Stop Screwing up Percentages!

I tend to read a lot of research in my line of work, and much of that research involves data and statistics. Of course, STEM fields are not the only ones which regularly use mathematics to convey ideas - consider all of the statistics that politicians, business people, and vloggers on YouTube like to throw around! The common thread with all of these numerical representations is the use of the percent sign "%" and yet percentages are so often misused and misunderstood.

For a fantastic explanation and lesson on percentage, check out this post at Math is Fun!

In case you didn't check out that site, a percentage is essentially some sub group of, or a collection of other groups including, some other number. For example, check out these flamingos from the Sacramento Zoo:

I count 11 flamingos in this picture; however, they are only a fraction, or percentage, of all of the birds in this picture. Within the flamingo population, a percentage of them are holding their heads up.
Of the 11 flamingos, 5 have their heads up; hence, 5 / 11 is the fraction of flamingos holding their heads up. As a percentage, that becomes 45.45%. In other words, 45.45 percent of the 11 flamingos are holding their heads up. Got it? Easy? Of course! But that's just the beginning of our story.

When it comes to research, this group of flamingos would be seen as a "test selection group" on which the research is based. Is it fair for me to conclude, based on this one photograph, that about 50% of all flamingos will have their heads held up at any given time? Of course not. In fact, here's another picture of those same flamingos with a few more of their flamboyance (that's what you call a flock of flamingos, seriously) showing most of them with their heads down:

The trouble is, a lot of societal research and polling is done in this manner - form a conclusion from data obtained by polling or studying a very small subset of a general population over a specific time frame, often with a bias or outright mission to prove your original hypothesis on the subject matter. I could go on and on about this nonsense, but that's not my point, so let's get back to that - percentages!

In the second photograph, I count 26 flamingos. I might be wrong, and the exact number isn't what's important here. What if these were sales numbers? Your boss might say something like, "in this quarter, we made X% more money" or "we had an X% increase in sales!" But do these statements really make any sense? That depends... does your boss know how to do math?

If this second photo is the entire flamboyance (seriously!) of flamingos, then the first showed a percentage of them: 11 / 26 * 100% = 42.31% to be more precise. We could also represent the increase in the number of flamingos as a percent increase. Here's the process:

Original number of flamingos: 11
Final number of flamingos: 26
Difference: 26 - 11 = 15
Percent increase: 15 / 11 * 100% = 136.36%

So we can say that the first picture showed 42.31% of the entire flamingo flamboyance, while the second showed a 136.31% increase in the number of flamingos photographed. Does that make sense?

One thing to always remember about percentages - they involve multiplication, not addition. You typically say "a percentage of" where "of" implies multiplication. That's why statements involving terms like "more" and "less" are so confusing - they imply addition and subtraction. The choice of words is incredibly important when trying to get your point across to someone; choosing the wrong words can often lead to you sounding like an imbecile.

When someone says "X% more" they really mean "(100 + X)% of." Similarly, "X% less" should be interpreted as "(100 - X)% of." As an example, if I wanted to take a picture of 10% more flamingos in my next photograph, then I need to find a flamboyance (sorry, it's just so fun to say) containing 110% * 26 =  28.6 flamingos. Would that include a teenage flamingo, or maybe one missing a leg? To test that, we can once again calculate the percent increase: (28.6 - 26) / 26 * 100% = 10%.

If you want a more practical use of percentages aside from calling your boss out on his stupidity, take shopping sales: if an item is part of a 70% off clearance, the sale price will be 30% of the original price. When using a 10% off coupon on top of that, just compound the percentages. The new price now becomes 30% * 90* ORIGINAL. Of course, these new numbers are found by subtracting the discount from the maximum of 100%: (100 - 70)% * (100 - 10)% * ORIGINAL. You never add these discounts together, rather, you multiply them.

Another obvious use is to calculate your tip at a restaurant (which you should be doing, even though it is a stupid practice that should be abolished, and servers should be paid a full wage by their boss). Let's say your meal cost $53.67. How do you figure out the tip? It's really easy...

10% = 0.1 * $53.67 = $5.37 (Let's just use $5.40) <- This is a crappy tip. Don't be cheap.
20% = 2 * $5.40 = $10.80 (just double the 10% amount!)

