?  Or does it mean that part time work has different value in different cultures?

I took a look around for some other examples, and found that in China, many women see working as part of a new found freedom.  At a conference I attended a few months ago, I talked to a man from Shanghai who mentioned that his wife went back to work because she couldn’t have handled trying to fight off the two grandmother’s, both of whom wanted to watch the child.  Due to the one child policy, this was the only chance they would get to have a grandbaby.  In many ways, it was actually the hierarchical/patriarchal culture there that pushed his wife to go back to work, as opposed to having her stay home.  

As the world continues to flatten out, and as America continues to welcome new immigrants, we must be conscious of who studies are actually looking at and how generalizable the results are.  In the sexism study, even the authors admitted their findings were meant to be a commentary on the US only….but it should raise some questions that they seemed to be chasing after a structure that doesn’t exist in some very liberal countries.

Something to consider, depending on the goal of the study.

Sexism and stay at home moms

I was just thinking I wanted to find a good marriage and family research paper to sink my teeth in to.

This one came across my inbox today, and I didn’t have to get much further than the abstract before I knew it was going to be a doozy.  Read for yourself:

In this article, we examine a heretofore neglected pocket of resistance to the gender revolution in the workplace: married male employees who have stay-at-home wives. We develop and empirically test the theoretical argument suggesting that such organizational members, compared to male employees in modern marriages, are more likely to exhibit attitudes, beliefs, and behaviors that are harmful to women in the workplace.

*Bias Alert*
My mother was a stay at home mom.  Therefore my father would have qualified for this study, and it is hard for me to even read their hypothesis without remembering that.  I happen to credit my father with giving me my passion for statistics and data analysis, and he has never once discouraged me from doing anything I wanted to professionally (with the exception of when I mentioned law school….that he soundly discouraged as a waste of talent….and this was  15 years before anyone was talking about a law school bubble).  I will not go in to all the details of my parents marriage here, but I doubt you could find anyone who would call my parents marriage anything less than an equal partnership focused on doing what was best for the family.

As an extra level of bias, I will be continuing my (full-time) job post baby.
*End Alert*

I’ve noticed a disturbing trend in both the general population and academic research: people seem to get very hung up on conflating “stay at home mom” with “traditional marriage”.  The study authors do this openly….they admit that they classify a marriage as “modern” based solely on whether or not the wife works full time.  The only criteria for “traditional” is that she doesn’t work at all, and part time work is all classified as “neo-traditional”.

To ignore the economic realities that drive families to make decisions about work seems to me to be an immense oversight.  I have met plenty of stay at home mothers who were in very equitable marriages, and I have met quite a few working mothers whose primary source of stress was their husbands continued expectation that they were still responsible for all child care/household duties.  I believe that using only one metric to rank a marriage as “traditional” or “modern” is a horrible over generalization….especially since most women with small children would prefer to work part time.  In fact (from the Pew study):

The public is skeptical about full-time working moms. Just 14% of men and 10% of women say that a full-time job is the “ideal” situation for a woman who has a young child. A plurality of the public (44%) say a part-time job is ideal for such a mother, while a sizable minority (38%) say the ideal situation is for her not to work outside the home at all.

So 90% of women don’t think the “modern” setup is ideal when there are young children involved.  If one of these women than chooses to stay home with her kids, has her husband truly regressed from “modern” to “traditional”?

For both the economic reasons and the “women’s choice” reasons, I reject studies that try to tie stay at home motherhood to anything else.  The sample is just too broad, and the reasons too varied.  It also undermines exactly how expensive child care can be….by my estimate, my mom would have had to bring home at least $4000 a month (in today’s dollars)  to pay for child care for 4 children.  $4000 after tax is a pretty hefty before tax salary.

I don’t argue that personal life can affect professional attitudes, and I would never advocate for sexism in the workplace.  In this study however, I really had to question the motives.  Is it really the best idea to fight gender stereotypes with stereotypes about very broad choices?  Is the point here that the workplace will only be fair when women participate as much as men?  Isn’t it a bit sexist to totally disregard the role women play in the decision to work or not work?  Shouldn’t we all just be able to do what’s best for our families, no questions asked?