Demystifying Statistics

Your Jewish Fairy Godmother’s 10 Commandments
for Coping with Esoteric Math and Strange Greek Symbols

 

We’ve all had that moment when we look like deer in the headlights: someone’s
making a presentation and using all sorts of mystical jargon and strange
symbols. They survey the room and seem to look straight at you, arched
eyebrow implying, You get it, don’t you? You can either fake it and nod, or admit
you have no idea what the person is talking about. You won’t actually be the only
clueless one in the room, but everyone else will be staring intently at you, eyes
carefully averted from the speaker.

 
The commandments below won’t substitute for a full-bore statistics class. But
they should be enough to get you out of the room with your ego and job intact.
Grab a pencil and paper, take them step by step, remember to breathe, and
you’ll see it’s not as tough as its reputation.

 
Commandment Number 1: Know your odds.

Everything in life is measured in odds. A sure thing has a 100% chance of
happening. It’s guaranteed, or, in statistical terms, an event with a 100%
probability. Events are how statisticians talk about things that happen. Probability
is a fancy way of saying odds. If you go to sleep tonight in your own bed, there’s
a 99.99% chance that’s where you’ll wake up in the morning. The world could
end in-between, or you could roll out, but we tend to assume life is more
predictable. Something that’s highly unlikely to occur, say that you’ll wake up an
amnesiac or in China, has a probability .00001, or that approaches 0%. Anything
you can describe or measure has a probability that ranges between 0 and 100%.
(See, this is e.a.s.y…). Just to be safe, statisticians rarely use the 0 or the 100.
They say, approaches 0, or approaches 100 (percent implied).

 
Commandment Number 2: Identify your population.

No matter what you want to measure, you have to define it. You might care about
the height of NBA players or the age of employees. The life expectancy of people
or lightbulbs. You need to set parameters, which is statisto-speak for criteria that
identify who or what you’re going to study and measure. If you need to know the
height of NBA players, the height of college players isn’t relevant. If someone
talks about “the height of basketball players” you have the right to ask if they
mean K-12, college, pros, or the kids playing in the neighborhood park. Your
studyvariable is however you define it. But once you say what it is, that’s the
definition you stick with.

 
Commandment Number 3: Know n from N.

Big N means every event you could possibly measure. Every NBA player. Every
light bulb manufactured. Every employee who works for your company. However
you define your population, that’s N. Little n is a sample of N. It represents the
data events that you’re going to do statistics on. If you tested every light bulb,
you’d have none left and would sit in the dark. So you use a sample, a
representative subset of N. There’re many possible n’s in N. Trust me on this, but
any group of 30 or more is considered a good size no matter how big N is.
Amazing but true. The goal is to find an n that is truly representative of N.
Generally randomness is considered a good way to eliminate bias. For example,
if you do a survey but ask only the opinions of your friends, that’s a biased
sample. Better to assign everyone in N a random number, put the numbers in a
hat, and have some stranger on the street draw out 30 of them. Then you have a
legitimate random sample size n = 30.

 
Commandment Number 4: Show off what you found out.

Even without measuring anything else, you’re already doing descriptive statistics!
The next step is to make them visual. In elementary school you learned about
Pie Charts: a circle broken into different size slices, each slice representing a
percent of the whole. Also, Bar Charts: the height of each bar shows how many
people are in a given category. There’s lots of other, fancier techniques. But for
almost all of them you’re limited to the two-dimensions of a piece of paper. In
computer programs you can make graphs look three-dimensional, but you need
to think about what you’re really trying to show. Generally speaking, in addition to
whatever you measured (in units of however you measured it), you have to
convey how many events got what score, the time period things change over,
perhaps contrasts between different groups (e.g. men and women, or salary vs
hourly, or technical vs sales). You can use different colors, footnotes, and other
tools. Your goal is to be able to show your chart to someone else and have them
understand it.

 
Commandment Number 5: Look at the shape of the distribution.

