Drug Testing Results and Why Positive Results are Only 50% Dependable

Logic is based in math. Understanding numbers and how to interpret them helps us to sift through the rubbish. This rubbish comes from the mass media, politicians and from so many sources today. 

Johnny Thunders - Chinese Rock

I have to thank that hysterical old fool named Arnie Gundersen for making idiotic statements that have inspired this series of posts... like the one he made that I referred to in an earlier post: Metallic Tastes in Mouths Proves Nuclear Disaster in Japan! Or Does it?


There is substantial evidence of ongoing nuclear chain reactions. Another piece of evidence - as pointed out by nuclear expert Arnie Gundersen - is that there are widespread anecdotal reports of people in Japan and the West Coast of the United States reporting a metallic taste in their mouths:




When I first blasted Gundersen for saying something stupid, many people came out of the woodwork to defend him. They've all disappeared now. There's no defending such asinine statements anymore. I think Gundersen might need to see a doctor. This nonsense ranting sounds like old age or Alzheimer's.


This post is based upon Marilyn Vos Savant's best selling book, The Power of Logical Thinking - Easy Lessons in the Art of Reasoning … and Hard Facts About Its Absence in Our Lives. That sub-title is what's so important today. The absence of reasoning in our lives causes so much confusion, consternation and panic. Especially in these days of earthquakes, political uprisings, tsunami's, economic turmoil and nuclear accidents.


I can't possibly deal with all those issues in one small blog post. so I am focusing on the mathematical probability of drug testing to show you how people lie with numbers.


Perhaps I should call this post's sub-title: Why drug testing isn't all what it is cracked up to be....


Yesterday's blog was about critical thinking and a comparison using drug testing. In that post entitled


Radiation, Drug Testing, Critical Thinking, Analytical Reading and Probability I asked: 




"A particularly and important question today is that of testing for drugs. Suppose it is assumed that about 5 percent of the general population uses drugs. You employ a test that is 95 percent accurate, which we'll say means that if the individual is a user, the test will be positive 95% of the time, and if the individual is a nonuser, the test will be negative 95% of the time. A person is selected at random and given the test. It's positive. What does the result suggest? Would you conclude that the individual is highly likely to be a drug user?"

I think that most people would say that the odds of this randomly selected person, who tested positive for drugs, are 95% correct. This is a very common misunderstanding. The tests show that this person has a 95% chance of being a drug user. But the result of a one-time random test is way off from the actual odds of this person being a drug abuser. The chances that this person is a drug abuser are nowhere near 95%. Understanding this should make people who consider the results of drug testing great pause.

The correct answer to this test, once again, lies in logic and math. 

I hope some reader will be able to solve this puzzle.


I also gave a hint away at the bottom of that article saying that I hoped it would be a 50/50 chance that dear reader would come back tomorrow for the correct answer. Well, one smart reader, James, got the answer correct the first time. He wrote:


"Fifty-fifty indeed!

Perform this test on one hundred people. 95 of them will be non-drug users, but 5% of them will get false positives on the test = 4.75 people. 

Five people will be drug users and will get true positives 95% of the time = 4.75 people. 

So out of the 9-10 people out of 100 that this test will flag as positive for drugs, only half of them will actually be drug users.

That right?"


James is absolutely right. James! Move to the front of the class with honors! Even though the drug test is considered "correct" 95% of the time, it is still only correct, in this example, 50% of the time.


Here's the results. Once again, from The Power of Logical Thinking - Easy Lessons in the Art of Reasoning … and Hard Facts About Its Absence in Our Lives by Marilyn Vos Savant::


Here's how the "fifty-fifty" answer is determined. Suppose the general population consists of 10,000 people. Of those people, we assume for this problem that 95% of them (9,500) are non and that 5% of them (500) are users.


Of the 9,500 non users, 95% of them (9,025) will test negative. That means 5% of them (475) will test positive. Of the 500 users, 95% of them (475) will test positive. That means that 5% of them (25) will test negative. These are the totals:

There are 475 "false positives" and 475 "true positives", a total of 950 positives, so when we find an individual in that positive group, there's only a 50/50 chance that s/he's a user.

But let's suppose instead that a randomly chosen person tests negative. From the above calculation, we can see that there are 25 "false negatives" and 9,025 "true negatives" - a total of 9,050 negatives - so for an individual in that negative group, there's an overwhelming chance that s/he is not a user. 

Understanding the above can help anyone of us to be able to better filter information that we are receiving daily from the mass media. It is especially helpful when we are fed numbers that have no meaning such as "Radiation levels in Tokyo are up 400%!" That was a headline that we all read a few months back. 400% up from what? After some research some of us discovered that, even though radiation in Tokyo went up 400% it was still at half or even 1/4 the rate of Rome, Italy.


