If at first you don’t succeed . . . statistical manipulation might help

Anti-fluoride campaigners are promoting yet another new study they claim shows community water fluoridation lowers children’s IQ. For example, the Fluoride Free NZ (FFNZ) press release Ground Breaking Study – Fluoridated Water Lowers Kid’s IQs which claims the study confirms“our worst fears, linking exposure to fluoridated water during pregnancy to lowered IQ for the developing child.”

Yet the study itself shows no significant difference in children whose mothers lived in fluoridated or unfluoridated areas during pregnancy. Here is the relevant data from Table 1 in the paper:

Mean IQ of children whose mothers drank fluoridated or unfluoridated water during pregnancy (SD =  11.9 – 14.7)

Nonfluoridated Fluoridated
All children 108.07 108.21
Boys 106.31 104.78
Girls 109.86 111.47

The differences between fluoridated and nonfluoridated are not statistically significant.

The paper has just been published and is:

Green, R., Lanphear, B., Hornung, R., Flora, D., Martinez-Mier, E. A., Neufeld, R., … Till, C. (2019). Association Between Maternal Fluoride Exposure During Pregnancy and IQ Scores in Offspring in Canada. JAMA Pediatrics, 1–9.

Surprisingly the authors do not discuss the data in the table above. Its as if the data didn’t exist, despite being given in their Table 1. I find this surprising because their discussion is aimed at finding a difference – specifically, a decrease in child IQ due to fluoridation – and surely these mean values must be relevant. Were the authors embarrassed by these figures because they did not show the effect they wanted?

So how did they manage to find an effect they could attribute to fluoride, or fluoridation, despite the mean values above? They basically resort to statistical manipulation – and this has opened up an intense controversy about the paper.

An unprecedented “Editor’s Note”

The journal editor, Dimitri A. Christakis, published a note alongside the paper (see Decision to Publish Study on Maternal Fluoride Exposure During Pregnancy), together with a piece in the Opinion section by David C. Bellinger (see Is Fluoride Potentially Neurotoxic?). This opinion piece is described as an editorial although Bellinger is not an editor of the journal or on the Editorial Board.

This is, in my experience, completely unprecedented. Editor’s don’t comment on the quality of papers or the refereeing process and I can only conclude that within the journal editorial board and those who reviewed the paper there were sharp differences about its quality and whether it should be published. While an editorial may sometimes bring attention to an article, in this case, it is likely that Bellinger was one of the reviewers of the paper and he is expressing his viewpoint on it and supports its publication.

Christakis writes “The decision to publish this article was not easy.” He goes on to imply the journal supports publication “regardless of how contentious the results may be.”  But surely there is no need to defend a good quality paper in this way just because the results may be “contentious.”

Interestingly, FFNZ interpreted the publication of the Editor’s note as making the publication of the paper more “impactful” not realising that the Note is probably not positive for the paper as it reveals controversy over the paper’s quality and whether it was worthy of publication. FFNZ also chose to describe Bellinger’s comments in his opinion piece as representing the views of the authors. However, it would be inappropriate for an editor to make such comments.

I think Bellinger has his own biases and preferences which lead him to advocate for papers like this. I commented on Bellinger’s role in the review of another paper promoting an anti-fluoride perspective in my articles Poor peer-review – a case study and Poor peer review – and its consequences.

A large amount of controversy

I am surprised at the degree of controversy around this paper – and it’s loudness. The fact that it started on the same day the paper was made public reveal various actors have had access to the paper and have been debating it for some time.  This could have been stoked by the unorthodox statistical analysis used and contradictions in the findings.

But it appears this controversy had gone far wider than the journal editors and reviewers of the paper because of the immediate reactions from anti-fluoride organisations like the Fluoride Action Network (see BREAKING: GOVERNMENT-FUNDED STUDY LINKS FLUORIDATED WATER DURING PREGNANCY TO LOWER IQS IN OFFSPRING), some leading Newspapers,  professional bodies (see AADR Comment on Effect of Fluoride Exposure on Children’s IQ Study) and the UK Science Media Centre which published a reaction from experts article (see expert reaction to study looking at maternal exposure to fluoride and IQ in children).