You’ve got your sample and measured whatever variable you‘re studying. Now
you want to understand what the results are telling you. The simplest way is to
rank the scores from biggest to smallest. Inferential statistics (ways to describe
the population N based on what you observed in your sample n), are usually
graphed in a curvy line on a grid with a horizontal and vertical axis. (Soon you’ll
understand the bell curve.) Imagine a horizontal line from left to right (the x axis),
and vertical one (the y axis) where the crossing point is zero. Mark the x axis with
key intervals (for example 5’-5’6”, 5’7”-5’,11”, etc). On the y axis you measure
count how many events/people/etc fall into a given category, Then connect the
tops of each category. If everyone scored the same, you’d have only a tall mark
in that category. If everyone was spread equally across categories, you’d see a
straight line across them. For most things you measure, there will be groupings,
tall categories with more observations and flatter ones with fewer. Look at the
picture and see what it tells you.

 
Commandment Number 6: Know one average from another.

Averages tell about the middle of your sample. There are three kinds of
averages. Each one tells you something different. If everyone scored exactly the
same, you could stop counting now. If you looked at all the observations in a
ranked list, the median is the number in the middle. For example, if you look at
the salaries of 101 employees, and rank them from lowest to highest, the median
is the salary of the 51 st person. The mode goes back to the shape of the
distribution. It’s the category with the most observations in it. For example, if
you’re looking at how long people stay with your company, and more of your
employees are in 3-6 years than any other group, the mode is 4.5 (the middle of
the biggest group, even if no single person has worked there 4.5 years). The
mean is the number you get if you share equally. It’s as if you added up all the
scores and divided them by how many people you measured. For example, if you
took the heights of all the players in the NBA divided by the number of players,
the mean height might be 6’3”, even though there are some short guys and some
giants. BTW, whenever someone says “average,” try to know which average
they’re using. In a perfect bell-shaped distribution, all three averages are at the
top of the bell.

 
Commandment Number 7: Know how different your group is from itself.

The fancy statistical name for this concept is standard deviation. It has to do with
how unalike the members of your sample n (and implicitly N) are from one
another. Imagine a startup firm, where everyone has worked there a very short
time. If you are measuring length of service among employees, there’d be a very
small standard deviation. If you look instead at a place like the US military, you
might find career soldiers in the same sample as new recruits. The standard
deviation would be much larger. For a different visual, imagine an NBA team
where everyone is between 6’1-6’5 (a small standard deviation), compared to
one with a guy 5’5 and another 7’2. the two teams might have the same
“average” height, but they’d look very different when they lined up for the pledge
of allegiance. Note: There’s math to calculate a standard deviation, but most
calculators will do it for you.

 
Commandment Number 8: Understand for whom the bell tolls.

The infamous bell curve (as in “Do you grade on a curve?) is a distribution
shaped like a bell, drawn from knowing only two numbers, the mean and the
standard deviation. (This is where it gets very cool.) You’ve been doing this
intuitively for years, as in: It takes me 30 minutes to get to work, give or take five.
That means, most of the time, you will get to work in 25-25 minutes. Less often
it’ll take 20-25 minute or 35-40 minutes. Rarely you’ll get there in less than 20 or
more than 40. By knowing only two numbers, the mean and standard deviation,
you can get a very good and surprisingly accurate picture of your population.
Generally speaking, for normally distributed variables, which is a lot of what we
measure, 68% of the population will fall within one standard deviation of the
mean (mean +/- 1 sd), 95% within mean +/-2 sd, and 99% between mean +/- 3
sd. Just from knowing two numbers, you can make a bell curve and get a pretty good picture of what’s going on in the world, all from measuring a random
sample of 30 or more. Amazing but true.

 
Commandment Number 9: Know what’s significant

This is probably the simplest and most sophisticated concept in statistics. Once
you have a mean and a standard deviation, you can do what are called tests.
Test are a fancy way of asking, if the truth is “this,” and in our sample we found
“that,” then what’re the chances that that by sheer dumb luck we’d have stumbled
onto a sample that would be very far away, improbably away, from “this?” It’d be
like concluding the average height of NBA players is 5’9”, just because we
happened to pick a sample that included a lot of the shorter guys. When people
say “our results are statistically significant,” what they’re really saying is, there’s
only a very small chance, say 1%, or 5%, that we’re wrong when we say the
mean is “that” (and it’s really “this’). One important note: the person doing the
stats decides how sure they want or have to be. If you’re testing an experimental
drug that has a side effect of death, you’d probably want to take a smaller chance
of thinking you’re right when you’re wrong than if you’re asking people which cola
they prefer.

 
Commandment Number 10: Get out your crystal ball.

