When data visualization obfuscates more than it illuminates

I am very enthusiastic about the visual display of data to achieve more effective communication. Link between health spending and life expectancy: US is an outlier by Max Roser is an example where the visual display actually fosters miscommunication. The problem isn't with the display but the context and underlying analysis.

The article includes this chart.

The US is indeed an outlier in terms of its expenditures on healthcare. It is worth understanding what is driving those outsized medical expenses. But the chart doesn't really help that process.

The root cause analysis by Roser is superficial or, at least, incomplete. Roser identifies three possible root causes for the cost differences. 1) The US has more violence - however, Roser seems to dismiss this as a real driver. 2) The US has higher administrative health care costs. 3) The US has more unequal healthcare spending.

So, one reading of this chart is that the US is more violent, more incompetent and more unfair because of inequality. That certainly comports with the nattering nabobs of the intelligentsia, but is it true?

I don't know what the real drivers of the cost differential are. I just know that the proffered suggestions are either substantially incomplete or are untrue.

For example, Roser seems to conflate inequality of healthcare spending with inequality of income.

One of the reasons for the underachievement of the US is the large inequality in health spending. The chart above showed that average per capita spending on health is exceptionally high, but the average does not tell you about how much each individual in the US receives. The US healthcare system is characterized by little access to care for some and very high expenditure on health by others.

The following graph shows this inequality. The top 5% of spenders accounts for almost half of all health care spending in the US.

[snip]

This graph should be read similarly to a Lorenz curve: the fact that the cumulative distribution of spending bends sharply away from the 45% degree line is a measure of high inequality (this is the intuition of the Gini coefficient that we discuss in our income inequality data entry). As it can be seen, the top 5% of spenders account for almost half of spending, and the top 1% account for more than 20%. Some concentration in expenditure is certainly to be expected when looking at the distribution across the entire population – because it is in the nature of healthcare that some individuals, particularly those older and with complicated health conditions, will require large expenditure –, these figures seem remarkably large and suggest important inequality in access.

But that is not what his second chart shows. The chart shows that some individuals receive a great deal of costly treatment. We do not know, however, whether they are also the people who are disproportionately wealthy. Roser has fallen into a tautological argument without evidence: If there is inequality in healthcare expenditure, it must be because of income inequality. Evidence of inequality in health expenditure is not by itself a function of income inequality (and vice-versa.) The compulsion to make data fit assumptions has overtaken the evidence.

Take the following as an example. A poor kid in Chicago is shot, as dozens are each week. The bullet decimates his liver and causes massive bleeding. The ER services in Chicago are excellent and they are accustomed to traumas you would never see anywhere but on a battlefield. All hospitals are obligated to serve regardless of capacity of the patient to pay. Access is not the problem that Roser posits. They swing into action and after 12 hours of surgery, stabilize the victim enough to hold until a liver transplant becomes available days or weeks later. The cost? Upwards of $500,000 or a million. This victim is a one percenter on Roser's chart even though his income might be in the bottom 5%.

The point is that income inequality has little or nothing to do with required medical services inequality.

What the chart does show is that the American medical system, with all its failures and successes, goes to extraordinary lengths to save lives and remediate bodies. We work harder and spend more to save dramatically premature babies, those suffering from traumatic injuries, the elderly, etc. Our aspiration to save everyone all the time is expensive. That's why we have a steep Lorenz curve.

In the chart above Like is not being compared to Like.

All the other comparison countries have at least three distinctions from the US. 1) The US is far more culturally and economically heterogeneous than any of the European countries (with each US group having markedly different attitudes and dispositions towards health, behaviors, etc.), 2) The US has a distributed system and the Europeans have centralized health systems, and 3) The US is richer than other countries (which increases the marginal propensity to spend).

In Europe, with centralized health systems, health expenditures are, simplistically, capped by the government. This tends to improve basic health at the expense of extreme health issues. Many European countries are well on their way to implementing Liverpool Protocol approaches to evaluating the cost of life maintenance. One could argue that the European approach is more rational but one could also argue that it is more immoral. Both would be at least partially true. Our American proclivity to expend vast amounts to save lives and even lost causes is noble but ruinously expensive. That is what Roser's second chart shows.

Europe has begun getting more heterogeneous immigration but compared to the US they still have very low volumes of immigration and low variability. The US healthcare system has to accommodate far greater variety in terms of behaviors, attitudes towards health, language, etc. That comes at a cost. In most fields of socioeconomic measure, when you track culture groups back to their originating countries/cultures/continents, the American groups almost always outperform in the culture-to-culture comparisons but not in the overall average (because we are averaging far more groups that are far more varied. This is the Wisconsin-Texas Paradox, also known as Simpson's Paradox.)