This suggests to me a large degree of lobbying. Not only from activists and anti-fluoride scientists or reviewers. But also from authors and their institute. I am not really surprised as I have often seen how politics, activism, commercial interests, and scientific ambitions will coordinate in these situations.

How to discover an effect from a nonsignificant difference

So how do we get from the data in the table above – showing no statistically significant difference between fluoridated and unfluoridated areas – to a situation where the authors (who don’t refer to that data in their discussion) say:

“higher levels of fluoride exposure during pregnancy were associated with lower IQ scores in children measured at age 3 to 4 years. These findings were observed at fluoride levels typically found in white North American women. This indicates the possible need to reduce fluoride intake during pregnancy.”

In their press releases and statements to media, where they are not constrained by a journal’s need for evidence and objectivity, they come out even more vocally against community water fluoridation.

Well, it appears to me, by statistical manipulation. One of the Science Media experts referred to above, Prof Thom Baguley, wrote:

“First, the claim that maternal fluoride exposure is associated with a decrease in IQ of children is false. This finding was non-significant (but not reported in the abstract). They did observe a decrease for male children and a slight increase in IQ (but non-significant) for girls. This is an example of subgroup analysis – which is frowned upon in these kinds of studies because it is nearly always possible to identify some subgroup which shows an effect if the data are noisy. Here the data are very noisy.”

It appears the authors found a significant effect of child sex on IQ so made a decision to do a subgroup analysis – of boys and girls – and this produced a significant association of IQ with maternal urinary fluoride for the boys. This resort to subgroup analysis may have, in itself, produced a misleading significant relationship.

Adam Krutchen, Biostatistics PhD student at the University of Pittsburgh, also illustrates how the relationship with child sex has confused the analysis. He comments on the data that he managed to extract from the paper’s Figure 3:

“There were drastic sex-specific IQ differences in the children, which is of course strange. We shouldn’t expect anything like that to happen. This difference is very significant. There’s also some outlier extremely low IQ values among the male children.”

He is saying that his regression analysis showed a strong effect of child sex on IQ. This is quite irrespective of maternal urinary F or drinking water F. However, once that effect of child sex is taken into account he found no relationship of child IQ with maternal urinary F. He says:

“with such a significant effect of sex on IQ, does fluoride have any remaining relationship? The answer is a resounding no in the digitized data.”

It appears that including child sex difference in the regression analysis produces the finding that there is no significant relationship of fluoride to child IQ after taking into account the significant relationship of IQ with child sex. But when the data is divided into subgroups and analysed separately (a technique statisticians “frown on” “because it is nearly always possible to identify some subgroup which shows an effect if the data are noisy”) a significant relationship of IQ with maternal urinary fluoride can be produced for boys (but not girls).

Interestingly, a second part of the Green et al., (2019) study investigated a relationship of child IQ with unverified estimated fluoride intake by the pregnant mothers. The estimation method was not verified so may be questionable). No sex difference appeared in that data set.

How strong are the reported relationships

Perhaps it is not necessary to go any further. Perhaps the data for mean IQ in the table above is sufficient to show there is no effect of fluoride on IQ. Or perhaps the critique of the analysis of subgroups used is sufficient to make the reported conclusions suspect.

However, perhaps a comment on the weakness of the relationships reported by Green et al is useful – if only because I took the trouble to digitally extract the data from the figures in the paper and do my own regression analyses on the data.

Of course, digital extraction does not get all the data – even if only because the points may merge. In this case, I managed to extract 410 data points from Figure 3A which showed the relationships of child IQ with the maternal urinary F concentrations during pregnancy. This is quite a bit smaller than the 512 data pairs the authors reported in their Table 1 and suggests to me they had not plotted all their data. However, the values for means and coefficients obtained by my own regression were very similar to those reported by Green et al., (2019).