There are many more complicated statistical techniques that try and predict
things. For those you generally need to look at more than one variable at a time.
For example , if you’re trying to figure out what you’d pay for a new pickup, you’d
want to know lots of things like: year, mileage, brand (yes, there are ways to
measure things that are names and not numbers), automatic vs 5-speed,
options, what part of the country you’re buying in, accident history, etc etc etc all
the way down to whether or not it has genuine leopard skin seats. If you have
enough info, you can predict what it should cost. That’s how the Kelly Blue book
works. These techniques are interesting, though complex, and you’ll need a more
advanced guide.

 
Try to think about statistics as looking like algebra but really being geometry.
You’re trying to draw a picture that shows someone what you think is true about
everyone you haven’t measured, based on the people you did measure. If you’re
interested, think about taking a class. If you can master this kind of thinking, it’s a
fast track to advancement.

 

When Your Boss is One Tough ***

Your Jewish Fairy Godmother’s 10 Commandments for

Learning Through Adversity

 

Everyone’s had a least one: the kind of nightmare boss that makes the sadistic drill instructor in some war movie seem like a kindly old grandmother. The kind of S** or B**** that makes you want to flee to the nearest corner bar and tank up, and then go home and vent for several hours.

 

Good news: you’re not alone. Even better news: Like cod liver oil or public speaking, this is an experience that’s not only good for you but going to improve you in ways you would never predict. Not saying it’s going to be fun and games along the way. Almost for sure guaranteeing that it won’t be. But the commandments below will help you minimize the pain and optimize the experience.

 

Commandment Number1: Sign up or get out.

You know the movie where they lead the convicted guy out of the courtroom in handcuffs, and he has this bleak look of imminent terror in his eyes as he shuffles to his doom? Handy tip: never look like that when you come into the office. If you really cannot imagine yourself working for this person another minute longer than you have to, work on your resume and devote every waking minute you can to getting a different job. But while you’re still there, follow the rest of the commandments.

 

Commandment Number 2: Take the loyalty oath.

You don’t have to love your *** Boss, but you have to accept his/her authority and leadership.  Nothing’s harder to deal with in a workplace than divided loyalties. While you’re in the job, you need to be on the team. Not half-heartedly, but with conviction and purpose. You need to be willing to make your boss look good, and make yourself look good in the process. Don’t go blabbing about his/her foibles and don’t do anything to undercut the success of your working group. As long as you are part of this team you are going to have to wear its colors. You can send out as many resumes as you want on your own time, but 8-5 M-F you are a devoted member of Team Tough.

 

Commandment Number 3: Cultivate respect.

Unless you work for an organization riddled with corruption or stupidity, there’s reasons (whether they be good, bad, silly, incomprehensible, nepotism, blackmail, or something like perceived merit, but very real) why your boss is your boss. S/he got promoted for achievement or potential that someone yet higher on the food chain than you are counting on to make the company money and/or do good deeds. Figure out what traits make your boss valuable in the eyes of the bossier bosses, and decide to appreciate them, perhaps even mimic them. Show your respect in how you speak and how you act, both directly to your boss and when you speak about him/her to others in the organization.

 

Commandment Number 4: Work hard, very hard.

A hard boss can be a good boss. A hard boss can also provide you an opportunity to show what an excellent employee you are. Anyone can skate under a lax or uncaring supervisor. But to shine under a tough boss will earn you the approval and respect of anyone who notices. And I can assure you that people do. Anyone in the working group will know what you’re facing and anyone outside it will be thanking their stars every day that they aren’t in the same boat. You may not know that folks in Human Resources watch this sort of thing, but they do Every organization has its own character and if you can demonstrate yours it will be to your great credit.

 

Commandment Number 5: Ask your boss to mentor you.

Take your finger out of your throat. Flattery is a wonderful lubricant. Make it work for you. There’s nothing more disarming than a person suggesting that you are a good role model or worth learning from. You may want to give your tongue a good cleansing scrape later, but if you can say something like the following to your boss, you may shift the dynamic from something bad to something better, or even to something good: “I know you’re a tough boss, but I want you to help make me the best employee I can become.” Then, no matter what the requirements, do your best to meet them.

 

Commandment Number 6: Learn, learn, learn.

