Tag Archives: Mathematics

Have the Laws of Probability Been Broken?

I've been trying to finish my next post involving a case study of the misuse and abuse of statistics to claim to prove global warming skeptics possess certain negative traits (my last post regarding this can be found here). Unfortunately, a number of things are getting in the way. Of special note is it's difficult to talk about statistics as I've largely lost faith in the laws of probability.
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Statistical Woes - Impossible Results

I've owed you guys a post for a little while now, and I apologize for how long it's taken. I just can't get past a certain problem. As you may recall, I recently discussed how "correlation is meaningless" in relation to a paper which claimed to demonstrate climate change "deniers" possess certain characteristics. For a quick refresher:

The reason the authors can claim there is a "statistically significant" correlation between these two traits is they collected almost no data from anyone who "denies" climate change. The approach the authors have taken is to draw a line through their data, which is how you normally calculate the relationship between two variables, then extrapolate it out far beyond where their data extends.

There are a lot of ways of describing this approach. When I've previously said correlation is meaningless, I used an example in which I demonstrated a "statistically significant" correlation between belief in global warming and support for genocide. It was completely bogus. I was able to do it because I used the same approach the authors used. Namely:

1) Collect data for any group of people.
2) Determine views that group holds.
3) Find a group which is "opposite" the group you study.
4) Assume they must hold the opposite view of the group you studied on every issue.

This will work with literally any subject and any group of people. You can reach basically any conclusion you want because this approach doesn't require you have any data for the group of people you're drawing conclusions about.

Today I want to move beyond simple correlation coefficients and get into some of the more complex modeling the authors performed. There's a problem though. You see, the results the authors published are impossible to achieve.
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Statistical Woes - Correlation is Meaningless

I've written a post titled, "Correlation is Meaningless" once before. It makes the same basic point I made in a recent post discussing the PhD dissertation by one Kirsti Jylhä. I'm going to continue my discussion of Jylha's work today to examine more of a phenomenon where people misuse simple statistics to come up with all sorts of bogus results. In Jylha's case, it undercuts much of the value of her PhD.
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Establishing Competency

A couple months ago I contacted a scientist asking to examine the data used in three papers which made up the bulk of her PhD dissertation. The initial response contained this:

Thank you very much for your email and interest in our publications.

We follow ethical guidelines from the American Psychological Association, and we are happy to share our data to other competent researchers. Would you please indicate your background and outline how you plan to use the data?

Which struck me as odd as I have no idea how one would determine which people are "competent researchers." I was pessimistic about this response as it seemed like this might be used as an excuse for not sharing data with me, but fortunately, the issue of whether or not I am a "competent" researcher never came up again.

After examining the data for these three papers, I came to the conclusion the papers were fundamentally flawed in a way which invalidated their analysis and conclusions. I informed the author of this thesis of my concerns and tried to give her time to examine the issue privately. I believe several months was long enough so now I'd like to discuss the matter in public. Hopefully, this will demonstrate I am in fact competent.
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The Laws of Probability

I've long had a nagging suspicion the universe isn't as random as we are led to believe. I don't attribute it to anything. I don't claim what I see is evidence of a divine plan or the intervention of celestial beings. I just can't shake this feeling the things I see aren't as "random" as they ought to be.

Is that crazy? Maybe. Maybe not. There is no inherent reason the universe must be random, but the idea a person could actually identify non-randomness in it is... difficult to believe. Humans are too prone to biases in how they perceive and remember things to expect them to reliably discern the difference between "random" and "non-random."

I get that. I really do. Still, I can't help but wonder if what I see is really random. Continue reading

Strange Comparisons

Today I am going to discuss something I find confusing, not because it is confusing but because so many people don't seem to understand it. To see what I'm referring to, look at this tweet:

If you follow the climate debate, you've likely heard this claim before. Part of the global warming debate is figuring out how much influence humans are having on the planet's temperatures. This tweet shows a "mainstream" position, that humans are causing all of it and more. You can find this argument posted in many locations. For one example, you can look here to see an argument humans might be causing as much as 160% of global warming.

I'm not going to delve into that today. People are so polarized on climate issues it seems most people will agree with you if you're on their "side" and disagree with you if you're not. I want to avoid that trap. I want to avoid it because what's wrong with that argument has nothing to do with climate or how it might change. It's entirely about logic and forthrightness.

Put simply, it is nonsensical and misleading to say humans have caused 110% of global warming just as it would be nonsensical and misleading to say Black people caused 894% of Hillary Clinton winning the popular vote in the recent United States presidential election.
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A Mathematical Interlude

So if you've read my last few posts, you can probably tell I could use a bit of a break. I was considering taking a few days off. I probably should. I just don't know if I could bring myself to. So instead, I'm going to try doing something different. I'm going to talk about math.

You might not know it, but I love math. I think math is beautiful. One of my biggest regrets in life is I never got much formal training in math. Even so, I think I still understand it in a more fundamental way than the average person. That's because to me, math is more philosophical than practical. I like the logical structure it imposes on arguments. I like how it makes you think in a rigourous manner.

So today I'm going to discuss math. It's about some work by Richard Tol, and if you've followed my blog, you'll know there is history there. That's not important though. The data errors previously found in Tol's work aren't important either. All that matters is the implicit argument found in one of his papers: the less data you have, the more certain you are of your results.
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56% of Americans are in the Top 10%

Today I saw a tweet about income inequality in the United States. I responded with a factoid I came across a few weeks ago:

I thought it was interesting. We're told it's bad half of all American income goes to the "top 10%." However, the roster which makes up the "top 10%" is different each year. If you look at everybody in it, not just the people for one year, you find the "top 10%" actually includes 56% of Americans.
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