The authors reported a significant (p=0.02) negative relationship of boy’s IQ with maternal urinary F. They do not discuss how strong that relationship is – although the wide scatter of data points in the figures suggest it is not strong. My regression analysis showed the relationship explained only 1.3% of the variance in IQ. I do not think that is worth much. With such low explanatory power, I think the authors overstate their conclusions.

I think this is another case of placing far too much reliance on p-values and ignoring other results of the statistical analysis. I discussed this in a previous article – see Anti-fluoride activists misrepresent a new kidney/liver study).

Conclusions

I think this paper has been overblown. It has problems with its statistical analyses as well as other limitations referred to in the paper. I do not think it should have been published in its present form – surely reviewers should have picked up on these problems. I can only conclude that intense arguments occurred within the journal’s editorial board and amongst reviewers – and most probably more widely amongst institutes and activist groups. In the end, the publication decision was most likely political.

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17 responses to “If at first you don’t succeed . . . statistical manipulation might help

  1. Some more comments on the paper https://1clickurls.com/FCDuS3O

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  2. Excellent, Ken! Other researchers are making the same observations about this agenda-driven mess. Upon failure to obtain their desired results with the meta-data, they resort to data mining of subgroups, with one or two outlier points driving the mean IQ difference within one of them.

    As for Bellinger…..he collaborated on the design and execution of the cognitive testing in the Bashash 2017 Mexican study, and was a co-author of the 2014 Choi/Grandjean Pilot Chinese IQ study. Hardly an objective observer.

    With the notable flaws, statistical manipulation, conflict of interest of the “editorialist”, and premature media sensationalism of this study, JAMA might very well be headed down the same road as did Lancet with Wakefield in 1998.

    Steven D. Slott, DDS

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  3. Bill Osmunson

    Although I agree with some of your points Ken, your bias is blazing. Seems you are alleging statistical manipulation and then desire statistical manipulation to prove your desired outcome.

    You argue data mining was done by the authors but then use data mining to show the data was not valid. . . “There’s also some outlier extremely low IQ values among the male children.”

    If the authors had removed the extremely low IQ values among male children, that would be data mining. Not necessarily bad, but still data mining.

    To understand sub groups such as socioeconomics, age, gender, education, etc. is not data mining. There is a difference between boys and girls. At your age you should have discovered that fact. Or do I need to go into more detail? There are some good books on the subject. . . .

    I would also suggest you listen to the podcast. The reluctance to publish was due to the potential effect it would have on policy, controversy. The authors were clueless that Europe is mostly fluoridation free and many large cities are not fluoridated.

    These Editors were cloistered in the myth of fluoridation and never looked at both sides of the data.

    And there are other questions which this study does not address.

    I agree with you the data on Table 1 (1.53 IQ difference for boys) does not match and their reporting (reported 4.49 IQ loss) and they should respond to that material concern. Perhaps they have and we have missed it.

    Raw data should be made available. . . or was it and I missed it.

    And Ken, you have failed for many months to address total fluoride exposure.

    And talk about the pot calling the kettle hot. . . .

    You are data mining all the time, refusing to answer the most fundamental questions:

    How much fluoride is “optimal” from all sources to mitigate dental caries?

    What is a desired urine and serum fluoride concentration to mitigate dental caries and is that safe?

    What percentage of children is acceptable to be harmed with dental fluorosis?

    Why are there more complete cusp fractures in fluoridated communities?

    We can do quality studies of benefit, not harm. What quality studies do you have, prospective randomized controlled trials, reporting efficacy of additional fluoride being added to public water?

    Until you provide answers to those and other questions, you are data mining to prove your bias of fluoridation efficacy.

    Bill Osmunson DDS MPH

    Liked by 1 person

  4. Bill Osmunson

    Ken,
    You inspired me to read the study by Green closer.
    The authors state:
    “A 1-mg/L increase in MUFSG was associated with a 4.49-point lower IQ score (95% CI, −8.38 to −0.60) in boys, but there was no statistically significant association with IQ scores in girls (B = 2.40; 95% CI, −2.53 to 7.33). A 1-mg higher daily intake of fluoride among pregnant women was associated with a 3.66 lower IQ score (95% CI, −7.16 to −0.14) in boys and girls.”

