August 31st, 2018 (Permalink)
The Puzzle of the Seven Locks
Good day. A stolen item code-named "the MacGuffin" is being held in a safe inside the embassy of a foreign power. Of course, the safe itself is locked, the MacGuffin is kept inside a locked box within the safe, the office in which the safe is kept is locked, the floor on which the office is located is locked, the embassy building itself is locked and, finally, the embassy is surrounded by a double wall with two locked gates. All of these are combination locks.
This means that there are seven locks that you and your team will have to pass through in order to retrieve the MacGuffin. Luckily, we will provide you with a top secret combination detector gadget that has a 90% probability of opening any combination lock. Unluckily, each of the locks you must pass through is connected to an alarm that will go off if the gadget fails to open it. Should the alarm go off, the embassy guards will surely catch you or other members of your team.
Your mission, should you choose to accept it, is to retrieve the MacGuffin from the locked box in the embassy safe. It is more important that you and your team not be caught than that the MacGuffin be retrieved. As always, should you or any members of your team be captured, the Secretary will disavow any knowledge of your actions. This message will self-destruct in five seconds. Good luck.
Should you accept this mission?
August 28th, 2018 (Permalink)
New Book: Factfulness
This new book is by the late Hans Rosling1, his son Ola, and the son's wife Anna Rosling Rönnlund. Hans Rosling was a physician and medical researcher2, but was probably best known―in America, at least―for his TED talks about the state of the world using animated statistical charts3.
"Factfulness" is a made-up word that means: "“The stress-reducing habit of only carrying opinions for which you have strong supporting facts4.” Like the Pew survey discussed here recently5, the book begins with a short quiz. You can take it online6, and I recommend that you do so, if you haven't already, before reading further.
Here's what the authors have to say about how people do on the quiz:
…[I]f you did badly on this test, you are in very good company. Over the past decades I have posed hundreds of fact questions like [this], about poverty and wealth, population growth, births, deaths, education, health, gender, violence, energy, and the environment…to thousands of people across the world. … [M]ost people do extremely badly. … Perhaps you think that better-educated people would do better? … I certainly thought that once, but I was wrong. I have tested audiences from all around the world and from all walks of life: medical students, teachers, university lecturers, eminent scientists…. These are highly educated people who take an interest in the world. But most of them…get most of the answers wrong. Some of these groups even score worse than the general public…. Everyone seems to get the world…[n]ot only devastatingly wrong, but systematically wrong. By which I mean that these test results are not random. They are worse than random: they are worse than the results I would get if the people answering my questions had no knowledge at all.7
What can explain results that are worse than random?
Why was this ignorance about the world so widespread and so persistent? We are all wrong sometimes…but how could so many people be wrong about so much? Why were so many people scoring worse than the chimps? … I realized the problem couldn't simply be that people lacked the knowledge, because that would give randomly incorrect answers―chimpanzee answers―rather than worse-than-random, worse-than-chimpanzee, systematically wrong answers. Only actively wrong "knowledge" can make us score so badly.8
As a result, the Roslings' began looking for sources of these systematic mistakes, and have rediscovered some of the fallacies and cognitive illusions previously discovered by logicians and psychologists. This is an unfortunate duplication of work, but it's good to know that researchers working independently arrive at similar conclusions. However, instead of calling them "fallacies" or "biases", the Roslings call them "instincts":
The human brain is a product of millions of years of evolution, and we are hard-wired with instincts that helped our ancestors to survive in small groups of hunters and gatherers. Our brains often jump to swift conclusions without much thinking, which used to help us to avoid immediate dangers. … We have many instincts that used to be useful thousands of years ago, but we live in a very different world now.9
The first ten chapters of the book, after the Introduction, discuss ten of these "instincts". As with all new books discussed here I haven't read this one yet, so I'm not sure what some of the "instincts" are. What I write below is based on dipping into the book using Amazon's "Look Inside!" feature:
- Chapter 1: The Gap Instinct: This is not the instinct to shop at "The Gap", but black-or-white thinking10, which is the tendency to divide things into two mutually-exclusive categories with a "gap" between them.
- Chapter 2: The Negativity Instinct: "…[O]ur instinct to notice the bad more than the good. There are three things going on here: the misremembering of the past; selective reporting by journalists and activists; and the feeling that as long as things are bad it's heartless to say they are getting better.11"
- Chapter 3: The Straight Line Instinct: This appears to be straight line extrapolation, that is, the tendency to extend trends in straight lines, though often they follow curves.
