Read posts about statistics

December 7

Lies, Damn Lies, and Statistics (Punkadyne Labs (Punkwalrus))

One of the lessons I remember from elementary school was a story about some guy who was a scam artist. It was in a film about how you can make statistics lie. I don't recall who put it out, but it was in some 1970s hygiene film format geared for my age group at the time.

The story was about this detective who wanted to expose someone he thought was scamming potential business owners. He'd loan money to music stores, and make them into a sort of franchise for his company name. Then the business would do poorly, and the owners would need bailed out. "Being kind hearted," he'd buy them out at half their investment, when by all rights, he could legally toss them out on the street with nothing. And this would repeat with someone else.

One set of former owners said that the scammer would supply them with lists of what music people liked. They would poll several thousand people from all over town, and ask them what kind of music they liked and bought. You could even verify the names they provided on the sample. So, based on this untapped market, these franchises would stock a lot of cello music. And very few people bought it. And so they'd be forced to go out of business. Now, most of you may be thinking you know where this is going: the list was rigged, and the sample pollers were plants. They weren't. In fact, they did sample several thousand random people from all over town. And 98% of them said they liked cello music. "Not enough places have a wide selection of cello music."

So, as you can imagine, that's quite a stretch that 98% of the population like cello music. So how did they get those perfectly legitimate figures?

They asked people leaving cello performances at the local music hall.

This lesson is the key to statistics. They can be easily manipulated. They are lies that someone will claim is fact because it involves math. "Aha," you say, my little nerdobites, "what about in a lab? Where they have controls and shit?" No, you have missed the point. Let's take a pretend controlled experiment.

You have three sets of mice exposed to the exact same environment, except one set listens to rock music all the time, the second set listens to classical music all the time, and the third listens to no music. After two weeks, you observe that the behavior of the classical music mice are more relaxed and stress free than no music, and the rock music mice are freaking out and one of them even dies. That's the end of your math right there. This is as far as you can go with this experiment and still stay objective.

But most people would extrapolate that rock music is unhealthy. One of the mice died! And classical music made them all calm. Which would you choose to play for elevator music?

STOP RIGHT THERE!

How many thought, even though they may have chosen the opposite just to defy me, "classical music?" Eh? For a second, you probably thought, "classical," and a few of you may have immediately stopped thinking and said, "I bet I am about to be tricked. That Punkie, always setting me up!" (Hopefully you did not say this aloud at work).

Now why would most people choose classical music? Think hard for 1 minute.

BZZZT! I tricked you. Look at that last sentence. "Now why would most people choose classical music?" Hmmm... see it? "Now why would most people choose classical music?" See the subtle trick? I put the suggestion right in the sentence. I suggested, totally pulling out of my ass, "most people." Did I say most people choose anywhere? Did I link to some survey? Show a scientific fact? Even have a lousy footnote or bibliography? No. And that's how I just influenced most of you.

I am chuckling at a few of you who are still arguing in your head about rock mice versus classical mice. Right before the experiment, I said "Let's take a pretend controlled experiment." It never happened. And look how I took that pretend mouse experiment and applied it to humans in elevators. In fact, that whole thing? Completely made up. Now, maybe someone did have that experiment, it sounds like a thing they'd have on Mythbusters. But while this seems like a pure experiment if someone did this, think again.

- What rock music? What classical? There are many types.
- How do we know it was the music, and not say, the frequency of the notes?
- How do we know what volume they played at?
- Why didn't we add bagpipe music? Or country? Or Yodeling?
- Why did we choose mice?
- Why did we do it just once? Why two weeks?

And so on. There's an old joke about experiments and preconceived notions.

A scientist trains a frog to jump at a command. "JUMP!" he screams, and the frog jumps. One day, he cuts off a leg. "JUMP!" he screams, and the frog jumps, but not as far. The next day, he cuts off another leg. "JUMP!" he screams, and the frog kind of does a hop-crawl. The next day, he cuts off the remaining two legs. "JUMP!" he screams, and the frog does not move. "My conclusion of this experiment," he writes in his journal, "is that when you cut off all the legs, the frog goes deaf."

So why this post? Because the media is using them extensively for the upcoming election. Penn and Teller did a bit on it that further explains my point.

Posted in: lies , penn and teller , polls , statistics
November 11

First exam result is in (Kilala.nl (Cailin Coilleach)) by Cailin Coilleach

I just checked Osiris (my school's online student administration site) and found my first test result.

Statistics 1 came back a G, which is equivalent to a 7, or a 7,5 if I'm not mistaken. My expectations were spot on :)

Posted in: college , exam , results , statistics
September 25

Got my first partial grades (Kilala.nl (Cailin Coilleach)) by Cailin Coilleach

About a week ago I turned in my first two reports for "Statistics 1 - Didactics".