Americans of European heritage are richer and score better on international education tests (PISA) than do their European peers. Likewise with Asian-Americans against Asia, Hispanics against Central and South Americans, African Americans against Africa.

I am pretty confident that the same would be true for longevity.

The point of all this is that Roser's graph looks to make an especially compelling argument that there is a problem. The challenge is that the graph is not displaying like-for-like results and therefore ends up being misleading. You would have to normalize for age, for income, for cultural tradition, education attainment, etc. Once you do those normal things that should have been done in the first place, you end up with dramatically different root causes as to what is driving the cost differentials. We do have the option to force people to live healthier life styles through coercive government action if we wish to do so. We do have the option of saving government money on healthcare by rationing that care. Those are the European choices and perhaps they are worthwhile.

But they are not obviously so.

College attendance a function of values and less to do with access to resources

Interesting. From Parental Resources and College Attendance: Evidence from Lottery Wins by George Bulman, Robert Fairlie, Sarena Goodman, and Adam Isen. From the abstract:

We examine more than one million children whose parents won a state lottery to trace out the effect of additional household resources on college outcomes. The analysis draws on the universe of federal tax records linked to federal financial aid records and leverages substantial variation in the size and timing of wins. The results reveal modest, increasing, and only weakly concave effects of resources: wins less than $100,000 have little influence on college-going (i.e., effects greater than 0.3 percentage point can be ruled out) while very large wins that exceed the cost of college imply a high upper bound (e.g., wins over $1,000,000 increase attendance by 10 percentage points). The effects are smaller among low-SES households. Further, while lottery wins reduce financial aid, attendance patterns are not moderated by this crowd-out. Overall, the results suggest that households derive consumption value from college and, in the current policy environment, do not generally face binding borrowing constraints.

In other words, whether people attend college is more dependent on social and cultural norms and less to do with access to resources.

We know that the only way to avoid error is to detect it, that the only way to detect it is to be free to enquire.

From "Encouragement of Science" by Robert Oppenheimer, (Address at Science Talent Institute, 6 Mar 1950), Bulletin of the Atomic Scientists, v.7, #1 (Jan 1951) p. 6-8

We do not believe any group of men adequate enough or wise enough to operate without scrutiny or without criticism. We know that the only way to avoid error is to detect it, that the only way to detect it is to be free to enquire. We know that the wages of secrecy are corruption. We know that in secrecy error, undetected, will flourish and subvert.

Oppenheimer had expressed a similar sentiment a couple of years earlier, as quoted in "J. Robert Oppenheimer" by L. Barnett, in Life, Vol. 7, No. 9, International Edition (24 October 1949), p. 58.

There must be no barriers to freedom of inquiry … There is no place for dogma in science. The scientist is free, and must be free to ask any question, to doubt any assertion, to seek for any evidence, to correct any errors. Our political life is also predicated on openness. We know that the only way to avoid error is to detect it and that the only way to detect it is to be free to inquire. And we know that as long as men are free to ask what they must, free to say what they think, free to think what they will, freedom can never be lost, and science can never regress.

That is what makes the trends in universities and government agencies so alarming. The Department of Justice, the FBI and the IRS all appear to have been suborned into suppressing speech and opinions. Our universities seem to have devolved into playpens for cognitive dwarves where no thought is to be expressed if there is a risk that someone might take offense. These are alien behaviors and creeds. We need to reclaim, and with conviction, the principles of freedom, especially freedom of speech and belief.

The level of concern is nearly rock bottom

This is interesting in light of another source of data I came across today.

Hayhoe laments the public's lack of climate hysteria: "the level of concern is nearly rock-bottom" pic.twitter.com/XSNSrJXNP8

— Tom Nelson (@tan123) October 10, 2016

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Note that Elizabeth Kahn's concern is that there is freedom of speech which allows the American public to ask questions about a valid but contested hypothesis, i.e. anthropogenic climate change (global warming). A very totalitarian position to take it would seem. You get the sense that this is a matter of secular faith to Ms. Kahn rather than an empirical question to be tested and that the frustrating things is that people have the nerve to question her faith.

She seems to see this issue of free speech as a uniquely American failing. That's where the other data source comes in.