Nevertheless, the news caused fear and panic.


A better understanding of mathematics and its use towards critical thinking and analytical reading skills will do much for many people to calm their fears and to help them understand exactly what is going on.


It all reminds me of my favorite saying of Mark Twain:


"I'm an old man now and have known a great many troubles, but most of them never happened."

Radiation, Drug Testing, Critical Thinking, Analytical Reading and Probability

I've written extensively on the ridiculous nonsense that passes for news and how too many people in this day and age seem unable to filter through the crap and make a logical assessment of what they should and should not believe.

SHIRLEY TEMPLE - POLLY WOLLY DOODLE

A traditional American song about nonsense.

Yesterday's article was a good example of junk that was being passed for "news". In "Metallic Tastes in Mouths Proves Nuclear Disaster in Japan! Or Does it?" I wrote:


Once again, Arnie Gundersen and a bunch of illogical panic stricken fools say something stupid about Fukushima and radiation. 

They are now saying that there is "anecdotal evidence" of people having a metallic taste in their mouths and, from this, they draw the wild conclusion that this means there is an uncontrollable nuclear chain reaction going on at Fukushima. This nonsense has no basis in science, reality, nor does it have any evidence backing it up. It is fantasy. I has no real meaning to anyone who actually has more than two brain cells functioning.


If you do a random search today on Google, you can find some people who have now "drank the poison" and, in their uncontrolled paranoia have begun to believe that they, too, have a metallic taste in their mouths.


This "anecdotal evidence" is pure idiocy. Anecdotal comes from the word, Anecdote. "Anecdote" in the Merriam Webster dictionary is defined as:

: a usually short narrative of an interesting, amusing, or biographical incident.

"Anecdotal" is defined as:

: based on or consisting of reports or observations of usually unscientific observers <anecdotal evidence>

: of, relating to, or being the depiction of a scene suggesting a story 

"Suggesting a story"? Indeed.


Once again, this question comes down to a problem of critical reading and analytical thinking abilities. In the above case, concerning that clown Arnie Gundersen, I find it astounding that anyone, for even a split second, would consider this "metallic taste" and "anecdotal evidence" nonsense as proof of a problem (other than hypochondria). I also can't believe that this guy opens his mouth up and says this stupid stuff and then doesn't want to crawl back into a hole in embarrassment.


These problems repeatedly come down to a basic understanding of logic which lies in an even more basic understanding of math and probabilities. I'm not sure what the percentage probability of "Anecdotal" is, but I would put it at about 0%.


Anyone care to debate that point?


Here's a good question for dear reader to consider. It is from The Power of Logical Thinking - Easy Lessons in the Art of Reasoning … and Hard Facts About Its Absence in Our Lives by Marilyn Vos Savant:


"A particularly and important question today is that of testing for drugs. Suppose it is assumed that about 5 percent of the general population uses drugs. You employ a test that is 95 percent accurate, which we'll say means that if the individual is a user, the test will be positive 95% of the time, and if the individual is a nonuser, the test will be negative 95% of the time. A person is selected at random and given the test. It's positive. What does the result suggest? Would you conclude that the individual is highly likely to be a drug user?"


I think that most people would say that the odds of this randomly selected person, who tested positive for drugs, are 95% correct. This is a very common misunderstanding. The tests show that this person has a 95% chance of being a drug user. But the result of a one-time random test is way off from the actual odds of this person being a drug abuser. The chances that this person is a drug abuser are nowhere near 95%. Understanding this should make people who consider the results of drug testing great pause.


The correct answer to this test, once again, lies in logic and math. 


I hope some reader will be able to solve this puzzle. The correct answer is actually quite simple and can be done with a pencil and piece of paper or with common sense. Of course, like the metallic taste in mouths, the common sense method is much better and more fun.

In a weaselly attempt to get dear reader to come back to this blog I will post the actual percentage of this person being a drug abuser with a simple explanation tomorrow. 


I wonder what my odds are of etting you to come back tomorrow? 50/50?

Critical Thinking Quiz & The Three Doors

UPDATE AT BOTTOM


The other day, I wrote a blog post criticizing many in the adult population today because of their inability to read critically and exercise basic analytical reasoning. 