    We both failed to read that section close enough and looked at Table 1 without also considering what the authors were doing.

    As you know, one concern with a study of harm is we can’t do prospective RCT’s to cause and thus prove harm. That would be unethical.

    Another problems is a threshold below which a toxin may not cause harm, or at least show the harm in the study due to limitations of the study at hand.

    Although Table 1 does not show the 4.49 IQ loss, when a 1-mg/L increase in urine fluoride was compared, a 4.49 IQ loss was found.

    That is significant.

    The authors were very clear, We simply did not read the article carefully in the first run through.

    Bill Osmunson DDS MPH

    Liked by 1 person

  5. Steven Slott

    So, Bill, your answer for the reported in effect in boys, but not girls is that “boys will boys”?

    Until these authors begin to adequately address the questions that are piling up about this study, the only conclusion that can be credibly be drawn from it is that the children in fluoridated and non-fluoridated have no significant difference in IQ.

    Steven D. Slott, DDS

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  6. Prof McGonagall

    No idea who Bill O is, but his language reads as desperate to prove his agenda, especially when he accuses others of ‘bias’ and ‘data mining.’ The irony is so thick I tripped over it. He does stumble on a few facts in his tirade. Primarily, we all agree the study never should have been published in its current form, and the data should be made available. I recommend Bill review https://www.sciencemediacentre.org/expert-reaction-to-study-looking-at-maternal-exposure-to-fluoride-and-iq-in-children/ to understand the errors they made in their analysis. Why JAMA peds didn’t catch this is also shocking. Ultimately, the study unleashed a pandemic of viral misinformation about fluoride that will be used to harm the most vulnerable. Much like the anti-vax mov’t. FYI other studies that assessed relationships with fluoride and IQ found no association. Neither did this one, yet they proceeded with a sub group analysis. In plain words, we call that a fishing expedition. I am reminded of one of Paul Offit’s statements, ‘junk science is not a victimless crime.’

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  7. Prof McGonagall

    Another good analysis of this study from Steve Novella https://sciencebasedmedicine.org/maternal-fluoride-and-iq/

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  8. Bill Osmunson

    Steven,

    I’m neither a toxicologist nor statistician. I have received FDA approval for a dental device, but not new drug application. My one course on statistics was great, but I have much to learn.

    The difficulty in testing harm without causing harm is obvious.

    I take a global view for judgment, which includes:

    I can fix teeth but not brains.

    If in doubt, protect brains.

    Ingested fluoride does not have good research or show current benefit, topical does.

    With more than 50 human studies reasonably consistently finding developmental neurotoxicity from ingested fluoride, the big picture is concern.

    With little or no benefit from ingested fluoride, the benefit is questionable.
    With the age of potential benefit during the first 6-8 years while the tooth is developing, prenatal a concern, infant formula with fluoridated water a concern and the EPA reporting most children are ingesting too much fluoride, and severe increases in dental fluorosis, adding more fluoride to water makes no scientific sense.

    And we have, here, reviewed the research on other harm from excess exposure.

    Remember when we gave pregnant mothers fluoride supplements?

    Remember when we used mercury fillings?

    Remember when we routinely pulled 4 bicuspids for easy ortho and closed the airway down and now get to treat their sleep apnea?

    Remember when we placed patients into a synarthrodial seated CR condylar position which we now find increases TMD?

    90% of the materials I was taught in school are no longer in my office.

    We grow and learn and improve. Just because we historically did something does not prove it is the best.

    Time for a reduction in fluoride exposure. Fluoridation cessation makes scientific and ethical sense.

    Bill Osmunson DDS MPH

    Liked by 1 person

  9. Bill, thank you for your personal opinions. However, they are irrelevant.

    Again, until the authors begin adequately answering questions which are rapidly piling up, the only conclusion that can be credibly drawn from this study is that there is no significant difference in IQ in the children living in fluoridated and non-fluoridated communities……as would be expected.

    No amount of hype and misrepresentation will change this.