No matter how tough your boss is, s/he has something to teach you. What got your boss the job that tells you what to do? Is it smarts, effort, persistence, or wily politics? Study your boss’s habits and see what you can learn about what your company values. Ask questions about how and why certain things are done as they are. Become a student of success and you will attract attention and kudos, perhaps from people even more important than your immediate supervisor. Remember, your goal is to get a promotion out of your current situation, so keep your eyes and ears open for chances to learn and to shine.

 

Commandment Number 6: Set goals and make them happen.

Nothing distracts from pain better than goal orientation and rewards for meeting them. You can use the goals your boss/mentor sets and/or set them for yourself. But be sure they are documented both before and after you meet them. When you have a review or evaluation, ask what would make you more of a success. Set standards and timelines, and identify short and long run rewards for yourself. When you’ve proven that you’re as good as your word, set an external goal and communicate it to your boss. As in, If I accomplish x, y, z could that merit me a raise? It raises the ante but will keep you focused.

 

Commandment Number 8: Keep your big mouth shut.

Like side-seat driving and Monday-morning quarterbacking, complaining about a tough boss is one of our favorite pastimes. It’s a way to vent the annoyance and frustration that builds up from feeling like you have no voice and that someone else has extraordinary and inappropriate power over you. You may desperately want to tell the tale of the latest abuse you’ve endured, in part to distress and in part for the need for raw sympathy. But remember that every story you tell has a life of its own, in the retelling by the listener who may not have your career goals in the center of their competitive bulls-eye. What your boss hears you have said may not be the truth and could come back to bite you somewhere tender.

 

Commandment Number 9: Network with your peers.

This may seem like a contradiction to Commandment number 8 but it is not. The truth is that on any given day any boss is a tough boss or a bad boss or an annoying boss. We all need to let off steam and we all need to know that everyone faces the same dilemmas. The trick is to be able to complain about the circumstances without personalizing it to the boss. If you can learn to do that you’ll be able to connect with others who are now lateral to you who might: get a promotion sooner and hire you away, be a better fit and want to swap places (note, also risky), or who might have networks in places they cannot move to but might be good for you.

 

Commandment Number 10: Take mental health breaks.

Most jobs have requisite break times for staff.  But I’m talking about actual unplugging from the 24/7 culture cultivated by tough bosses that assumes the boss has a higher place in our lives that family, health, or even God. Make sure you get downtime on weekends and on actual vacations. Even if it is a complete lie, say you’re going to be backpacking, sailing, or otherwise out of cell range. Make sure you have all your chores done before you leave the office and keep your files well documented. Because if something completely explodes when you do not answer you will certainly get the blame. But if you can keep things wired tight you should be able to unwire yourself enough to come in Mondays feeling optimistic and challenged, instead of angry and resentful.

 

One final note: It really is okay to have a beer, and to vent, and to find non-lethal ways of stress reduction. But remember never ever to let any of your frustration leak into your office. Everything you say will live on in someone’s memory and you do not want to become the target of an angry boss who can send you packing.

 

Look on this period the way you would boot camp. It’s a chance to develop some muscles that will serve you well when you land in easier places, and help you shine among colleagues who haven’t had the chance to learn climbing up these same tough hills. You may not believe it now, but some day you may even thank your tough boss for the chance to toughen up yourself.

 

 

 

Where’s Your Edge?

Your Jewish Fairy Godmother’s Prescription for

Leaping into Your Next Challenge

 

The alarm goes off. You brush your teeth, brew some caffeine and head in. What day is it? Monday-ugh; Tuesday-yawn; Wednesday-halfway (hooray!); Thursday-hang in there; Friday-TGIF!!!

 

What’s the problem? You know the drill. You know your job. You can script every day of the week, not down to the labels on the lost files but pretty close. You’re okay: secure, entrenched, safe, and yikes, can you say it out loud, totally bored,. You don’t want to die in this job but how’re you going to find the energy to prepare yourself for what happens next? Where did your energy and ambition go? Where’s your edge?

 

It’s a not uncommon lament. We’re all looking for that scent of danger, the utter vitality than comes from feeling completely alive. Not that we walk around wanting to face off lions or tigers; usually bosses are scary enough. We don’t really want to know first-hand if a parachute will open; giving a presentation is enough of a life-threatening thrill. But often we crave, secretly or not, the intensity and zeal that comes when we’re fully focused. And we tend to be most focused when we take risks, when we’re willing to leave the safety of a predictable week and test ourselves, see how we do in a new and different world.

