Basic Statistics: Classical Measurement Theory

What is classical measurement theory? It’s a fancy way of saying, “How badly did we screw up our data?” Something a lot of statisticians find themselves saying daily (I’m just guessing. After all, I’m not a statistician myself).

No collected data is without errors. You might even say, “To err is data.” But just because it’s not perfect does not mean that it’s not useful – at least, if the errors are correctly identified. That’s what classical measurement theory helps with: identifying the errors.

Understand everything so far?

Let’s keep going.

Here’s the formula:

X = T + E

Here’s what you need to know: It requires three parts, observed measurementtrue score, and error. X represents the observed measurement, which is the sum of T (true score) and E (the error).

Let’s create an example. Let’s say you measure a cup of water. The measurement shows that the cup contains 8 ounces of water. However, you know that the true measure of water is 2 ounces less. You would then plug those numbers into the formula like so,

8 = 6 + 2

See? It’s simple. Unfortunately, both T and E are hypothetical, since in the real world you would never know the truth value of measurements, and can only make estimates about whether the data is correct or not.

Congratulations, you just took a baby step to be a master of statistics. Give yourself a pat on the back. You deserve it.

The Functionality of Stoicism.

I recently started reading Seneca to learn more about Stoicism. I found myself awestruck by the clarity of his words and the directness of his style. In a world where philosophy is so muddied by flowery and circular rhetoric, his straightforwardness caught me a bit off guard. It was, then, not surprising to me when I learned that the philosophy he subscribed to was just as functional and direct.

The stoics believed that life itself is about maximizing function and living life “according to nature”. Since life is already short, one’s goal should be to make progress for progress’s own sake. To quote the former Caesar of the Roman Empire, Marcus Aurelius: “Waste no more time arguing about what a good man should be. Be one.” It’s a philosophy that strives to promote urgency in doing good in the world. It essentially comes down to, “Live meaningfully and excellently, for tomorrow we die.”

This sense of urgency is not meant to cause panic. Panic is not very stoic-like. Instead, Stoicism is meant to promote detachment from things that are not controllable. You can’t control death, therefore you should not fret over it or let it prevent you from doing things that you know in your heart are right. You should live for the sake of excellence, but not let excellence preventing you from living well. It’s the perfect balance.

What can I say? The dots are connecting now. I believe I understand the purpose of the entire philosophy more than I ever have. It’s a good feeling.

Basic Statistics: Discrete Data Vs. Continuous Data

You might say that discrete data isn’t very extraverted. It likes to sit by itself, isolated from the overly-complicated. Discrete data is a minimalist, and infinity is the enemy. Basically, anything that has a reasonably limited number of options is discrete.

The of sides on a dice? That’s discrete data. Available space on my flash drive? Discrete. Why? Because there’s only a certain number of available numbers that would work as a solution (e.g. there’s only 64 or less megabytes of storage on a 64 megabyte flash-drive).

Discrete data is the complete opposite of continuous data. Whereas discrete data is defined as something of reasonably limited possibilities, continuous data isn’t limited in possibility. Unlike discrete data, continuous data loves large amounts of possibilities and complicated muck (why do I seem so biased against continuous data? What has it ever done to me?). Either way, the differences are good to know.

Discrete Data: Reasonably limited in possibility.

Continuous data: Data that can take any value.


Basic Statistics: Nominal Data

What on earth is nominal data? The term itself is intimidating, yet its meaning is astonishingly simple.

Ever notice how sometimes we use words to describe things that don’t really mean anything by themselves? For instance, we use words like man and woman to describe different sexes (although that might change soon). But do the titles actually mean anything on their own? What if they were switched around? If we called men, women and women, men, would there be any real difference? Probably not. The words themselves are arbitrary titles we chose to classify different kinds of people. That’s nominal data.

To put it briefly, nominal data is data where subjects are merely allocated to distinct categories for the specific use of classification.

Product Repackaging, Companies, and Snuggies.

Successful companies aren’t necessarily about creating new products. They’re mostly about finding creative ways to repackage old ones.