If you think 15% is a good number, then give somewhere in the middle of those... like $8.50. This is really closer to 16%, but you just did that in your head, showing your mathematical superiority to your friends. See, percentages are simple and useful.

The real moral of the story is to always double check your numbers and make sure you are correctly representing data; otherwise, your entire point may be seen as invalid. Sadly, this type of ignorance is not only found in in the non-technical, but can regularly be seen in otherwise great research articles and technical documents.

Tax Season... More like Refund Season!

I'm sure you've all seen the H&R block commercials. They air them pretty much nonstop about this time every year. You guessed it, tax season is upon us once again, and all of these companies really want you to use their services to ensure you get the absolute highest possible refund...

Some of them try a little too hard...

But should you really be getting that high of a refund? Let's stop and think about how taxes work for a second. Let's say you worked really hard for a year and earned $100 (unrealistic, but it makes the maths easier for the non-math savvy to understand). Now let's say you owe a total of 20% tax to government agencies. Forget about state, federal, and other tax types for a moment, and just focus on the numbers. You owe $20 in taxes and get to keep $80. That's pretty simple, right? The problem is that we don't just pay that amount all at once because no one would be responsible enough to save all year for their taxes... we pay our taxes in increments - a little bit out of each paycheck. The trouble with that is the rate isn't exactly constant and can vary based on location, total pay, and a plethora of other factors. There is no way to know exactly how much we will end up owing during tax time, so we fill out forms that aim to make an educated guess based on previous income, living situations, and overall awesomeness (or the opposite) at life.

This is where the whole thing goes south. I was always taught, as most people are, that I should "claim 0" on my W-4 forms so the maximum tax is withheld. Hold the phone, why would I want the maximum tax withheld? Simple, you reply, because you will get a huge refund at tax time. At first, this sounds awesome, who doesn't love refunds? Um, me, that's who. Do you know what a "refund" actually means? It means that someone owes me money, and that someone happens to be the IRS.

I'd like to think I am pretty responsible with my money. I save, shop smart, and live well within my means. However, I know plenty of people who live paycheck to paycheck. I'm not here to brag or to judge, but an extra bit of money each pay cycle would go a long way with a lot of people. So why are people giving that extra money to the IRS each week just to get it back later (without interest)?

Let's look back at those simple numbers again... If you make $100 and will probably owe 20% in taxes, you should shoot for paying exactly 20% at each paycheck. Of course, it's impossible to know exactly what you will owe, but those forms do a pretty good job at guessing. Why is this so important? Let's look at some more numbers, just for fun.

There are 52 weeks a year, but you take off 2 of them, so you will get 50 weekly paychecks of $2 each. If you claim 0 dependents, the maximum tax will be withheld from those paychecks. That could be easily be 35%. Now, you are paying 35% taxes all year, keeping only $1.30 each paycheck.

Yes, yes they are...

At the end of the year, you have kept 65% of your $100 annual pay which amounts to $65. However, your savings, living expenses, and a few of life's unexpected events cost you $75. That excess cost was likely absorbed by your credit cards.  No big deal, everyone has credit card debt, right? Then comes tax time, and you have a huge refund waiting for you: $15. One thing you might be aware of... people who are constantly out of money are not very good at keeping it once they find some. So you spend that money on a new TV, or a vacation, or to remodel the bathroom. 

Let's say you actually decide to be responsible and you try to pay down your debt. If this year you added $10 to that pile, it was probably already pretty high from the previous years. Assumptions aside, you will owe more than your $10 debt. You will owe interest on that debt - likely 15% or more. That bill just climbed from $10 to $11.50. So you pay that off and come out ahead by $3.50. Hooray! Now let's see how that year could have gone...

Since you filled out your W-4s more accurately, you only had 20% withheld each paycheck, so you got 50 paychecks of $1.60 each. At the end of the year, you made $80 and ended up neither owing tax nor getting a refund. Also, that extra little bit in each pay check was enough to pay for all of your expenses for the year, so you didn't add any debt to your name. In fact, you walked away with $5.25. Wait, how did $80 - $75 = $5.25? Easy, rather than blow that excess money, you invested it all year to the tune of 5%.

So there you have it:

 Plan to get a refund and get 3.50% of your annual salary.

Plan not to get a refund and get 5.25% of your annual salary.