This morning I came across Global Issues from the UN. 9,700,000 people from across the world who have identified which are the issues of greatest importance to them. You can see the results by gender, by age, by education attainment level, by type of country (Low, Medium, High, and Very High levels of development.)

The sixteen options are:

A good education
Better healthcare
Better job opportunities
An honest and responsive government
Affordable and nutritious food
Protection against violence and crime
Access to clean water and sanitation
Support for people who can't work
Better transport and roads
Equality between men and women
Reliable energy at home
Political freedoms
Freedom from discrimination and persecution
Protecting forests, rivers, and oceans
Phone and internet access
Action taken on climate change

Not only are those the options, but those are the options in order of priority by all 9,700,000 participants.

Seems like for the whole world, the "the level of concern is nearly rock-bottom." Nothing to do with the dreadfulness of free speech or the pigheadedness of Americans. Nobody thinks that climate change is a priority.

If you are an adherent of anthropogenic climate change religion, I think it is hard to realize just how much skepticism the faithful's actions generate. The constant rejiggering of data, the leaked emails showing the efforts to hide results, the documented efforts to suppress alternate views, the extravagant and unsupported claims, etc. All those behaviors, even for keen conservationists such as myself, lead one to question whether this is actually a scientific endeavor or whether it is simply a massive scam.

The above listing isn't an anomaly. Virtually every demographic discounts the importance of climate change. Males and Females, Old and Young, the highly educated and the lesser educated - all rank it at the very bottom or next to bottom of concerns. Only one demographic ranks global climate change in the top ten (at tenth position) of concerns - those in Highly Developed Countries. In other words, this is a rich man's indulgence.

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You can search by individual country as well. For the US, climate change actions are also in tenth place in terms of concerns.

It is not that Americans, or anyone else, is ignorant of climate change. I think there are two factors at work - 1) there are more immediate concerns of greater tactical and strategic importance and 2) climate change advocates have not been able to separate themselves from all other blatantly self-interested groups. They come across as scammers doing a hard sell in order to enrich themselves and gain power over others. The US has invested hundreds of billions in regulations and laws, to improve the environment, to protect the environment, save wildlife. The will is there to sacrifice for identifiable and believable goals. Climate change advocates simply have not mustered the credibility to exceed that low bar.

The free market is just as effective as building codes to reduce energy consumption

This is interesting. From How Much Energy Do Building Energy Codes Save? Evidence from California Houses by Arik Levinson

We have a tendency to visualize great social policy changes (healthcare, pre-school, education, etc.) to achieve noble ends without grounding those policies in demonstrated data around which a consensus can form. We instead paint a beautiful picture of all the benefits and omit the costs. The justification is usually that there is an issue of compelling social fairness at stake or, even more commonly, we simply can't afford to wait. We have to act! Now!

It is the pattern observed by Lord Melbourne, that the promises and benefits fail to materialize and that we would have been better off to have waited till we had information in which we could be confident rather than rushing in to seem to do good, instead of actually doing good. More specifically William Lamb, 2nd Viscount Melbourne said:

What all the wise men promised has not happened, and what all the damned fools said would happen has come to pass.

Affordable Care Act and Head Start both seem to fit.

Levinson is researching the impact of well intended regulations to reduce energy consumption via building regulations in California. From the abstract:

Regulations governing the energy efficiency of new buildings have become a cornerstone of US environmental policy. California enacted the first such codes in 1978 and has tightened them every few years since. I evaluate the resulting energy savings three ways: comparing energy used by houses constructed under different standards, controlling for building and occupant characteristics; examining how energy use varies with outdoor temperatures; and comparing energy used by houses of different vintages in California to that same difference in other states. All three approaches yield estimated energy savings significantly short of those projected when the regulations were enacted.

Laws and regulations always dampen the resilience and flexibility of an economy and remove freedom of decision-making and autonomy from the individual citizen. This is not to argue for anarchy, merely that laws and regulations have strategic costs. As long as their proposed benefits outweigh those costs, there is at least an argument to be had about whether to enact those laws and regulations.

Too often, as Levinson is documenting, we get all the costs of the laws and regulations and little or none of the benefit. Not infrequently there is an additional, unintended cost as well. Someone almost always benefits from laws and regulations, it just isn't, necessarily, the public.

Tyler Cowen summarizes the findings as:

1. In 1978 California started to enact some of the world’s most ambitious residential building energy codes. These building codes have been updated 13 times since.

2. The promise was for 80% savings for new buildings constructed after 1990. These assumptions assumed everything would go according to plan and there would be no behavioral adjustments.