WEIRD AL YANKOVIC - I LOST ON JEOPARDY

The title of that blog was Critical and Analytical Thinking are Lost Arts Amongst Many of Today's Adult Population. I wrote:


Most unfortunately, I'm getting the impression that, judging from the comments I often hear and from reading comments on Social Media websites, at least 85% of the adult population are incapable of well-executed critical analysis and reading. We live in a society today whereby far too many people have lost the ability to perform even the most basic levels of critical/analytical thinking when it comes to what they see or hear on TV or what they read in print. This is a very sad situation. People are not able to extract facts from conjecture. They seem to be incapable of deeply considering the motivations of the people they see/hear or read on the mass media.
Proper critical analysis will always examine a person's possible motivations for what they say or write. Too few adults today seem able to exercise this most basic ability.  


I then went on in that post to give several examples of how this works (or doesn't work) in real-life situations. I especially thought it was important because of the recent Fukushima disaster and how many people panicked and fled Japan without thinking carefully through the problem before making any decisions on what to do. It had much to do with how people filter the information that we receive daily from the mass media and how people today seem to be unable to rectify numbers and their relation to what they mean to our lives.


Of course, again, I got many comments criticizing me and even some people wrote nonsense and humorous comments like, "I give your reasoning an 'F' for failure." Most of those comments were deleted because they were so poorly written or were just outside of commenting guidelines. Those sorts of comments are, I believe, mostly from the people who are believers of AGW or think that dolphin slaughter in Japan is a crime... These are people who are definitely blinded by dogma and cannot fairly see the forest for the trees. (I will write separately on that too later).


I did get some mail (to my private mail account too) that were supportive. Thanks.


Now, I'd like to do a very simple logic experiment with you, dear reader. The fact of the matter is that critical reading skills and analytical reasoning are all based on mathematics (thinking with the left-side hemisphere of the brain is for logic, reasoning and math). These mathematics are not difficult. They are, though, in many cases counter-intuitive.


Let's take this short one question quiz and see how you do.

You are a contestant at a game show. There are three doors in front of you. The doors are marked doors, "A", "B" and "C". Behind one of these doors is $1 million USD in cash. Behind the other two doors are ham sandwiches.


You are asked to pick one door. For the sake of this quiz, let's say that you choose door "A". The game show hosts then shows you that behind door "B" is a ham sandwich. He then asks you if you want to keep door "A" or switch to door "C".


Question: What should you do? Should you stick with door "A" or switch to door "C"? 


(scroll down for answer)
...
...
...
...
...
Answer: You should now switch to door "C" as door "C" now has a 2/3 chance of winning. Staying on door "A" is a bad choice because door "A" only has a 1/3 chance of winning.


Just because the host has shown you that behind door "B" is a ham sandwich, that doesn't make your original choice of door "A" a 50/50 chance of winning. 


It is unmistakable that switching will increase your odds of winning from 1/3 to 2/3.


Now, I expect that many will comment (I hope you do) so that I can help you to see that switching is the correct answer and guarantees a 2/3 chance of winning.... Think about it, in old movies guys would do the peanut under the cup gambling with suckers? How do you think they always won? They don't have to cheat.


UPDATE :


Here's a typical example of how the recent Fukushima nuclear disaster is used to spread fear by use of illogical reasoning. If anyone is bothered to investigate or think about it, they'd see that the chart below says many things:

Unfortunately, most people who view this chart and see the numbers and think, "Oh my God. Even Tokyo is under heavy radioactive fallout." The way this chart is drawn makes it look like all of Japan is under the area of dangerous radioactivity.

Look at Tokyo. It says, "0.064" microsieverts per hour. That sounds terrible, doesn't it? But what does that mean? Most people won't bother to think about it and will fear.

Let me give you an example of what this means.

Tokyo is experiencing 0.064 microsieverts per hour radiation. The typical one-way flight from Narita airport to New York is 190 microsieverts. If we must fully understand and gauge and compare our risk in Tokyo, then we must understand these terms and their relation.

So let's calculate the risk. The typical one-way flight from Narita airport to New York is 190 microsieverts. 

Now Tokyo is experiencing 0.064 microsieverts per hour radiation. Let's equalize that with our flight. What is our risk?

To calculate this very simple problem we divide 190 by 0.064. This equals 2,968.75 microsieverts. Divide that by 24 hours in a day equals 123 days. That means that the dose of radiation you get from living in Tokyo for 123 days is equal to the dose of radiation you get from one one-way flight from Tokyo to New York. 

- Thanks to Marilyn Vos Savant for the Monty Hall Dilemma in "The Power of Logical Thinking"


NOTE: I want to be the first one to admit that I had something wrong, or make a mistake. When I first posted this, I had miscalculated the radiation on the flight to New York. The flight to New York is 190 microsieverts per hour. It takes 10 ~ 11 hours to fly to New York. I had it calculated at 190 microsieverts total. So the amounts above are recalculated to show this error on my part. Sorry for the trouble.