Of course, all of these numbers are totally made up estimations, but for the the mean American household income of $54,000, smart planning could be an additional $1000 in your pocket at the end of the year. Taxes may be unavoidable for most, but you have the advantage of knowing they are coming. Think ahead, plan out your expenses, and stop getting so many refunds.

I am right; the research proves it!

As a nurse, my wife is commonly asked what her opinion is on various procedures and methods and what the accepted research has to say about a wide variety of things. She almost always answers the same way, but a few nights ago (and for the first time ever) another nurse beat her to it by saying, "[...] they can make the research say whatever they want it to say [...]." This is an opinion shared by my wife and I, but few other people seem to realize this obvious assertion. Have you ever noticed how every side of every argument has research to back up their claims? We've heard it all. It would seem that everyone has an opinion they want heard, but no one wants to listen to anyone else.

My wife deals with a plethora or interesting topics at work concerning health care procedures. They can't all be right, can they? Well, yes, that is, depending on how they conduct their research. It all comes down to the selection pool. A few (hundred) years ago, surveying just the people that live in your town might have been sufficient for a scientific study, but in today's overpopulated society, there are far too many different types of people in different walks of life from different backgrounds for this to be effective. In any given major city in the United States, there are typically millions of people, but only some of them are from that area. Others moved from smaller towns or a completely different kind of metropolitan area, and others migrated from another country, continent, or (maybe some day) planet! Some are healthy; some are obese; some have children; some are single; some are in college; some have grandchildren in college; some are insane; some are insanely intelligent; some workout; some work from home; some don't work at all. I think you see where I am going with this. Every aspect of someone's life shapes their beliefs, ideas, thoughts, and even their health. Ideally, all of these variables could be used to further enhance a study - to show the differences in people of different cultures, ages, and origins, and they sometimes are - but far too often, these differences are used as a tool to skew the outcomes of a study.

As an engineer, I am no stranger to the scientific method. It was a staple of most of my education. The first step is obvious: ask a question. The second step is just as important, but often overlooked: do a bit of background research. It's the third step that really trips people up: form a hypothesis. And with that, it's game over - you have just asked the person conducting the experiment to have an opinion on the matter. Now, some people may be above such a complex, but most of us are at least somewhat prideful. Even if we don't show it in public, deep down inside, we all want to be "right." Having an opinion about something instantly turns us all into selective scientists - taking note of every little thing in our lives that might help to prove our point. It's this behavior that can all too easily slip into the formal research being conducted. Soon enough, a study is no longer about bettering humanity, but about making a statement or proving a point. Honestly, who wants to spend days, months, even years conducting research only to find out we were wrong from the start?

But then again, if someone isn't passionate about a topic, they probably aren't going to invest the time and resources to do a study in the first place. A random man on the street would probably never decide to start researching the effects of "pushing mag" on a laboring woman unless he works in that field, is close with someone who is pregnant, or had a bad experience with his own child's birth and is trying to find out what went wrong. Here is where the supposed solution would come into play: the independent research consultants. These are (unbiased) groups of people who are contracted to research a topic and present the results. But even this approach has its flaws, primarily, the paper trail. Who is asking them to do the research, and who is paying for the research to be done? If my entire research operation was being funded by a major pharmaceutical company and they asked me to conduct the effects of a new drug on the "average" human being, you better bet that on some sub-conscious level, even the most upright and unbiased researcher will have this thought lingering in the back of their mind: "I hope our results are favorable so the company doesn't pull our funding or cancel our contracts..."

Which brings me back to my original situation: the patient in the hospital asking a nurse what the research says. You would like to think that a hospital conducting research would have the patient's best interest in mind, but even those so called "non-for-profits" have a CEO who likes to make money, and there is always a chance that every study conducted has some monetary skew in place. All too often, the only reason something is done in a specific way is to save the hospital expense - not that the patient would ever see a reduction in their bill. Don't believe me? Talk to a labor nurse working at five different hospitals (not all in the same "network" of hospitals) and see what they have to say about the ancient art of child birth. Then again, maybe I'm wrong about all of this. I didn't exactly cite any research here...

An Excuse for my Absense

I know I've been a bit behind on my posts lately, but suffice it to say a lot has been going on. I have been playing catch up for a while, and I hope to be back up to speed in the new year. Thanks for sticking with me!

