The Importance of the Sample

In my work researching and writing about occupations, I encounter a lot of statistics. And this year, with an election coming ever closer, we are likely to see the results of many surveys of voters. I want to emphasize that numbers reported from surveys tell less than half of the story. They are the results of mere tabulation. What makes the numbers meaningful is the nature of the sample. Or, to put it another way, you can’t understand what a study tells you unless you understand the sample it’s based on.

To illustrate this point, I like to bring up two anecdotes. I think you’ll find them interesting even if (maybe especially if) you’ve never taken a course in statistics.

The first anecdote is based on the research that social scientists did when they essentially invented the science of jury selection. This happened in 1972, when seven radicals were about to go on trial in Harrisburg, Pennsylvania, for conspiracy to raid draft boards and destroy records, among other planned antiwar actions. This was a time of great political polarization and in a place that is characterized by political conservatism. The researchers, working on behalf of the antiwar activists’ lawyers, wanted to find a way to predict the political leanings of jurors so the lawyers could seat a jury that would be less conservative than one chosen at random from the Harrisburg population. The lawyers would not be able to ask the potential jurors flat-out about their politics; instead, they needed an indirect way to assess this.

The social scientists surveyed citizens of that community to identify their political attitudes and then correlated these attitudes with other facts about the jurors. They discovered that the surest way to predict a Harrisburger’s politics was to ask how much education the person had: The more educated the person was, the more conservative that person’s politics.

The researchers eventually realized why this was so: Young people in Harrisburg who became highly educated acquired the occupational mobility to leave the region if they were not conservative; therefore, the sample of highly educated people who remained had to be quite conservative. If the results of their survey surprised you, it’s because you didn’t stop to think about what the sample really was: not everyone who ever lived in Harrisburg, but rather those who remained—by choice or because they were less able to move out.

The second anecdote is from the Second World War. British bomber planes flying missions over Germany were often shot down by anti-aircraft fire. The Royal Air Force wanted to shield vulnerable parts of the aircraft with armor, but they wanted to use a minimal amount of armor to avoid weighing down (and slowing down) the planes. The RAF commissioned the statistician Abraham Wald to examine the planes after bombing missions to determine where on the planes’ undersides it was most critical to apply anti-flak armor.

Wald counted bullet holes in the planes and recommended that armor be applied where there were the fewest bullet holes.

This may seem like a mistake to you. Maybe you’re thinking that armor is supposed to protect against anti-aircraft fire, so shouldn’t the RAF have armored the places that got hit the most?

Again, consider the sample: Wald was not looking at every bomber that flew a mission, but rather those that returned from missions. Bombers that got shot down were removed from the sample. The bombers that returned and made up the sample were the ones that were hit only in places that were not critical for staying airborne. The places where the surviving planes were not hit, therefore, were the most likely to be critical and in need of armor.

If you’re wondering why I’m writing about this subject in a blog about careers, consider this blog entry a look at how complicated statisticians’ work can be, not so much in terms of the mathematics, but rather in terms of the concepts that must be understood.

The nonstatistical lesson to take away from these anecdotes is that you have to be careful when you make a generalization about a population—for example, the notion that educated people are more liberal politically (or, to draw on today’s politics, the notion that people of one religion are a greater threat to security). Such generalizations may be true in some global sense, but the particular population you are dealing with may really be a subset of the global population, either self-selecting or selected by some exterior factor you have not considered. The global generalization may be a poor fit for this subset, or the subset may be a misleading basis for a global generalization.

Changes in Skill-Income Payoff Over 10 Years

Everybody knows that a high level of skills is associated with high earnings, but perhaps you have been wondering which skills have the highest payoff. I actually answered that question just about a year ago in a blog that I wrote called “Transferable Skills with the Biggest Payoff.”  When I did the research for that blog, I wanted to use a statistical approach to seeing which skills are linked to the highest earnings, so I computed the correlations between the skill ratings of occupations and their median income. In the blog, you can see that Judgment and Decision Making, Complex Problem Solving, and Active Learning were the transferable skills with the highest payoff.

Now, a year later, I have been thinking about career trends and decided it would be useful to see whether these correlations changed over time. So I ran correlations again, using 2002 and 2012 earnings data from the Bureau of Labor Statistics. If you want to understand how I calculated correlations, as well as the significance of correlations as a technique, I suggest you look at the earlier blog.

As you might expect, the payoff for some skills increased over that ten-year span and decreased for others. Even the largest differences were not very big: the correlation of one skill gained by .06. Keep in mind that correlations are computed on a scale in which 1.0 means total correlation. You may think of the numbers as equivalent to percentages, which means that the biggest gain in correlation was equivalent to 6 percent.

