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?

Why the Three Doors is Not Such a Difficult Problem

AL GREEN - TAKE ME TO THE RIVER

I posted an article yesterday entitled, "Critical Thinking and the Three Doors." I used a famous logic question as an example that I learned about examining problems. Trust, folks, that I am not mathematics whiz. Far from it. But one good reader questioned my method. They wrote: 


This is one of the world's most famously difficult logical problems, and many of the world's top mathematicians got it wrong at first. If you're going to test people's critical thinking skills, may I suggest that it may be be better not to choose a problem that has stumped Nobel-Prize winners and the world's best mathematicians? 


My only retort is to say that, "Yes, this might be one of the world's most famous logical problems but the fact that it stumped some of the world's top mathematicians and Nobel prize winners shows the extent of the poor critical analysis problem today and that even that these 'highly educated' people having poor problem solving abilities and highlights my original thesis in that "85% of all adults today show poor critical reading and analytical reasoning skills."


Like most, I got this wrong at first. But quickly understood it when I diagrammed it out. It was easily understood when it was first explained to me, because I was taught to diagram problems on paper first by my mother when I was a kid. Even though it is counter-intuitive, these things can take practice but when diagrammed are quite simple.


Try it yourself. Diagram out the three possible outcomes. 


Here's why, this is not a difficult problem and how diagramming things out on paper can help you to "see" what your intuitive mind misses.


Here's a graph showing you all possible outcomes of this game show problem. It is very simple and any 5th grader could have figured this out. The top graph , "Switch from Door 1"shows the possible outcomes if you picked door #1 and switched. You can see that, with all possible outcomes, you get a higher odds of winning if you switch. The bottom graph shows "Stay on Door 1." Staying show, with all possible outcomes, that you will have a 2/3 chance of losing if you stay. 


Like I said, this is simple and any diagramming of this problem would show you the answer. You choose door #1 in every example. In the top, you switch. In the bottom, you stay.

That so many of the world's top mathematicians can get such a simple problem wrong shows the sorry shape of our institutions today. Any elementary school child could graph this out on paper and see what the results are. 


This is also why the "America's top economists" were and are often wrong about the economic situation today. But that is another calamity for another day.


Don't believe that writing things down on paper is not a very simple way to solve problems? Well, it is, and I can prove it to you again. It's not difficult math. The try this one. The old boy, boat, chicken, dog and bag of seeds riddle.


It goes like this; You are a small boy. You have a tiny boat. You are on one side of a swift river. You need to cross the river but your boat is too small for more than you and one other item (the dog, chicken or bag of seeds).


If you take the dog first, the chicken will eat the seeds. If you take the seeds first, the dog will eat the chicken.


If you take the chicken first, fine, but then what happens when you bring over the dog (or seeds) and the have to return to pick up the other? No matter what, under this scenario, something must be left alone with the other.


Oh, and by the way, there are piranhas in the water so you cannot swim along side the boat. 


What do you do? 


I'll let you answer this by yourselves. I can say that if you pull out a piece of paper and do not trust intuition, the answer is simple. The problem is that too many people - even Nobel Peace Prize Winners - do not diagram things on paper and their intuition is completely wrong.


Some recent examples of Nobel Prize winners who are completely wrong might be Al Gore or Barack Obama. Need I say more?

Nowadays, Nobel Peace prizes are given out to people who are completely wrong

Earthquakes & Global Warming in this Little Shop of Horrors!

In a follow up to my article yesterday about today's sorry state of affairs whereby most adults are unable to critically read or judge information by use of analytical reasoning what they see / hear in the mass media. I'd like to expand upon that by posting and commenting on this completely ridiculous article that I stumbled upon soon after the Tohoku earthquake and tsunami and subsequent Fukushima nuclear accident.

LITTLE SHOP OF HORRORS

You'd think it would be just too completely insane and outrageous to try to link the natural disaster in northern Japan with Man-Made Global Warming (AGW) but this guy tries to do it. 


He is a miserable failure.


Actually, this is funny... Well.... it would be funny excepting far too many people will believe this to be true.


Alternet (a supposedly reputable "Alternative Internet publication" that actually still supports idiocy like AGW) reports that Man-Made Global Warming is causing these earthquakes since 10 million years ago. Gee, I didn't know that man was causing AGW 10 million years ago. Heck, I didn't even know man had cars and factories 10 million years ago. Just goes to show what great "science" you can learn from publication like Alternet:

"... scientists have for the first time released a study that indicates that man made changes to our climate are also quite probably effecting the movement of tectonic plates around the globe as well. The implications of their research are far ranging as well as frightening:

An Australian-led team of researchers from France and Germany found that the strengthening Indian monsoon had accelerated movement of the Indian plate over the past 10 million years by a factor of about 20 percent.