3. The actual results?: “For electricity, post-1978 houses in California may be using up to 15 percent less than pre-1978 houses, but do not use less per degree-day when the weather gets hot, and do not use relatively less than similar post-1978 houses in other states with less strict building codes.” For natural gas there is a 25% savings, noting that this trend and the electricity trend both predate the 1978 legislation.

4. Levinson conjectures that most of the savings are coming from natural turnover in the housing stock disfavoring the least energy efficient units.

The goal (reduced energy consumption) was a worthwhile one. One choice was to simply let the market adjust. Other jurisdictions chose that approach and according to Levinson, they seem to have accomplished the same outcomes as did California without the costs of the regulations and the associated corruptions.

It is rare that we do post-implementation diagnostics of social policies and yet it is critical to do so. We cannot improve if we do not understand where we have failed. The incentives are almost always to pass the legislation, hope for the best, and then hide the results.

There was a light on the far shore

Hound and Horn was a literary magazine founded in 1927 by two Harvard alum and, though independent of Harvard, focused on Harvard students and alumni. It ceased publication in 1934. Below is an excerpt from a poem by Oppenheimer in June 1928, describing memories of New Mexico.

Crossing
by Robert Oppenheimer

It was evening when we came to the river
With a low moon over the desert
that we had lost in the mountains, forgotten,
what with the cold and the sweating
and the ranges barring the sky.
And when we found it again,
In the dry hills down by the river,
half withered, we had
the hot winds against us.

There were two palms by the landing;
The yuccas were flowering; there was
a light on the far shore, and tamarisks.
We waited a long time, in silence.
Then we heard the oars creaking
and afterwards, I remember,
the boatman called us.
We did not look back at the mountains.

Racoon bypass system

Alright, I can't vouch for the veracity, but if true, does this elevate your respect for military personnel resourcefulness or reduce your respect for military personnel disregard for animals. Or maybe increase your sense that there is karmic justice.

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Networking is a consequence of sociability not an end in itself

Yep.

The problem with most networking events is they bring together professionals who are there for different reasons https://t.co/JgaMKDzFIy

— Harvard Biz Review (@HarvardBiz) September 30, 2016

Meandering research on hate and crimes

Just how much hate, racism, etc. is there in America? The SJW claims are extreme and unmoored in reality, but what is the truth? What proxies might get you to something like the truth?

Violent crime statistics are readily available and pretty dramatically opposite the popular SJW message. It is not popular to point this out but those numbers are hard to undermine if people will listen to them at all in the first place. But let's set those aside for a minute and try and get at the subtler, and possibly more pervasive issues of hateful ideologies.

I won't go so far as the SJW for whom any countervailing opinion is triggering and endangering. It would appear that these people simply have some sort of psychological problem.

No, I am more interested in actual intimidation, assault, patterns of behavior that are intended to achieve some sort of ideological outcome. Not bar fights where insults are hurled. How common are sustained acts of ideological oppression and bigotry? How many people have robes in the closet or sit around talking about bringing harm to others because of their skin or their religious beliefs, etc.?

These are incredibly hard numbers to find.

I have in the past looked at the numbers for those formally charged with hate crimes. I have my suspicions about that whole process. It seems from all accounts that being charged with a hate crime is highly context dependent, usually part of the charging strategy and discretion of the District Attorney, and nearly random. I have seen cases where it was very clear from the evidence that victims were chosen specifically for an attribute (they were white or black or LGBT or Christian, etc.) but the perpetrators are not charged with a hate crime, usually because that is harder to prove and the actual underlying crime is open and shut. If you are the DA, why complicate the case with a more difficult charge? You have limited resources.

Likewise, it appears that some are charged with hate crimes simply to increase the charge list in the hope of striking a plea deal.

So all sorts of issues that call into question whether convictions of hate crimes are an adequate proxy for hate.

I tend to dismiss hate crime statistics as informative. I think they both undercount and over-count without predictable patterns. If you do accept hate crime convictions as a proxy, then the conclusion has to be that hate crimes are vanishingly few, declining, and that the patterns of those crimes do not support the SJW view of a white monolithic culture keeping down people of color. Anti-semitism remains a big deal, though we no longer talk about it.

In 2014, there were 5,479 hate crime incidents (a third property related and two thirds violence against individuals). That's in a country with some 310 million citizens and 20.7 million total crimes (about 25% against individuals and 75% against property). 0.02% of all crimes are hate related. That's simply noise in the system. Significant to the victims but not systemic or predictable.