- Chapter 4: The Fear Instinct: The media exploit our fears in ways that lead us to be overly-fearful:
…[H]ere's the paradox: the image of a dangerous world has never been broadcast more effectively than it is now, while the world has never been less violent and more safe. … If we look at the facts behind the headlines, we can see how the fear instinct systematically distorts what we see of the world. … Fear can be useful, but only if it is directed at the right things. The fear instinct is a terrible guide for understanding the world. It makes us give our attention to the unlikely dangers that we are most afraid of, and neglect what is actually most risky. … The world seems scarier than it is because what you hear about it has been selected―by your own attention filter or by the media―precisely because it is scary.12
- Chapter 5: The Size Instinct:
You tend to get things out of proportion. … Getting things out of proportion, or misjudging the size of things, is something we humans do naturally.13
- Chapter 6: The Generalization Instinct: Sweeping generalizations, perhaps?
- Chapter 7: The Destiny Instinct: Am I fated to find out?
- Chapter 8: The Single Perspective Instinct: I can't see this chapter from my current vantage point.
- Chapter 9: The Blame Instinct: It's Amazon's fault that I don't know what this is.
- Chapter 10: The Urgency Instinct: I can't wait to find out.
The Introduction ends with the following stirring words:
So here is this book. It shares with you the conclusions I finally reached―based on years of trying to teach a fact-based worldview, and listening to how people misinterpret the facts even when they are right there in front of them―about why so many people, from members of the public to very smart, highly educated experts, score worse than chimpanzees on fact questions about the world. … This is a book about the world and how it really is. It is also a book about you, and why you…do not see the world as it really is. … So, if you are more interested in being right than in continuing to live in your bubble; if you are willing to change your worldview; if you are ready for critical thinking to replace instinctive reaction; and if you are feeling humble, curious, and ready to be amazed―then please read on.14
I, for one, am ready.
- He died last year.
- Hans Rosling, Ola Rosling & Anna Rosling Rönnlund, Factfulness: Ten Reasons Why We're Wrong About the World―and Why Things Are Better Than You Think (2018), "Biographical Notes". Subsequent page number citations are to this book.
- Here's a good one, but don't watch it until after you take the quiz linked in note 6, below: Hans & Ola Rosling, "How not to be ignorant about the world", TED, 9/11/2014.
- "Factfulness", Gapminder, Accessed: 7/18/2018.
- Fact Vs. Opinion, 6/22/2018.
- "Gapminder Test 2018", Gapminder, Accessed: 7/15/2018.
- Pp. 6 & 8-9, emphasis in the original.
- Pp. 10-11.
- P. 15.
- The Black-or-White Fallacy.
- P. 65.
- Pp. 107 & 122-123.
- P. 128.
- Pp. 13 & 17.
August 17th, 2018 (Permalink)
A Cherry-Picking Study1
One key to understanding reports of medical, health, or nutrition studies in the news media is to pay attention to the terms in which their claims are framed. Often such reports give an impression of making much stronger claims than they actually do because the claims are qualified by hedging words and phrases. For example, here's a headline from a recent press release:
New emerging research suggests Montmorency tart cherries may help enhance gut health2
The research reported on in this headline is hedged by the word "emerging", but just what is "emerging research"3? It's research which produces "emerging science"4 based on "emerging data"5. In other, unhedged words, it's preliminary research that hasn't been replicated and is therefore inconclusive. This doesn't mean that the study is necessarily bad, or poorly done―after all, somebody has to be the first to research something―but a single study is seldom conclusive.
In addition to "emerging", the headline includes the hedging words "suggests", "may", and "help", as does the following excerpt from the article beneath the headline―I've highlighted the hedges:
Montmorency tart cherries may play a role in improving gut health, suggests a first-of-its kind human trial of nine adults…. An international team of scientists found that Montmorency tart cherries helped to positively impact the gut microbiome….2
In addition to all the hedges, the claims made for the cherries are weak: "improving gut health" and "positively impact[ing] the gut microbiome". In the next paragraph we read: "The gut microbiome holds great promise…although the research is still evolving and larger, long-term human intervention studies are needed.2" "Evolving" is another hedge to add to "emerging", and both of these words indicate that this research is new and unsettled.