    Steven D. Slott, DDS

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  10. Bill Osmunson DDS, MPH

    The authors answered Ken and my question in the article, we failed to carefully read it.

    And I would suggest you carefully read the study again. It will answer some of your questions.

    Bill Osmunson DDS MPH

    Liked by 1 person

  11. Bill, yes, your confirmation bias makes you see what you want to see in this study. However, I’m guessing that Ken will speak for himself in regard to whether or not he has “carefully read it”, and what questions are answered.

    While you and the study authors are fine with such things as…….ignoring data which clearly shows no IQ difference between fluoridated and non-fluoridated communities, mining of data within subgroups, scattered data points that look like a cluster of stars in the sky, no explanation for the discrediting finding of effect in boys yet not girls, and inability to properly control for confounders…….objective reviewers are not.

    JAMA made a grievous error in judgement but publishing this thing, which I suspect it may be realizing.

    Steven D. Slott, DDS

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  12. Bill Osmunson DDS, MPH

    Prof McG.
    Sorry you are tripping over the facts. Just because they don’t fit in your paradigm, doesn’t mean they are wrong.

    Steven Novela wrote a response which has so many errors, but he claims to be science based. Really? Here is part of it with my comments:

    Novella: “A recent study published in JAMA Pediatrics claims: “Association Between Maternal Fluoride Exposure During Pregnancy and IQ Scores in Offspring in Canada.” This is getting a lot of press, but also a lot of pushback. The study is at odds with a large body of evidence showing no association with normal fluoride exposure and IQ. . . .”

    Osmunson: Really? Lets start looking at the “large body of evidence showing no association with normal fluoride exposure and IQ. Name one and lets start looking at it.

    Novella: “There is still an open question about high levels of exposure – higher than is added to some public water systems – but there is no association at <2ppm (fluoridated water typically has 1ppm). . . "

    Osmunson: Total exposure must be considered, not just water fluoride concentration. Good god, when will fluoridationists admit there is more fluoride exposure than just water.

    Novella: "While many aspects of the methods used by the researchers were reasonable, the results are curiously at odds with prior research, and have come under significant criticism, at least in their interpretation. Perhaps the most significant curious aspect of the results is the stark difference between boys and girls in the study. It’s hard to believe that a drop of 4.49 IQ points in boys was missed by prior research, and why is that effect so large while there is no effect is girls (just a non-statistical trend toward increased IQ).. . ."

    Osmunson: Why was 4.49 missed by prior research? Well, it was not missed in over 50 human studies. Why boys and not girls? Good question. Fluoride's effect on osteosarcoma seems to be more for boys than girls also.

    Now, look at the other research on fluoride and the brain. Read it. Novella is not the only one surprised by so much research on fluoride's effect to the brain. Hard to keep up on research in all areas.
    Consider the list at https://fluoridealert.org/issues/health/brain/

    Bill Osmunson DDS MPH

    Liked by 1 person

  13. Bill, you claim I argue “data mining was done by the authors but then use data mining to show the data was not valid. .” and provide this quote as evidence – “There’s also some outlier extremely low IQ values among the male children.”

    Search through the article – I do not use the term “data mining” once. And the quote you give is not mine but Adam Krutchen’s, a Biostatistics Ph. D. student at the University of Pittsburgh. Incidentally, Krutchen is quite correct to note outliers and other strange values. A good statistician always looks at the quality of the data as their first step.

    Nobody is arguing for the removal of data – simply commenting on the quality of the data. The authors themselves removed several data points they thought questionable (as you will know if you had read the paper).

    You claim that “The reluctance to publish was due to the potential effect it would have on policy, controversy.” Do you not understand political statements and excuses. No sensible journal would debate publications simply because of controversy (except controversial methodology as in this case). I have been in the business of research, publication and peer review for some time. I have experienced pressures not to publish and to promote shoddy work. Such scientific politics arise because of commercial interests, institutional kudos, the personal ambition of scientists involved and intervention of political and activist interests.