Read that again.  It says, "the strengthening Indian monsoon had accelerated movement of the Indian plate over the past 10 million years by a factor of about 20 percent." You call that frightening? Did you know the sun will burnout in about 4.57 billions years? Now that's scary! 


This scientist that they base this sensationalist nonsense also adds (in another article):

"Laffaldano stressed that his study did not mean that global warming would translate to stronger earthquakes happening more often, with the relevant patterns developing over "the order of millions of years."

"Of course earthquakes do occur at the boundaries between plates because of plate motions, but our work doesn't imply at all that we will see an increase in these types of events," he told AFP.

Gee.... Well, what does that mean? He just said 10 million years in the previous paragraph. That's a long time too.  Homo sapiens (that's us - in spite of your sexual preferences) didn't even appear on earth until about 120,000 years ago. How could anyone equate that with AGW? I mean, how could anyone with a brain larger than half a peanut equate that with AGW? 


Logically, I don't know. But the writer of this article tries to do it. 

Millions of years running fossil fuel guzzlers like this 150 million year B.C. Dino model has raped the environment and destroyed the landscape. Is it too late to reverse the Global Warming damage we've done? Many scientists say it is, "Yabba dabba doo?"

The article continues:

Lead researcher Giampiero Iaffaldano (sic) said Wednesday that although scientists have long known that tectonic movements influence climate by creating new mountains and sea trenches, his study was the first to show the reverse.


And where, pray tell is this guy's evidence? Not to be found in the article at all. The writer continues with this idiocy:

I am no scientist, but many scientists have been telling us that the changes we see are now locked in and will occur even if we ended all carbon, methane and other greenhouse gases today. 


Nope. You are right. As for the first point, no argument there. You are no scientist. You are also definitely not trained well enough to be a decent reporter who checks facts either. Many scientists have been telling us!? Oh, really? Like who, may I ask? Mr. Giampiero Laffaldano? No, he hasn't. In fact, upon checking, it looks like you, Mr. Writer (who is only named as "Steven D" on the credits - no wonder!) have been taking Mr. Laffaldano's research way out of context. Shame on you! Not only are you a crap writer, Steven D., you are dishonest too... No wonder you are too embarrassed or ashamed to put your real name on such drivel! 


In his report about this very same subject, that you are quoting, Mr. Laffaldano, says nothing about AGW. He only speaks about long term climate change in the terms of millions of years. I already pointed out that us humanoids have only been here for about 120,000. There's a pretty hefty difference between 120,000 and tens of millions... But hey! What's a few coins change amongst friends, right, Stevie? Here is a direct quote from Mr. Giampiero Laffaldano's own report: 

“The 100km-thick outer shell of Earth, the lithosphere, is divided into pieces called tectonic plates. Plates move in different directions at speeds in the order of centimetres per year, comparable to the speed of fingernail growth in humans.

“The significance of this finding lies in recognising for the first time that long-term climate changes have the potential to act as a force and influence the motion of tectonic plates," said Iaffaldano.

"It is known that certain geologic events caused by plate motions – for example the drift of continents, the closure of ocean basins and the building of large mountain belts – have the ability to influence climate patterns over a period of a million years.

"Now we know that the opposite holds as well: long-term climate change, or the natural changes in climate patterns over millions of years, can modify the motion of plates in a feedback mechanism.” 


Steven D., the writer of this tripe then goes on to say,


"We are now only at a point where the only valid debate the extent of the damage (sic) that will occur to life on this planet if we can end or do not curb greenhouse gas emissions and other human activities that are driving climate change."


We are now at the point "where the only valid debate the extent of the damage"? Atrocious writing. Simply terrible. Does Stevie mean, "Where the only valid debate is the extent of the damage?" or "Where only the valid debate the extent of the damage?" 'Valid,' in this case, I suppose, would be meaning the people 'who are qualified and not nuts.' I think. This sentence is so poorly written that I have a hard time understanding what the writer really wants to say.


The reason I am not sure what this clown, Steve D., wants to say is that, like yesterday's posting showed, here is another person who fails miserably at the basic skill of critical reading and analytical reasoning. This sort of article is laughable. No wonder he doesn't sign his name.


Too bad far too many people read this nonsense and believe it without examining it for faults and poor reasoning.


Seriously. How embarrassing.... Embarrassing for the writer and the gullible reader both. The writer can't be helped. But at least he's smart enough to know to hide his identity and lock the door when he writes this science fiction tripe. Too bad there will be far too may readers (one is too many) who will read this crock and use it as evidence of AGW. Pathetic. Really.

LITTLE SHOP OF HORRORS TRAILER (1986)