Statistics

 

            If you truly want to understand differences among humans, then you must learn at least a small amount of statistics.  Fortunately, and probably to your chagrin, this chapter on stats will be the funniest in the entire book.

            What?

            Stats?

            Funny?

            Are you kidding me?

            Actually, statistics are a unifying thread that binds us together.  You see, all humans share at least one thing in common.  We all share a total lack of ability to understand statistical analysis.  Even the experts will tell you that they don't really understand it.

            For example, neither the blackest Tanzanian nor the whitest Swede is capable of grasping the fact that they are statistically the same animal.

            Statistics run counter to our most basic tendency to be inherently bias when we analyze anything.  Have you ever heard of statistical bias?  The actual stats don't really have bias but our interpretation of them usually does.

            The thing that I find funny about stats is that they are misused by people who want to make stuff up but the actual stats usually tell the truth.  Imagine that in order to lie you choose to use something that actually tells the truth.  Then, everyone believes the lie even when you show them the truth.  How funny is that?

 

            I'm going to talk about penis size as a clever trick to keep your attention as I talk about stats.  Otherwise, 90% of males would not be paying attention.

            The actual figures above are not necessarily precise but I am using them anyway.  I'm pretty sure that they are fairly close to being accurate.  In any case, these stats are for all humans.  Any sub population may have a mean that is shifted up or down.  The smaller the sub population the greater distance the mean can move but the width of the bell curve will decrease so the upper and lower limits may not change much.

            So, what group has the best penis size?

            Notice that I said best and not biggest.  Too big is actually not good.  You want to be able to fully penetrate a woman without hurting her, don't you?  As with all characteristics, the mean is the optimal place to be.  I know this for a fact because my ex-wife told me that my six inch penis was the perfect size and … well … let's just say that that she had a bit of experience prior to me.

            A median or average size penis will best fit a median or average size vagina.  A good fit is what you want.  Why would you want to have a penis that fits very few vaginas?  I think that most men have a huge desire to have a penis that fits very few vaginas.

            Nevertheless, penis size is culturally significant and most people think it is evidence of virility.  Actually, if your pecker is so big that it hurts, then most girls won't want to have sex with you.  Therefore, you will be functionally less virile.

            You can find some small groups of men that have statistically large genitalia compared to the general population.  Porn Stars would be good example.  But when we look at large groups like Africans compared with Europeans the bell curves match up pretty well.  The Africans have a larger variance on all characteristics so the few individuals on the far ends of the bell curve are farther from the mean in the Africans.  This means that there are individual Africans that have the largest and the smallest penis size.  However, 95% of all Europeans and Africans share pretty much the same percentages of individuals in size categories on the bell curve.

            So, what does this mean?

            It means that the classic stereotype of blacks having big dicks is accurate.  But it also means that this statistic is misused by the general population.  First of all, being in the largest .0001% is actually not good and this individual suffers severely as a result.  Second, the absolute number of individuals that are at this extreme position on the bell curve is very few.  Third, any two reasonably large groups of Europeans and Africans will have pretty much the same pecker size variability.

            Remember, Johnny Holmes was lily white.

 

            Finally, there is absolutely no way of being able to look at a man's skin color and determine the size of his penis.

            I hope that this illustration demonstrates that you have to interpret statistics in order for them to be meaningful.

            Often times an interpretation requires expertise in a particular field of study.

            As another example, I am always hearing that some study showed no statistical advantage of using an antidepressant medication and therefore these drugs are worthless.  I am a psychiatrist and I understand how research works and I know how hard it is for humans to do it well.  I understand what depression is and the difficulties of studying it.  I know that you can't begin to draw conclusions until the bulk of the evidence points in a certain direction.  I also understand how the media only wants to report things that have shock value.  The average lay person may not know all this.  Most people think that the phrase, "this study says," and the phrase, "in conclusion," are essentially the same thing.  In reality, it is probably more like, "these 250 studies seem to suggest," is essentially the same thing as, "a preponderance of the evidence would seem to indicate."

            Statistics are only one type of information.  You have to interpret them correctly for them to be meaningful.  You must not inflict your personal bias on them.  Remember that a study is an exercise in logic.  You put together a few premises and then draw a conclusion.  If a single premise is inaccurate, then a perfectly logical study will produce an incorrect conclusion.

            Humans have an overwhelming desire to cling to their bias and tend to reject or re-arrange stats that don't comply.  Any good scientist will tell you that to avoid this error one must heavily scrutinize any data that supports a previously held opinion.  Human nature would have us do exactly the opposite.

            So, what does all this have to do with understanding human differences?