When we think of a successful company, we automatically think of a massive company that disrupts entire industries with groundbreaking new products or services, like robots, artificial intelligence, etc. We have a tendency of thinking that successful companies create revolutionary new products just like Apple, Amazon, and Google did. However, nothing could be farther from the truth.

Big companies with revolutionary new products are rare. That’s because it’s much harder to “reinvent the wheel” than it is to simply create something that already exists. Most companies tend to “repackage” old products by selling them in a way no one ever thought of before.

Take the Snuggie for instance. Don’t lie, you’ve seen a Snuggie before. It’s fun. It’s fluffy. It’s comfy. But it’s by no means “new”.

Before its popularity as a product exploded in mid 2008, many other companies had tried and failed to launch similar products. Sleeved blankets had been around for many years before the Snuggie, but nobody wanted to buy them.

Then Snuggie started branding the product as a new “cultural phenomenon”. Suddenly everybody wanted one, and now they’re for sale almost everywhere. I’m wearing one now.

No, successful companies don’t have to offer new kinds of products or services. They just have to sell old products in brand new way.

Read lots, but not too much

Reading a lot is just fine, but spending all of your time reading is a waste. Those who read too much prevent themselves from incorporating what they’ve read into their own lives.

Reading is about temporarily trading places with someone else. You’re literally choosing to look at the world through the author’s eyes the moment you pick up a book. It’s an extremely helpful tool for self improvement. However, when you start reading too much, all of the valuable information you sifted through and collected starts becoming worthless.

In the words of the evil dictator, Adolf Hitler, “Reading is not the ends in itself, but a means to an end.” Start incorporating. If you read a lot but incorporate nothing, then you’re missing the entire point of reading altogether.

An Old Man, Death, and Your Character

There are a lot of things in life that you can’t control no matter how hard you try. When it comes to things like weather, politics, crime, or sometimes even your own destiny, you might be completely powerless. But there is one thing that you will always be able to control, and it’s the most important: whether or not you’re a virtuous man.

A few years ago, I remember hearing a story about an old man who lived in a small Mexican village. At first glance, he would’ve probably seemed uninteresting. He wasn’t married, owned no property, had no education during his lifetime – but he didn’t let those things prevent him from doing what he knew in his heart was right.

The old man always wanted to be on the side of the angels. He would never let anything slide… ever. If he felt he had taken advantage of someone else, he would apologize and set things straight immediately even if it was inconvenient for him. A neighbor finally asked him why he always went out of his way to deal with trifles. The old man’s response was clear and powerful: “My word and my character are all that I have, and I’ll be damned if I lose control of ’em before I die.”

It’s easy to feel powerless in this big world. It’s even easier to just give up. But no matter what happens, your character is something only you control. Even if the other parts of your life suck, whether you go to your grave a virtuous man or not depends entirely on you.

The Key to Writing

“The art of writing is the art of discovering what you believe.” – Gustave Flaubert

Nothing gives me more satisfaction than being able to organize my thoughts well enough to put them down in words. I find that trying to explain ideas helps me get a better understanding of how much I really know.

If you find it difficult to write about what you believe, it’s not your writing skills that are at fault – but your lack of beliefs. That’s because writing itself is easy. But having something worth writing about? That’s the tricky part.

End Those Bad Habits

The reason bad habits seem so harmless is because they usually are. Most of the time they can be easily fixed. If they aren’t fixed, that’s when you should really start to worry.

Bad habits exist only if you let them. If you purposely choose to ignore them, it’s your own fault and reveals a lot about your character.

Buddha once wrote, “He who does not rouse himself when it is time to rise… never finds the way to knowledge.”

It all essentially boils down to this: People too lazy to fix their flaws are people too lazy to succeed.

The Purpose of It All

If you’re going to do anything in life, you better give it your best shot. You won’t be given any second chances once your time runs out.

You have a window of opportunity to leave behind something beautiful – whether it be quality work or simple bits of wisdom for the next generation. Anything, so long as it has a positive effect on the world.

It says in the Bible that each of us are expected to be good stewards with our lives. In Mathew 13:12, it even says, “Whoever does not have, even what they have will be taken from them.”

The Bible is very clear about our purpose. Life is about contributing and accumulating; getting things worth having and giving things worth giving.