    This obviously occurred in a big way here. I suspect that the political pressure overrode objections of at least some of the reviewers.

    The publication of an Editor’s Note is unprecedented and indicates to anyone who has seen this sort of behavior before that a huge controversy had occurred and the final publication decision was political – as was the Editor’s Note itself.

    You say “I agree with you the data on Table 1 (1.53 IQ difference for boys) does not match and their reporting (reported 4.49 IQ loss) and they should respond to that material concern. Perhaps they have and we have missed it.” No, we have not missed it. They should have commented on this in the paper itself. And, no, they do not report a 4.49 IQ loss – how the hell did you get that?

    As for you other questions – they are simply a diversion. You have been offered space here for a scientific exchange where these and other questions (and particularly dental fluorosis) can be discussed. I am keen for such an exchange to progress but you have yet to send me a suitable document with properly cited references and corrected figure. The ball is in your court on this.

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  14. Bill, you say “Ken, You inspired me to read the study by Green closer.” Good, but surely it is normal to read an article or paper before getting into a debate on it. The problem is that most people promoting this paper have actually never read it but rely on activist reports of its content.

    You then quote a section which you claim “We both failed to read that section close enough and looked at Table 1 without also considering what the authors were doing.” Where have you been? I have been debating this very section with you and Richar Saubuear on another forum and discussed these relationships and their lack of importance in quite a lot of detail.

    Bill, your statement here that “when a 1-mg/L increase in urine fluoride was compared, a 4.49 IQ loss was found.” is just not true. Perhaps we should discuss why in some detail.

    You admit your knowledge of statistical analysis is poor – nothing to be ashamed of. Most people don’t have statistical skills and even many academics who do often use statistics naively.

    In separate comments, I will explain to you what these statements actually mean and provide some extra information from my own statistical analysis of the data to show how meaningless they really are.

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  15. Prof McGonagall

    I don’t have time to explain fluoride metabolism and excretion to you and shouldn’t need too. I am not going to read anything from the Fluoride Propaganda Network. Give me a break. Wait, wait, are you the same Osmunson that was a past campaign director for the FAN? If so, this is all making sense to me now. I recall current FAN director Connett’s three part fluoride series with Alex Jones on Infowars. You know, the Alex Jones that thinks the government is controlling the weather, the Sandy Hook Massacre was ‘staged’ and chemicals are turning frogs gay, to name a few tin hat pearls. No legitimate organization or scientist would ever appear on Infowars and walk away with any credibility. Bye Felicia!

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  16. Bill I will try to explain what the statistical analysis of data in this paper means. In this comment I will refer just to the reported association between MUF and IQ for boys – as in your quote from the paper:

    “A 1-mg/L increase in MUFSG was associated with a 4.49-point lower IQ score (95% CI, −8.38 to −0.60) in boys, but there was no statistically significant association with IQ scores in girls (B = 2.40; 95% CI, −2.53 to 7.33)”

    1: Please note this does not say “when a 1-mg/L increase in urine fluoride was compared, a 4.49 IQ loss was found” as you claimed in a previous comment. Please note the words “associated with.”

    This is because of the obvious – correlation is not causation. A statistically significant association or relationship may have nothing to do with causation. It may simply indicate fluoride is acting as a proxy (as I showed with the ADHD paper see Perrott, K. W. (2018). Fluoridation and attention deficit hyperactivity disorder a critique of Malin and Till (2015). British Dental Journal, 223(11), 819–822.)

    2: Further, it does not say the coefficient (the slope of the best-fit line) was exactly 4.49. It quotes a 95% confidence interval – in this case -8.38 to -0.60. There is a 95% chance the coefficient will be in this range.

    3: That is the coefficient – but what would be the associated IQ values be. [Please don’t forget the word “associated” – it is too easy to fall into sloppy thinking and assume we are talking about an actual loss caused by fluoride. That has not been shown at all.]

    The figures relate only to the best-fit line and that range of coefficients indicate values for the best-fit l line at a MUF of 1.0 mg/l in the range of 105.72 to 113.50. (I am using a constant for the line of 114.10 estimated from the papers Figure 3).