            Despite the fact that Darwin first hinted at it in 1872, we now know for sure that changes occur gradually and indistinctly in the human species and that all humans are very much the same animal.  We have mapped the entire human genome and we now know that differences are superficial from a genetic standpoint.

            Biology failed to support the basic tenets of racism.

            Genetics are the smoking gun.  The other shoe has fallen.  OK, I can likely think of several more worn out sayings but the point is that the premise that human differences are distinct and biologically meaningful is a false premise.  Therefore, all of the research for the past 200 years that has started with this premise has produced inaccurate results.

            Wait just a gol-darned minute!

            I grew up with racial stats.

            I've heard them all my life.

            You know … 53% of Hispanics this and 23% of African Americans that.  In the last election 33% of white males voted for so-and-so and 25% of black men are in prison.  Black women have the longest life expectancy by … I don't know … by a few years anyways.

            I'm comfortable with these stats.  They're a part of me.  I'm used to them.  Please don't take them away!

            OK, you can use these stats but realize that they apply to a culturally significant premise that is not accurate on a biological level.

            For example, "I know an old-fat-bald-white guy who told me that he has an unscrupulous business partner who is Jewish.  He went on to say that he used to think Jews were alright but he now believes that all Jews are cheaters and back stabbers and they have no moral compass."

            Never mind that this guy is a good friend of mine and totally knows that I am Jewish.

            I calmly looked him in the eyes and said, "You know, your friend is an old-fat-bald-white guy.  I think that anyone who is an old-fat-bald-white guy is a cheater and back stabber and has no moral compass."

            Of course, the irony was lost on him.  He even repeated the statement at a later date.

            I hope that you appreciate that these two statements are equivalent.  Ten million Jews compared to ten million gentiles compared to ten million old-fat-bald-white guys (who are a combination of Jews and gentiles) are not statistically very different from each other and since his sample size was one, his assessment made no sense.

            It made no sense biologically but it made sense culturally, which is why I should have punched him in the gut.  Well, he's a lot bigger than me.  On the other hand, I'm smarter than he is.  I decided to use irony that he didn't get.  It would have felt better if I had hit him but you have to go with your strength, especially when you're a skinny little Jewish kid.

            In case you aren't following this let me provide an analogy.  Let's say that you want to study apples.  You want to know which apples taste the best.  You decide to look at 1000 apples.  You divide these apples into four distinct types based on their visual appearance.  Type one is a bit longer.  Type two is a bit wider.  Type three has more folds and type four has longer stems.  We will apply a name to each type.  Why don't we arbitrarily call them trees, meatballs, rolls, and sticks?

            Of course, you can prove that it is possible to divide the apples up into these divisions.  You can also prove that there are some statistically significant differences between these groups.  You can design a very good study that logically concludes that apples with long stems hang on the tree longer or fall harder to the ground or are able to swing better in the wind.

            There is just one little tinsy tiny problem.  These differences are not biologically significant.  Surely you would agree that if any difference is going to affect the flavor of the apples it must be a biologically significant difference.

            But wait … why did you even get the idea to do it this way in the first place?  What made you think that the length of the stem had any relationship to the chemistry of the apple?  

            It is because you think like a human.  Vision is your best sense and you rely on it the most.  Also, you like to categorize things for simplicity.  You simply looked at the apples and noticed some visual differences.  Despite the fact that these visual differences change gradually you saw distinct categories.  You were attempting to simplify things so your tiny brain could manage the information easier.  Then, you just made up the premise that these divisions were biologically meaningful with absolutely no evidence what-so-ever to even suggest that this was the case.

            The premise that stem length is causally related to flavor is false.  Therefore, the conclusion that apples that swing more and fall harder taste better is even more false.  Every study you did that began with the premise that these distinct categories are valid produced conclusions that are false!

            I'm sorry to disappoint you but there is a way out.

            You can save your research if you want.  What you must do is correctly word your conclusion to allow for the possibility that the premise was false.  For example, rather than saying, "The swing or fall causes the flavor to be better."  You could say, "The swing or fall may have an association with flavor or it may not."  Then, you won't be wrong but you also won't be very interesting.

            I have an idea.  Why don't you try to use premises that actually have some kind of rationale?  You know, like … Hmmmm … you could say that maybe the shade of color is related to sugar content and that could affect the taste.  Now you have a premise that has a chance of being accurate.  You didn't just make it up.

            That is how we do science, grasshopper.

            This is the problem that plagues racial statistics.  Since race is a cultural concept and not a biological one, it needs to be treated as such when we draw conclusions.  When biological data began to contradict our previously held notions we should have done the anti-human thing and really scrutinized these findings.  Most social scientists and anthropologists did not.

            That is why all the serious race stuff is now done by geneticists.