On Running...

I can't be the only one who thinks this... can I?

Oh Motivation, Where Art Thou?

Let's be honest... I am not very good at this whole blogging thing. I have a lot of information in my head that I would love to get out (to make room for more), but I am just never in the mood to do it. I did maintain a blog in college with some success, but that was back when free time was abundant and I was more in touch with my ... feelings. I guess I will just have to force myself into a routine - come up with some sort of schedule for doing this.

Have something you would like me to write about? Hit me up ... I could always use the inspiration!

Contact K.E.C.

What Exactly is a Robot?

Although there is no exact and accepted definition of "robot," I believe one to be an electro-mechanical structure that can perform tasks at least semi-autonomously. I have long since argued that the typical "robot" we think of as a walking, talking humanoid clone is incredibly far fetched, but I am surprised everyday with advancements in technology. However, I struggle to see how many of today's "robots" can really be classified as so.

For example: the Roomba from iRobot is an incredibly stupid machine that drives in circles avoiding obstacles, but it has a vacuum attached to it so it at least doing something productive. It needs no human input to function beyond turning it on, so it could even be considered completely autonomous. On the other hand, the killing machines seen on shows like the classic "robot wars" are no more robotic than a child's remote control car - they just happen to have spinning blades attached to them. Somewhere in the middle are the unmanned vehicles and drones currently used by the military. They are not yet capable of autonomous operation, but do work on a semi-autonomous level. 

Then again, so does an airplane. Think about it, a pilot pushes buttons and pulls levers and the plane flies. Would flying the plane from a remote location through use of cameras suddenly classify the plane as "robotic?" This is where I struggle with the labeling of much of today's technology. Modern vehicles are becoming more autonomous, for example, cars with Ford's "park assist" can somewhat park themselves. Are they then considered "robotic cars?" 

To me, the term robot does not apply to the capability or function of a machine as much as it does the intelligence and autonomy of the machine. I mentioned earlier that a Roomba is a "stupid machine," but at least it makes all of its own decisions, once a human has turned it on. Does a UAV decide to take off and spy on some area or fire a missile because it decided that a target was found? Or can it only do so when instructed to by an operator. 

Even though I label her as a 'robot,' by my own definitions, Flora is just a humanoid remote controlled apparatus. She had no sensory feedback - the arms moved in accordance to a pre-programmed loop, no different than the speed of a flashing light on some toy. Her mechanical makeup and appearance alone makes her no more robotic than a Volkswagen. With that in mind, if she had some way of sensing where her arms were or how full her flower basket had been and then been capable of making some decisions based on that data, an argument could be made that her semi-autonomy would classify her as robotic in nature.

Flora on her big day

As a further example of my point, when I push the correct sequence of buttons on the microwave, a light comes on, the tray spins, and the microwave radiation begins until a set time has passed, at which point it 'bings' and shuts off. An HVAC system even has sensory feedback. The machine makes its own decisions as to when to turn on and shut off. Is it robotic? Is it so different from the Roomba that drives around in circles until you turn it off? I just wonder what the magic line is it that separates 'robot' from 'remote controlled apparatus' or other automated equipment. I think our society's infatuation with the possibility of devices which can cook and clean for us has created a market for anything labeled with the R word.

The First of May

While many people around the world have celebrated today as "May Day," it is also known as "Law Day" here in the United States. This non-government holiday was first decreed by then President Dwight D. Eisenhower as a day to reflect upon and remember the importance of law in this great nation.

The First of Many - Part Two

This blog was created to supplement my primary website, Projects by K.E.C. I had intended on including a blog within that website for the purpose of allowing visitors an in depth look into the catacombs of my mind - a place to discuss the origins of technology, society, and existence  man's obsession with himself, and what I had for breakfast that morning.

At first, it seemed to work OK, but the formatting was odd, and the style was not what I had in mind. In the end, posting something became too much of a hassle, and so I rarely used it. That is where this site comes in. I don't see this blog as a separate site, but more of an extension. The content will continue to be relevant to whatever I decide relevancy to be on that particular day, but thoughts about matters that most of the population could not care less about are sure to flourish. So without further ado, I present the thoughts, theories, and things that keep me up at night!