I certainly don't doubt that Montmorency tart cherries are good for you, but are they any better than pomegranates, which were a fad about a decade ago, or blueberries, which were the fad fruit before that6? The press release gives no reason to think these other fruits aren't also "gut-friendly" ones that "positively impact" your microbiome.
This press release was put out by the Cherry Marketing Institute (CMI), which describes itself this way:
The Cherry Marketing Institute, a not-for-profit organization funded by U.S. tart cherry growers and processors, provided financial support for the study. … CMI’s mission is to increase the demand for Montmorency tart cherries through promotion, market expansion, product development and research.2
Now, my point in drawing your attention to this fact is not to dismiss the study out of hand. However, it's important to take into account where this information is coming from, and the biases of its source. The press release was not written by a neutral reporter, but by someone working for the CMI, whose job is to sell you cherries. In other words, the article is really an ad for tart cherries masquerading as a news story. This wouldn't be so bad if you realize that it's a press release, but many of the news media reports on this study are no more than rewrites of the release7. Some are not even rewrites but simply reposts of the release with no notice that it is a PR document8.
Thankfully, this study has been thoroughly evaluated by the Health News Review9. It's a good idea to check this or some other reliable source before acting on the basis of a press release from a marketing group about an industry-sponsored study.
- Thanks to Lawrence Mayes for drawing this study to my attention.
- "New Emerging Research Suggests Montmorency Tart Cherries May Help Enhance Gut Health", Cherry Marketing Institute, 8/7/2018.
- "Emerging Research", 6/18/2009.
- "Emerging" Science, 3/26/2009.
- "Emerging Data", 8/7/2017.
- See: Verena Dobnik, "Pomegranates the newest fad fruit", The Seattle Times, 6/4/2008.
- For instance: Alexandra Thompson, "Drinking tart cherry juice for just five days can transform gut health, finds study", Daily Mail, 8/8/2018.
- For instance: "New Emerging Research Suggests Montmorency Tart Cherries May Help Enhance Gut Health", New Kerala, 8/14/2018.
- Michael Joyce, Kathleen Fairfield & Kathlyn Stone, "Big Cherry claims about health benefits leave a sour taste in our mouths", Health News Review, 8/10/2018.
August 10th, 2018 (Permalink)
The Paranoid Style in American Journalism
Last month1 I pointed out an error in Sharyl Attkisson's new book, The Smear, but that was just a warm-up. The error itself wasn't very important, but it suggested that Attkisson's research was at best superficial. On the same page where that error occurred, Attkisson continues her pseudohistory as follows:
Postwar, the CIA remained in the forefront of the propaganda game. The spy agency was apparently responsible for promoting the phrase conspiracy theory for use as a powerful device in the lexicon of the smear artist. Before the covert CIA effort, which we can pinpoint to a secret memo in 1967, there was nothing controversial about discussing or exposing "conspiracies." … Yet after the CIA secret memo, the public and media were brainwashed into dismissing out of hand those labeled as "conspiracy theorists"….2
First of all, let's assume that Attkisson's factual claims in this passage are correct, and examine her reasoning. She claims that before the memo "there was nothing controversial about" conspiracy theories (CTs), but after it "the public and media were brainwashed"―except for Attkisson, I presume. This before-and-after claim is the only evidence that she provides for thinking that it was the memo that caused the "brainwashing" of the rest of us. A clearer example of post hoc3 would be hard to find.
Many conspiracy theory (CT) sites on the web make a stronger claim than Attkisson, namely, that the CIA "invented", "created", "developed", or "coined"4 the phrase "conspiracy theory". To Attkisson's credit, she doesn't go that far, but before we return to her book let's examine this as an example of the sort of claims made by conspiracy theorists (CTists).