            On the other hand, and this is where the true weirdness of my personality comes out, humans are really very smart.  All that time spent trying to prove that Northern Europeans are the superior race paid off in a big way.

            What in the hell am I talking about now?

            Everything I have said up to now is true, however, being logical and rational is not all it's cracked up to be.  Let me explain something about the true genius of the human brain.  Even though a large collection of networked human brains jumped to the conclusion that physical appearances are somehow biologically significant and tons of bogus research was done, something wonderful came from it.

            We learned how to do social statistics!

            Humans were so driven and motivated to prove that "us is better than them" that they worked feverously into the night to figure out how to show it mathematically.  Of course, the guys like Newton and Einstein who were doing real science came up with a lot of mathematical and statistical innovation but what they were doing did not convert well to the area of social sciences.  New ways to do statistics had to be invented in order for us to understand similarities and differences between large groups of humans.

            Today, we have a wealth of very sophisticated statistical procedures that allow an elegant analysis of our society and help guide our public policy.  Embarrassingly, if you read the history about who came up with the ideas about how to do all these stats it is a rouges gallery of the most horrible racists.

            Perhaps, if humans had not thought like humans then there would not have been such an impetus to develop statistics. The funny thing about us is that when you have a sneaking suspicion somewhere deep down inside that is telling you that you might be wrong, that is when you are the most motivated to prove you are right.  And you don't give a damn about what is real, you just want to be right.  But this misguided motivation is nevertheless motivation and your hard work could pay off in a way you never saw coming.

            I think that is the haphazard way that our species has survived.  It is a remarkable way to understand the true genius of how our brains think in an intelligently illogical way and how this is actually superior in many ways to thinking logically and rationally.

            We came up with social statistics!  How in the hell did we do that?  We stumbled and blundered our way through the fog and came out smelling like a rose!  What a truly human thing to do.

            Sort of how Eli Manning won the Super Bowl.

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The whole enchilada

            In my experience, the statistical concept that people have trouble with most frequently is the difference between very large things and very small things.  Don't feel bad.  Even Einstein famously had trouble doing this. 

            The problem is that we have yet to figure out a theory of everything.  We don't have a single mathematical formula that works in every conceivable situation.  So, when things are very big or when they are very small the rules that govern how things work change dramatically.

            Here is a perfect example from the recent political debate:  "If you don't live within your means, then you will be hopelessly in debt in the future.  Therefore, we cannot allow the government to fix health care at a cost of one trillion dollars." 

            This statement makes perfect sense for micro-economics but it makes no sense at all for macro-economics.  Nevertheless, did you see how whoever said it mixed the two?  The first part said "you" and the second part changed to "we."  And you probably didn't even notice.

            Economics, like physics and all the other sciences including the social sciences operates on two levels:

1. The huge

2. The tiny

            To run a statistical analysis on your families personal finances, OK, I understand that.  However, when Mr. Geithner talks about running a statistical analysis of the future health of our economy based on how all 300 million of us collectively spend money today, I'm totally lost.  Therefore, I do the human thing which is to retreat to my comfort zone and only talk about micro-economics even though the discussion is about macro-economics.

            The same problem exists in the social sciences when we are talking about human differences.  You can produce wonderful statistics that show huge genetic differences between small groups of humans but as the number of people you include in the study increases these differences decrease.  Europeans and Asians aren't very dissimilar genetically but Swiss watch makers and Chinese field workers probably are.  Race is about large populations.  It isn't about small groups.

            It makes no sense to look at two small groups or even at two single individuals and make generalizations about entire populations.  The statistics that you would use to compare two groups of 100 are totally different from the statistics you would use to compare two groups of 1,000,000.

            The reason has to do with distributions of variance.  The larger your sample size the closer you get to reality.  It's hard to answer a scientific question with an n=2.  It is easier with an n=100 and easier still with an n=1,000.  However, with and n=1,000,000,000 you are finally getting close to the truth.

            Enough numbers to produce an accurate bell curve with an appropriately realistic variance is what you are after.  The problem is that the mathematical and statistical formulas, and your ability to understand them, change when the numbers get big.  At really high numbers it is no longer OK to just use a mean value or to simply calculate total amount.  You must use a statistical analysis that actually tells you what is happening in the population and you must have the expertise to interpret it.

            When you measure 10 people who are genetically different you can easily grasp the concept and you can use simple statistics.  When you measure 5,000,000 people you need a totally different kind of statistical analysis and some expertise to interpret it.

            Human differences can be large on small scales but they get tiny on large scales. That is why you can divide people up into small groups but not into large groups. 

            On a large scale, we are all the same species.       

 

Science

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