 

So what’s it take to get ready? What do you have to do? Not just updating your resume and searching the help wanteds. What do you have to do on the inside? How do you leave behind the emotional baggage that’s weighting you down?

 

One way to face risk is to leave a safe distance between you and the edge. Look for an internal promotion. Be sure you have a secure financial safety margin. But what happens if you push the envelope a little? If you take the essentially risk-averse parts of your nature, the ones that usually run the show, and muzzle them for a while? If you allow yourself a flight of fantasy, visions of what you think you’d create, would become, would be if only.

 

The key is the ‘if only.’

 

Because if all you do is dream and then tuck those disruptive little thoughts away, or smile indulgently and then go back to your desk, sit back in the familiar chair of your predictable life, you’re doing yourself a great disservice.

 

That’s not to say that today is the day to quit your job and start a dot-com (or even to proclaim your adoration to the secret crush in an adjoining cubicle). But it might be the day to remember how to dream. To leave some space for an edge to appear, and then not to run from it.

 

Most of us have been trained to be parakeets. Too few were encouraged to become eagles. No one ever said: You can learn to fly. The ‘If only’s’ are the doubts that weight your wings, the words that keep you on the ground, safe in your cage. Take some time to think about what it means to fly. Because that’s what an edge is really all about. It’s what happens when you go over the side and trust that your wings will carry you.

 

How can you encourage yourself to take risks? And how can you figure out which risks to take?

 

The answer: start talking to yourself more and trusting the answers you come up with. In you is a great sense of understanding of what you really want, what makes you happy, what you’re willing to work and strive for, what you simply no longer are willing to put up with, and what you’re willing to sacrifice to reach some goal.

 

If you can learn to listen you will let yourself over the edge more often. You will probably make some ‘mistakes,’ but they won’t harm you more than you can bear. Though you may end up with a few tattered feathers, you’ll also learn something powerful. If you do it often enough, with a proper sense of joy and exploration, with fewer ‘if only’s’ weighting your wings, flying will begin to feel as effortless as swinging out of bed on a workday morning.

 

Risks don’t have to be big to give you the benefits you aspire to. You don’t have to throw yourself over a steep edge to feel the rush of pure air. You just have to want to take them badly enough to banish doubt from your mind.

 

Go for your dream, whatever it is. And if you aren’t sure, clear some space in your life for it to show up. When it does, fly with it.

 

 

 

Finding Your Wings

1. Commit half an hour completely to yourself. You can do this at home, (though turn off all phones), or in a library or a park. The key is insulating yourself from all distractions.

2. Take a blank sheet of paper and draw a line down the page. At the top of the left column, write Topic, and above the other one write Failure/Worst.

3. Write the following words in the left-hand column: Job; Salary; Job Search; Interview; Promotion; Boss; Colleague; Project; Learning Experience; Challenge. Feel free to adapt or add others.

4. You may come up with answers while you are writing the list. Jot down whatever comes to mind. This is a Working World  Rorschach test. Grab what’s in your forebrain first, so you remember it, and then peel it back and see what’s below. Most important: be honest.

5. Go through the list the way you would a crossword puzzle. Ideas and memories will trigger more ideas and memories. Your goal is emptying out all the fears, fixed ideas, and blocks you have about your work history. It may take you a while to put something in every category, but persist until you feel empty.

6. Take a week off from this project. Then go back and do the same thing, but label the right-hand column Success/Best. Repeat the previous steps till you’ve got the good things identified. Then reread both lists. What you’ll find out is:

Your failures, embarrassing moments scary times, will feel less bad to you. They are history. You’ve learned from them. You can move on. Burn the first list.

Your successes will give you strength and courage. Look at what you’ve already done! Read that list every day for a week. Keep it on your desk and add anything good that you remember or do.

7. Take a new sheet of paper and describe the next job you want. Be explicit. List everything from work hours to pay, title, responsibilities, whatever you feel you can imagine now and anything good you think of while you search.

8. Tape the list to your bathroom mirror and read it every time you brush your teeth.

9. Every time you send out a resume or go to an interview, remind yourself you’re the best person they could hire.

10. Repeat as needed until you believe #9 or reach your goal.