Wednesday, May 17, 2017

Statistical Fallacies - Carver

While we were in Ireland, we went to Blarney Castle. What you need is a bit of background information. The story goes that Queen Elizabeth I was with the owner of Blarney Castle. Legend has it that she said about what he was saying, "This is all blarney! What he says, he never means!" So that basically defined the word "blarney."

A sign in the Blarney Castle was saying that Winston Churchill kissed the Blarney Stone. Later, he went on to make great speeches.

In Statistics, this is a selection bias. There are others who were very eloquent and never kissed the Blarney Stone. I also suspect that there was someone who kissed the Blarney Stone and wasn't very eloquent, even afterwards. This is basically choosing the specific people who kissed the Blarney Stone and were very eloquent. I said it was blarney. My Dad already made a blog post about the selection bias in Cape Town. He also made a post about the Blarney Castle. However, this is not nearly so bothersome as the second fallacy I will point out because this one was about a legend.
Selection Bias Blog Post
Blarney Castle Blog Post

Also in Ireland, we went to Waterford and toured the Waterford Crystal Factory. We saw how the crystal was made and blown, and how someone drew in pen on it so that someone else would know where to carve on it. We saw how it was polished. We learned that it only takes seven minutes for the standard design of vase to be made from start to finish. We learned that it takes six months to make a crystal guitar. We learned about the history of the factory.
Spinning the glass

Spinning the glass continued

Crystal Clock

Look! The pendulum works!

video video

All over were signs about what was happening. And one of them said that the glass is heated at 1200 degrees Celsius, 12 times the boiling point of water. But that's not true. In Statistics, there are two types of Interval-Ratio Data (data that is measurements), Ratio Data and Interval Data. Something is Ratio Data if division makes sense. In other words, if zero is the lowest it can be, then it is Ratio Data. One example is height. If you are six feet tall, you are twice as tall as someone who is three feet tall. Interval Data is Data that is not Ratio. One example is years. The year zero is not the start of all time. Therefore, the year 2000 is not twice as far along in time as the year 1000. Similarly, you can have negative degrees Celsius. So Celsius is Interval Data. Adding and subtracting makes sense but multiplying and dividing doesn't. Let me prove my point. 1200 degrees Celsius is 2192 degrees Fahrenheit. And water boils at 212 degrees Fahrenheit. This would indicate that it is heated at approximately 10.34 times the boiling point of water. These conflict. The real way to do it would be to convert everything to Kelvin. 0 Kelvin is the coldest anything can get. Kelvin is Ratio Data. 1200 degrees Celsius is 1473.15 Kelvin. Water boils at 373.15 Kelvin. So in truth, the glass is heated at approximately 4 times the temperature of water. That is two-fifths of what they said (because that is Ratio Data.) And when they put it on a sign, they should have it correct. Now you know about Ratio vs Interval Data and you will know when there is a mistake like that.

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