The first report focused on maths education using the Getal en ruimte (Numbers and space) method. My final conclusion was that G&R; is a nice enough method, teaching students the whole gammut of statistics. IMHO, the big downside to the Getal en Ruimte books is that they're so damn distracting. Each page is a colourful, multimedia explosion. Each assignment and piece of text has markers/identifiers in the margin to further confuse matters.

The ironic thing is that I used the same G&R; series in high school. Back then they were awesome books: clear, transparent, not too hectic and a joke here and there. Things have changed a lot since I was a kid.

The second report covered the final terms for maths education in VMBO. I couldn't get my hands on all of the required books, but I managed to wing it. The Getal en ruimte method proved itself again for VMBO, readying the student for his final terms. I think the books may have glossed over a few terms a little lightly, but most students should be fine for their exams.

Both reports received a "ZG" score which translates into "Very Good". Awesome! :3 I'm definitely going to try my best to keep this score up!

Posted in: college , didactics , grades , reports , statistics
September 22

The Monty Hall problem (Kilala.nl (Cailin Coilleach)) by Cailin Coilleach

My white board, with decision trees.
For one of my school assignments I was asked to write three class openings for the subject of statistics. The object of a class opening is to draw in the students, to capture their attention and to motivate them.

The opening I presented at school involved the McNuggets problem (aka the Frobenius problem). It was well received, though most of my class mates thought it better suitable for a class on analytical math. I tend to agree with them now.

One of the other openings I've designed involves the famous Monty Hall problem. The one that involves a gameshow, three doors, two goats and a car. Ring a bell?

Because this problem is so counter-intuitive it tends to throw a lot of people off. Their gut instinct tells them that the chance of winning a car (after revealing one of the goats) should be 50%. They are unfortunately incorrect.

Before we continue, some of you may enjoy a snippet from the TV show Numb3rs. The character of Charlie Eppes doesn't explain the solution very clearly, but does make a nice job of explaining the problem.

Numb3rs-MontyHall.mov

I tried to come to the proper solution by myself by using a decision tree (boom diagram in dutch). It took me a while, but I got there :) My tree looks a bit different from the one Wikipedia shows (linked above), but that's because I use two trees instead of combining them into one.



Going from left to right:
* The original tree, unconstrained, given that you get two choices.
* The gameshow host takes away one of the goats. He asks you whether you want to switch doors.
* The decision tree, should you stay with the door you chose.
* The decision tree, should you decide to switch doors.

The red X-es show the option taken away by the host. The purple X-es show the option taken away by your own choice.

Yes, it's counter-intuitive, but switching doors after having one goat revealed IMPROVES your chances. Instead of having a 1:3 chance, you now have 2:3! Nice!

And this is why I think this problem would make a nice opener for a high school course on statistics. It stumps the kids, makes them curious and them amazes them :)

Posted in: boom diagram , decision tree , monty hall problem , statistics , statistiek
September 11

XKCD: statistics and the dating pool (Kilala.nl (Cailin Coilleach)) by Cailin Coilleach

A comic joking about statistics and dating


Funny that this comics should come up on XKCD, just while we're studying statistics at school.

I love the XKCD comics. Just how mr. Munroe succeeds in making stick figures so emotive is beyond me!

Posted in: dating pool , maths , statistics , xkcd
September 9

Slugging through my homework (Kilala.nl (Cailin Coilleach)) by Cailin Coilleach

Wow, this is a lot of work :)

Yesterday I raced through a large part of my first dossier assignment for Statistics 1. The didactical part of the course, that is. I'm about halfway through that assignment, though what remains will take more effort than what I did yesterday.

How do I know this? Because the second part of that assignment requires that I work through each maths assignment that I picked for my report. And judging by today's progress through the other part of Statistics 1 (the real maths), I'm going to need a long while.

My homework for Monday said that I'd need to study paragraphs 1.0-1.3 and 1.4-1.6. Sounds rather simple right? Well, it looks it too, since each paragraph is only two pages. However, looks can be deceiving since so far I've needed about an hour-and-a-half per paragraph! Ouch!

Talk about underestimating the workload! Tonight's gonna be an all-nighter.

Luckily, productivity blog LifeHacker provided me with something useful today! They posted about the why and how behind power naps. I took one this afternoon before studying and I'll take another one around 20:00.

EDIT:
Meanwhile, the cat's asleep on her pillow. She's actually snoring! That's so cute! <3

Posted in: college , didactics , homework , instituut archimedes , statistics