For me, all that demonstrates is the unreliability of formal hate crimes as a proxy for assessing the degree of hate in America.

At this point, I am getting pretty far up the data creek and I still don't have much of a paddle.

It occurs to me that perhaps you could do a head count of certain notorious groups. How many Aryan Brotherhood members are there? How many active members of the KKK? Its easy to treat the KKK as a minuscule relic, but are they? The Aryan Brotherhood has 10,000 members, in and out of jail. The KKK has about 5,000 members scattered around the nation.

The first issue I have with these numbers is that they are not very empirical, more guestimates really, and that they are used by groups who have a real stake in magnifying the threat. But let's use them as a weak proxy.

The other problem is that I recognize AB and KKK but how many other groups are there out there and how many are actually not in prison?

Yet further up the creek, I am.

At this point it occurred to me that there is a group who does track hate groups and crimes, The Southern Poverty Law Center. SPLC has a storied history fighting for civil rights but in recent decades it has seemed to devolve almost into a parody of an hysterical SJW group, frightened of and demonizing anybody who doesn't adhere to their ideology. I have long been deeply skeptical of any of their numbers as they have an SJW expansive definition of hate groups and hate crimes. Anybody who does not subscribe to the Frankfurt School of Reform Marxism seems to fall into their catchment. The Catholic Church, Boy Scouts, Girl Scouts, church goers, anti-crime groups, libertarians, people opposed to open borders immigration, Jewish groups, people concerned about terrorism, the Family Research Council, etc. SPLC is a far left group, well funded, and they have both a financial and ideological stake in exaggerating the extent of hate crimes and hate groups in the US. At a peevish level, I have also found it quite irritating that they posture themselves as fighting hate and yet their words and actions often seem to drip with disdain and hate as they demonize those with differing opinions from their own.

That said, why not start with their expansive definition and whittle it back? If anyone has a stake in categorically measuring hate, the SPLC does. So I visited the SPLC website for the first time in more than a decade. Fascinating.

They are very sophisticated in their data presentation and it is actually quite useful once you get past the posturing and the ideology. They claim that there are some 892 hate groups in America, down some 10-15% in recent years. They have a Hate Map where you can view hate groups by state.

I started with Georgia. There are 10.1 million Americans in Georgia. How many hate groups in Georgia? According to the expansive definition of the SPLC, there are 39 hate groups operating in Georgia. 14 are Black Separatist groups, 3 KKK, 2 Neo-confederacy groups, 4 Neo-nazi groups, 3 White nationalists, 2 Anti-Islamic groups, 2 Anti-LGBT, 2 Christian groups, and 2 general hate groups. That's quite a mixed bag.

No membership numbers. Other than Nation of Islam, KKK, and Skinheads, none with any sort of activities or presence in the state media. I clicked through on a couple to understand quite what we are dealing with. One of them is the League of the South which is either, according to the SPLC, "rabid, writing about potential violence, criticizing perceived Jewish power, and warning blacks that they would be defeated in any “race war”" or a traditionalist group deeply interest in Anglo-Celtic history if you accept their own definition. It seems hard to mesh the SPLC's description with the fact that the Southern League was founded by a bunch of PhDs at a Historically Black College or with their description at Wikipedia. Frankly, it looks like a traditionalist group that does not fit with the SPLC SJW ideology. Certainly there seems no concerted actions to bring violence to anyone.

I simply do not know and it may be that it is my ignorance at play here. But I suspect not. One of the challenges with the SPLC is that they tend to be very anti-First Amendment. They classify groups as Hate Groups simply for speech. Which is what makes SPLC kind of creepy. Very repressive.

My inclination, looking at the SPLC data and stripping out groups who are there simply because they are not Reform Marxists, is to cut the group number from 39 to perhaps 20. Skinheads, Anti-LGBT, Neo-nazis, perhaps Black Separatists, those all seem like the kind of hate groups that actually do things rather than just talk.

SPLC also has a Hate Incidents log. So how many incidents have there been in Georgia (remember, 10.1 million people)? Yikes! 62! Oh, never mind, that is over the past 13 years. About 5 incidents a year. Anything more than zero is too many but out of 10.1 million people, that's close to zero for the nearest approximation.

But is it really 62? Looking at the details, there is a lot of double counting. More importantly, most of the incidents are people saying things the SPLC doesn't like, handing out fliers, graffiti, holding rallies. Having gotten rid of the duplicate reports, there appear to have been 52 incidents in 13 years, four per year. Of these, 17 incidents were rallies or fliers being distributed by KKK, neo-nazis, etc. Objectionable, but entirely within the First Amendment. Omit these and we are down to 35 incidents in 13 years, about three a year.