The following is an excerpt from historian Richard Hofstadter's 1956 book The Age of Reform:
The financial argument behind the conspiracy theory was simple enough. …[W]hat both the Greenbackers and free-silverites held in common was the idea that the contraction of currency was a deliberate squeeze, the result of a long-range plot of the "Anglo-American Gold Trust." Wherever one turns in the Populist literature of the nineties one can find this conspiracy theory expressed. …One feature of the Populist conspiracy theory that has been generally overlooked is its frequent link with a kind of rhetorical anti-Semitism.5
Hofstadter's book is a history of the period in American politics "From Bryan to F.D.R.", according to its subtitle. He examines both the progressive and populist political movements of this period, and one of his concerns was the tendency towards conpiratorial thinking among the populists. For instance, he writes:
There was something about the Populist imagination that loved the secret plot and the conspiratorial meeting. There was in fact a widespread Populist idea that all American history since the Civil War could be understood as a sustained conspiracy….6
So, in this book, published over a decade prior to the CIA memo, Hofstadter uses the phrase "conspiracy theory" three times in its contemporary meaning, which is enough to debunk the notion that the CIA "invented" it in 1967.
Attkisson does not make the false claim that the phrase "conspiracy theory" did not exist until the CIA cooked it up in some secret memo; rather, she writes that "[b]efore the covert CIA effort…there was nothing controversial about discussing or exposing 'conspiracies.'" That this is also false can be shown by a later article also by Hofstadter, and a resulting book, published a few years before the memo, both entitled: "The Paranoid Style in American Politics"7.
Hofstadter's phrase, "the paranoid style", did not catch on the way "conspiracy theory" did, but it refers to what gives rise to CTs, as can be seen from the following excerpt from the expanded, book-version of the essay:
I call it the paranoid style simply because no other word adequately evokes the qualities of heated exaggeration, suspiciousness, and conspiratorial fantasy that I have in mind. … In the paranoid style, as I conceive it, the feeling of persecution is central, and it is indeed systematized in grandiose theories of conspiracy.8
The phrase "conspiracy theory" has gained wider currency since Hofstadter wrote in the mid-'50s9, but President John F. Kennedy was assassinated in 1963. This was the assassination that launched a million CTs, so it's no great surprise that the phrase took off in its aftermath: after all, we needed a term for the type of pseudotheories that began to spring up around it. Hofstadter's use of the phrase was probably not as negatively charged as it is nowadays, but it has had over three score years to pick up negative associations because of all the CTs we've been inundated with.
But what about that memo? Have I forgotten all about the infamous CIA memo? Perhaps it contains a "smoking gun" revealing the CIA's conspiracy to brainwash us. Prepare to be disappointed: the phrase "conspiracy theory" does not even occur in it, though the phrases "conspiracy theories" and "conspiracy theorists" occur once each. Here is the entire passage:
Conspiracy theories have frequently thrown suspicion on our organization [the CIA], for example by falsely alleging that Lee Harvey Oswald worked for us. The aim of this dispatch is to provide material for countering and discrediting the claims of the conspiracy theorists, so as to inhibit the circulation of such claims in other countries.10
That's it. We've already seen that the CIA did not invent the phrase in question. Where's the "smoking gun" indicating a plan to spread or promote it? As you can see from reading the entire dispatch, and as is summarized in the above quote, the purpose of the document is to counter the spread in foreign countries of CTs about JFK's assassination. It offers suggestions of arguments and an example of how to do this. Among those suggestions, there is nothing about spreading or promoting the use of the phrase "conspiracy theory". In fact, the appended article supplied as an example of how to counter JFK CTs does not even use that phrase in any form11.
Instead, the two occurrences of the phrase in the dispatch undermine the claims made by contemporary CTists that the CIA either invented or promoted the use of it. The fact that the author of the document referred to "conspiracy theories" by "conspiracy theorists" with no explanation or definition offered indicates that the phrase was in sufficient currency not to require either. Moreover, the author was writing about how to counter theories that there was a conspiracy to assassinate JFK, as opposed to the Warren Commission's conclusion that Lee Harvey Oswald had acted alone. It's only natural, then, to refer to "conspiracy theories" by "conspiracy theorists". If anything, it's surprising that those phrases only occur once apiece.
Fittingly, the notion that the CIA was responsible for the bad reputation of CTs is itself a "conspiracy theory" in the contemporary sense of the phrase. Apparently, CTists just assume that their audience will not bother to actually read the "secret memo" that they base their claims on, and I guess they must be right in doing so. If you wonder why CTs have gotten such a bad name, don't look to the CIA; look at the fallacious reasoning and lousy research of the CTists themselves.
Finally, my misgivings about Attkisson's minor error were justified, because this is not a small mistake. This is itself an attempt to smear those of us who are critics of CTs and CTists, by suggesting that we are dupes of the CIA. If anyone is a dupe, it's Attkisson who has been misled by the CTists' shoddy excuse for research.