So here are the skills that gained the most from 2002 to 2012, which is to say that their connection to earnings increased the most:

	2002 Correlation	2012 Correlation	Gain
Technology Design	0.34	0.40	0.06
Management of Material Resources	0.41	0.45	0.05
Management of Financial Resources	0.46	0.50	0.04
Installation	-0.08	-0.05	0.04
Management of Personnel Resources	0.57	0.60	0.03

I find it really interesting that three of these skills are managerial. What I take away from this is that compensation for management has probably been increasing over the last decade relative to compensation for other occupations.

I’m not surprised to see Technology Design posted the largest gains. Here’s how this skill is defined: “Generating or adapting equipment and technology to serve user needs.” It is well known that technology jobs are in high demand, but this skill is about practical uses of technology rather than scientific principles. The increasing correlation of this skill with earnings gives reinforcement to the idea that what increasingly drives the U.S. economy is innovation in applications of technology—think of the iPhone, for example.

I’m intrigued by the large gain for Installation. You’ll notice that the correlation is still in negative territory, which means that the more of this skill you use, the lower your earnings are likely to be. However, over the past decade the correlation got .04 closer to zero, which means that having this skill as an important part of your work has become less of an income liability. Perhaps the occupations with a heavy emphasis on installation are becoming better compensated as the level of technology that they use increases. In other words, as technology becomes simultaneously more complex and more important in everyone’s lives, it is becoming increasingly necessary to pay good wages to people who can install the sophisticated software and hardware that we use constantly.

Only four skills had lower correlations to earnings in 2012 than in 2002, meaning that there is less of a payoff now than there was then. These are the four:

	2002 Correlation	2012 Correlation	Loss
Repairing	-0.18	-0.19	-0.02
Operation and Control	-0.18	-0.19	-0.02
Equipment Maintenance	-0.19	-0.20	-0.01
Science	0.58	0.57	-0.01

Note that three of the four have negative correlations, meaning that they already were associated more with low earnings than with high earnings and only got more so. These three skills—Repairing, Operation and Control, and Equipment Maintenance—are characteristic of rust-belt occupations that are being replaced by robots and foreign workers.

I was quite surprised, however, to see that Science had lost ground. The contrast with the performance of Technology Design is instructive and tells me that applied scientific knowledge has gained in earnings even while abstract scientific knowledge has lost slightly. It is consistent with the disappointing national trend toward diminished funding for basic scientific research and reminds me of how a member of my family recently quit her job in medical research and became a software developer. I looked at how the correlation for Science changed on a year-by-year basis and found that it actually climbed during the first half of the decade, peaking in 2008, and then began its downward slide. This suggests that the Great Recession brought on the comparative decrease in pay for scientific research jobs.

It’s important to understand that none of the nine skills I focus on in this blog is among those with particularly high correlations with income. The movement you see here happened in the middle and bottom of the pack. If income is very important to you, I suggest you look at the earlier blog and aim at occupations that involve Judgment and Decision Making, Complex Problem Solving, Active Learning, and other skills with the highest correlations.

The Importance of Outlook Information

In my new book 2011 Career Plan, which comes out this month, I focus on industries and occupations that are projected to have high growth. This week, I fielded an inquiry from a journalist who wanted to know whether growth projections are actually useful in career advice. Read on to see what I told him.

First of all, to understand the outlook for an occupation you’re considering, you have to be careful not to go solely by the figure for growth. You also need to pay attention to the projected number of job openings. Growth and openings are not the same thing. Consider the occupation Hydrologists, which is projected to grow at the outstanding rate of 31.6 percent. There should be lots of opportunities in such a fast-growing job, right? Not exactly. This is a tiny occupation, with only about 8,000 people currently employed, so although it is growing rapidly, it will not create many new jobs (about 1,000 per year). Now consider Secondary School Teachers, Except Special and Vocational Education. This occupation is growing at the sluggish rate of 5.6 percent. Nevertheless, this is a huge occupation that employs more than one million workers, so although its growth rate is unimpressive, it is expected to take on more than 93,000 new workers each year as existing workers retire, die, or move on to other jobs.

In fact, some very large occupations have so much job turnover that they provide tens of thousands of job openings even though they’re shrinking in size. Size of the workforce is not the only cause. Occupations that are easy to get into and/or low-paying are also easy to walk away from, so Home Health Aides, for example, has huge turnover. Contemplating such career options, you have to ask yourself whether you’re looking for a long-term career or a job where most people sojourn only briefly.

Next, consider the possibility of local variation. A national boom in an occupation may bypass your region. You really need to check with local employers to get a sense of the local outlook, unless you’re planning to cast a nationwide net in your job search. Something similar applies to variation by occupational .specialization. Here again, it helps to talk to employers in the specialization that interests you.