23 of the incidents involve vandalism, generally spray painted graffiti on homes and cars, just under two a year. The biggest category of victims were Jews, with 48% of the vandalizations being anti-semitic. There were 10 assaults in the 13 years with 50% of these directed at LGBT victims (of the remaining, four victims were black and one was white). Finally there were two cross burnings.

In summary - even given the most expansive definitions of hate crimes, we are talking about a very small number of groups (perhaps 20 or less). They have virtually no presence in the media or in terms of what they do. They are objectionable groups no doubt. The pattern of violence and actual crimes apparently motivated by hate are very few, perhaps 35 over thirteen years. Jews are the biggest victims (from vandalism), LGBT are the next (from assault), and African Americans are next with 7 vandalisms (plus 4 assaults and two cross-burnings). The numbers are small and the patterns are mixed. Blacks, Whites, Hispanics are all contributors to this small portfolio of hateful crimes.

Where does this leave us? I can't quite say. Relying on an expansive definition of hate crimes it seems like we have a very small number of disorganized local groups who may, perhaps, make a lot of noise, but don't do much (2-3 incidents a year or 0.0008% of all crimes in Georgia in 2014), and rarely anything violent. These hate groups are swamped by run-of-the-mill crimes of which there were 365,949 in 2014.

The data would not seem to support, even when accepted expansively, that there is any sort of systemic pattern or volume of hate crimes or hate groups exerting any sort of power other than episodic and random crime.

Those SJW groups, who seek to bring attention and focus to hate, usually from an ideological commitment, are misdiagnosing the nature of the problem. A focus on hate crimes won't do anything to improve community quality of life that would not be achieved simply and more effectively by focusing on crime at large. You could bring hate crimes to zero and no one would notice because they constitute such an insignificant percentage of all crimes.

15-30% Window

The Social Justice Warriors stay very busy finding things to be outraged about. The most recent is the idea that senior tech industry leaders don't follow enough women on Twitter. First World Problems doesn't even begin to cover the farcical thinking. Guess What: Top Women in Tech Follow Mostly Men on Twitter, Not Other Women by Lukas Mikelionis reports on the absurdity and points out that the problem is not distinctively about men. Top tech industry women also fail to follow women.

I am not interested in the SJW argument. It is just another corporate shakedown scam by activists to extract lucre. Sooner or later companies will learn the lesson Rudyard Kipling summarized in his poem, Dane-Geld. It seems to make sense to pay nasty people to stop saying nasty untrue things about your company but it never works.

It is always a temptation for a rich and lazy nation,
To puff and look important and to say: --
"Though we know we should defeat you, we have not the time to meet you.
We will therefore pay you cash to go away."

And that is called paying the Dane-geld;
But we've proved it again and again,
That if once you have paid him the Dane-geld
You never get rid of the Dane.

What caught my eye in the article was the proportions. As you might be aware, I have repeatedly reported the intriguingly pervasive 15-30% number. In just about every field, you can expect about 15-30% of the field leaders to be women. Regardless of field, history etc. There are exceptions but they are few and far between. What is magical about 15-30%? Nothing. It is just a product of the individual decisions (major, field, industry) combined with familial structure decisions (single no children, married no children, married with children dual income, single bread winner, etc.). To be at the very top of any field, you have to devote large volumes of hours over long periods of time to develop and demonstrate the levels of accomplishment necessary. The disproportions arise from the cumulative decisions that either enable or subvert that level of invested hours.

So what are the proportions of women followed by senior tech industry female executives?

YouTube CEO Susan Wojcicki follows 296 accounts: 120 men, 37 women, the rest are brands and news organizations. That is 24% female

HP CEO Meg Whitman follows 298 accounts: 58 men, 19 women, the rest are brands and news organizations. That is 25% female

Apple Senior VP Angela Ahrendts follows 146 accounts: 64 men, 21 women, the rest are brands and news organizations. That is 25% female

Yahoo CEO Marissa Mayer follows 343 accounts: 239 men, 65 women, the rest are brands and news organizations. That is 21% female

Facebook’s Sheryl Sandberg follows 17 accounts: 5 men, 10 women, 2 brand accounts. That is 66% female

Sandberg is the outlier here. All other female tech industry leaders follow on average 24% - Squarely in the middle of that 15-30% range.