- New Book: The Smear, 7/23/2018.
- Sharyl Attkisson, The Smear: How Shady Political Operatives and Fake News Control What You See, What You Think, and How You Vote (2017), pp. 12-13. Italics in original.
- See: Post Hoc Fallacy.
- I've seen all of these words used on conspiracist webpages, but I refuse to link to them because I don't want to send them traffic. However, you can easily check this for yourself with a websearch, which is generally a good practice to adopt. If more people would do so, then the CTists would lose their audience.
- Richard Hofstadter, The Age of Reform: From Bryan to F.D.R. (1956), pp. 74-75 & 77. Emphasis added.
- Richard Hofstadter, The Age of Reform: From Bryan to F.D.R. (1956), p. 70.
- Richard Hofstadter, "The Paranoid Style in American Politics", Harper's Magazine, 11/1964. See the following note for the book.
- Richard Hofstadter, The Paranoid Style in American Politics and Other Essays (1965), pp. 3-4.
- Google's Ngram Viewer shows that use of the phrase "conspiracy theory" in books has increased steadily since the 1950s, except for a plateau in the '70s. See here: "conspiracy theory, conspiracy theories, conspiracy theorist", Google Books Ngram Viewer, accessed: 8/9/2018.
- "Dispatch: Countering Criticism of the Warren Report", section 2, emphasis added. Attkisson, with her usual lack of scholarship, gives no citation for this document beyond calling it "a secret memo in 1967". However, the above dispatch is the only one cited by the various CTists that claim the CIA either created or promoted the phrase "conspiracy theory". Moreover, the dispatch was classified as "secret", dated 1967, and uses variants of the phrase. Finally, I've been unable to find any other CIA memo from 1967 that seems to have anything to do with CTs. For these reasons, I'm assuming that this is the memo that Attkisson refers to.
- The dispatch refers to a second appended article taken from Look magazine, but it is missing from every copy of the dispatch that I've seen. See section 3b and the appended "Background Survey of Books Concerning the Assassination of President Kennedy", page 3, section 6. I haven't been able to find a copy of the Look article, so if any reader has access to it please let me know.
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July 30th, 2018 (Permalink)
A Once in a Lifetime Puzzle
What occurs once in a second, once in a minute, twice in a day, but only once in a lifetime?
July 23rd, 2018 (Permalink)
New Book: The Smear
Whoever can be trusted with very little can also be trusted with much, and whoever is dishonest with very little will also be dishonest with much.7
I had just begun reading reporter Sharyl Attkisson's latest book, The Smear when, in the first chapter, "Birth of the Modern Smear", I came across the following dubious quote. In discussing Nazi propagandist Joseph Goebbels, Attkisson writes: "…[A]pplicable remarks found within the pages of the Goebbels diaries include: … 'The truth is the greatest enemy of the State.'1"
I'll leave it to you to check Randall Bytwerk's "False Nazi Quotations" page to see the reasons for thinking this alleged quote spurious; it's the first quote on the page2. Anyway, it's not my purpose here to discuss why the quote is probably not Goebbels', but what it's doing in Attkisson's book.
In a previous entry3, I discussed the role of factual statements in fact-checking. Attkisson's claim is certainly a statement, that is, it's either true or false that Goebbels wrote that in his diary. Moreover, it should be possible to search the diaries for this statement, at least theoretically, which means that it is a factual statement. So, this is the type of statement that fact-checkers should check. Unfortunately, there is no citation given for this quote in the book, other than the attribution to the lengthy diaries, which makes it exceedingly difficult to verify4.
The quote is exactly the sort of thing that should have been fact-checked, if not by the author herself then by the publisher. It's not difficult to find out that the correctness of the quote is disputed by experts: all you have to do is cut and paste it into a search engine, and Bytwerk's page on fake Nazi quotations should be one of the first few results. Doing such a search and then reading Bytwerk's page would have taken only a few minutes.5
Attkisson has done some good reporting in the past, but this shows either non-existent or extremely lazy research. Whatever reasons Attkisson herself may have had for making this mistake, where was the publisher? The electronic copy of the book that I have was published by Harper, a reputable and long-established publisher. Apparently, it no longer does even minimal fact-checking on what it publishes, assuming that it ever did.