Then there’s the question of personal satisfactions. It’s true that you won’t get any satisfactions (earnings, working in your interest field, leadership, helping others, prestige--you name it) from work if you don’t have work. This is one reason why job opportunity is so important. However, if your personality is comfortable with taking risks, you may strive for an occupation with a somewhat poorer-than-average outlook because of the potential for a high payoff in satisfactions.

When I write my books, I don’t encourage people to defy the odds, because the books are aimed to do the most good for the greatest number of readers. However, there are always people who are the exceptions to the rule, who beat all the competition and get the job even though only a handful of openings are available. (Maybe you saw the movie “The Pursuit of Happyness.”) These people either are risk-takers or they have extraordinary abilities or credentials. They are uncommon enough that I don’t usually address them in my books. If they do read one of my books, they probably have enough well-earned self-confidence to be able to ignore my warnings about limited job opportunities.

Another minority of readers whom I choose to neglect are those interested in doing work that almost nobody else wants to do. They may be willing to pursue a highly specialized occupation, such as repairing antique clocks and watches, or an occupation with work conditions that almost everyone else finds repulsive, such as cleaning up houses where obsessive cat collectors have lived and died. The job outlook for such occupations is actually good because there is almost zero competition for job openings, but the number of job openings is so minuscule that the occupations are not worth including in a book of general interest. Like the übermenschen I discussed in the previous paragraph, these uncommon people probably will find their way to their obscure career goal without needing my help.

So, in conclusion, outlook figures are very useful, but be aware of figures for both growth and openings, verify them as they apply to your region and specialization, decide how much risk you’re willing to undertake, and weigh how much you’re willing to do the unconventional.

New Data on Women's Earnings

The Bureau of Labor Statistics recently released a report on the 2009 earnings of women (PDF). This annual report always makes for fascinating reading, and this year's edition is no exception. Surprise, surprise! On average, women are still earning less than men. However, I was able to find some interesting tidbits about the variations within that overall average.

Start with this chart, based on figures from the report, that indicates the earnings of women at various levels of education, measured (on the vertical scale) as a percentage of the earnings of men at the same level of education.


Given these categories for level of education, the more education a woman gets, the greater the disparity in her earnings. It looks as if it's pointless for women to get more education, doesn't it?

Yet, paradoxically, it turns out that (again, on average) women actually gain a greater advantage than men for each additional level of education they attain. The following chart, also based on figures from the report, shows the advantage of various levels of educational attainment for men and women over workers of the same sex who did not complete high school.


The difference for women is not great, but it's consistent, and it's greater (1.3%, 2.1%, and 11.5%) with each additional step up the ladder.

Now, here's another chart based on data from the report. This one looks at the wage differences for different age brackets. Like the first chart, it shows women's earnings as a percentage of men's earnings (in the same age bracket):


You'll note that younger and older women earn a better-than-average percentage of the male wage, whereas middle-aged women earn less. I'm only guessing, but I think that younger women earn more because they have higher expectations of fair treatment and because the earnings-limiting lifestyle choices that many women make have not yet taken a toll on their wages. I also speculate that older women have acquired enough work experience to make up for some of the ground that they lost earlier, and this explains their higher earnings.

Now, here's one more chart derived from the report, yet again showing women's earnings as a percent of men's. In this case, the average is broken down into various levels of hours worked per week:


This chart reveals that women who work part-time earn higher wages than men working the same number of part-time hours (except for those women who work fewer than 5 hours). This difference partly reflects the kinds of jobs that women and men are working in. For example, some women who work part-time as nurses on night duty earn very impressive per-hour wages. It may also reflect the attitudes of employers toward workers. That is, working part-time may seem a more conventional behavior for women workers, whereas male workers who choose this arrangement may be perceived, rightly or wrongly, as less committed to their careers.

I doubt these disparities will ever vanish, but we do seem to be making progress. A female friend of mine who got her bachelor's in chemical engineering from The Johns Hopkins University about 15 years ago told me that there are now more women in the JHU School of Engineering with the same given name as her as the total number of women enrolled when she was an undergraduate.

Finally, here are some occupations in which the percentage of female workers has increased by more than 10 percent between 2007 and 2009. I limited my analysis to occupations with a total workforce of more than 100,000 in order to exclude small-sample occupations, for which the male-female percentages are likely to be unreliable:

Occupation Name	Increase
Medical Transcriptionists	23.7%
Library Technicians	23.2%
Instructional Coordinators	21.3%
Demonstrators and Product Promoters	13.3%
Administrative Services Managers	12.1%
Telemarketers	11.6%
Medical Scientists, Except Epidemiologists	10.6%
Paper Goods Machine Setters, Operators, and Tenders	10.2%

This blog entry is dedicated to the memory of Sarah Doshna.