Now, you may think: big deal! Sure, she made a mistake, but it's trivial. True enough, but it would have also been trivial to check. While in itself the error is small, what effect should it have on our confidence in Attkisson as a reporter and her book? Can we be sure that the big claims she makes are correct? If she, her researchers, or her publisher fail to do a fact-check that takes a minute or two, can they be expected to do so when the research is long and difficult?
This case reinforces a point that I've made before6, but it's worth repeating. In this time of fake news and punditry masquerading as reporting, we need to be willing and able to do our own fact-checking, because many of our institutions are failing to do it.
I was looking forward to reading Attkisson's book, but now I'm not so sure. If she can't be bothered to fact-check her book, I don't think I can be bothered to read it.
Update (8/1/2018): In Attkisson's book, four additional quotes are attributed to Goebbels' diaries. I was a little doubtful about a couple of the others, but I concentrated on the one above because it was all I needed to make my point. Randall Bytwerk has now looked into all of these quotes, and I leave it to you to check out his findings8. I will just add that a pattern seems to be emerging.
- Sharyl Attkisson, The Smear: How Shady Political Operatives and Fake News Control What You See, What You Think, and How You Vote (2017), p. 12.
- Randall Bytwerk, "False Nazi Quotations", German Propaganda Archive, accessed: 7/23/2018. Last year, I discussed quote 4; see: Who is Adolph Hitler and why does he keep saying these terrible things?, 9/11/2017, and quote 5; see: Passage of Propaganda, 7/28/2017.
- Fact Vs. Opinion
July 6th, 2018 (Permalink)
Poll Watch: Is President Trump more popular than the FBI?
According to the following headline, he is:
Trump Approval Jumps As Attacks From Critics Backfire;
Trump Now More Popular Than FBI: IBD/TIPP Poll1
The July poll found that 41% approve of the job Trump is doing. That's the first time he's been above 40% since March 2017, and just 1 point below his highest approval rating of 42% during his first month in office.1
So, an alternative headline for this story would be:
Trump's Approval Rating Unchanged Since Taking Office
But you won't be seeing that anywhere but here.
Here's what supports the headline's comparison of Trump's approval rating with that of the FBI: "The poll found that just 39% have a favorable view of the FBI1." So, the difference between Trump's approval and that of the FBI is two percentage points. Most modern public opinion polls have a margin of error (MoE) of at least 3 percentage points, so this is not a significant difference. A more accurate appraisal of this result would be that Trump and the FBI are about equally unpopular. At the end of the article, where they always hide this information, you can read5:
Methodology: IBD/TIPP conducted the July poll from June 21 to June 29. It includes responses from 900 people nationwide, who were asked questions by live interviewers on phones. The poll's margin of error is +/-3.3 percentage points.1
This is actually a slightly small sample for a national public opinion poll, and the difference between the President's and the FBI's approval ratings is well within the margin of error2. There's another logical problem with the reporting of this poll, the first sentence of which reads:
Increasingly bitter and aggressive attacks on President Trump managed to bolster his approval rating, which climbed 5 points to reach the second highest level of his presidency, the latest IBD/TIPP Poll finds.1
This sentence claims that attacks on Trump served to "bolster"3 the approval rating, meaning that they supported it, which is a causal relation. However, the most that we know from this poll is that Trump's approval rating increased 5 points from the previous IBD/TIPP poll, and the attacks in question presumably happened either before or during the time that the poll was taken. Of course, it's possible that the attacks may have actually backfired, but it's also possible that Trump's approval rating would have increased even more if it hadn't been for those criticisms. Also, it's possible that the 5 point change was simply a random fluctuation. So, inferring causation in this case commits a causal fallacy4.
This is one of those polling reports in which, if you remove all the exaggeration, speculation, innumeracy, and illogicality, nothing much is left.
- John Merline, "Trump Approval Jumps As Attacks From Critics Backfire; Trump Now More Popular Than FBI: IBD/TIPP Poll", Investor's Business Daily, 7/2/2018.
- See: How to Read a Poll: Margin of Error Errors.
- A bolster is either a long cylindrical pillow that is used to support the human body, or a structural part of a building that provides support. So, as a verb, to bolster means to support something.
- See: Causal Fallacy.
- I originally wrote here that the difference between Trump's approval rating and that of the FBI was only one percentage point, but it was two. The paragraph has been corrected.
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