    4: Now here is the figure with the data points taken from the paper:

    canada

    5: Please note that the values from the quoted statement refer only to the line. 114.10 – 4.49 = 109.61 = the IQ value of the line at MUF of 1 mg/ml. The CIs indicate a 95% probability of values in the range105.72 to113.50. That range is indicated by the blue shade showing the place the best-fit line could occur.

    6: Now note that at a MUF of about 1 mg/L ACTUAL values occur WELL OUTSIDE THAT RANGE. At least 75 to 125 or even wider (approximately 50 – 145) at slightly lower values of MUF.

    In fact, only a few of the values are in the range given in the quote.

    This tells you that the reported association [“a 4.49-point lower IQ score (95% CI, −8.38 to −0.60)”] is an extremely poor predictor of what the actual values associated with the MUF will be.

    7: The reason should be obvious. The data has a very wide scatter and the fitted line explains only a very small percentage of the true IQ variance. This can be calculated from a normal regression analysis – the authors would have the figures but did not report them. I think that is a major deficiency in this paper and similar papers from this group.

    My estimate (using digitally extracted data from the figure) is that the reported association explain only 1.3% of the IQ variance. That is a very small value.

    8: Finally, the author’s rely on p-values (in this case 0.02) and conventionally we say a relationship is “significant” if p is less than 0.05. By itself, p-values can be very misleading – and are often simply used to confirm a bias. Authors should provide all the information for their statistical analyses. In this case, an R-squared value of 0.013 (which they refused to report) would have told us that the reported association was meaningless. I do not think this is honest or objective reporting by these authors
    On the other hand, I must compliment them for at least showing us some of the data – this enables us to come to our own conclusions about the significance of their results. Of course, anti-fluoride activists will only be discussing the p-value in their misrepresentations.

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  17. Bill I will use the second association to provide you with a similar explanation of what the statistical analysis of data in this paper means. In this comment I will refer just to the reported association between F uptake and IQ for all children – as in your quote from the paper:

    “A 1-mg higher daily intake of fluoride among pregnant women was associated with a 3.66 lower IQ score (95% CI, −7.16 to −0.14) in boys and girls.”

    1: I hope you are now familiar with what the word “associated” mean. Particularly it should not be seen as some sort of proof of a cause.

    2: Again, it does not say the coefficient (the slope of the best-fit line) was exactly 3.66. It quotes a 95% confidence interval – in this case –7.16 to -0.14. There is a 95% chance the coefficient will be in this range.

    3: That is the coefficient – but what would be the associated IQ values be. [Please don’t forget the word “associated” – it is too easy to fall into sloppy thinking and assume we are talking about an actual loss caused by fluoride. That has not been shown at all.]

    The figures relate only to the best-fit line and that range of coefficients indicate values for the best-fit l line at a MUF of 1.0 mg/l in the range of 103.13 to 110.15. (I am using a constant for the line of 110.29 estimated from the paper’s Figure 3).

    4: Now here is the figure with the data points taken from the paper.

    canada 2

    5: Please note that the values from the quoted statement refer only to the line. 110.29 – 3.36 = 106.93 = the IQ value of the line at MUF of 1 mg/ml. The CIs indicate a 95% probability of values in the range 103.13 to 110.15. That range is indicated by the grey shade showing the place the best-fit line could occur.

    6: Now note that at a MUF of about 1 mg/L ACTUAL values occur WELL OUTSIDE THAT RANGE. At least 74 to 140 or even wider.

    In fact, only a few of the values are in the range given in the quote.

    This tells you that the reported association [“3.66 lower IQ score (95% CI, −7.16 to −0.14)”] is an extremely poor predictor of what the actual values associated with the MUF will be.

    7: The reason should be obvious. The data has a very wide scatter and the fitted line explains only a very small percentage of the true IQ variance. This can be calculated from a normal regression analysis – the authors would have the figures but did not report them. I think that is a major deficiency in this paper and similar papers from this group.
    My estimate (using digitally extracted data from the figure) is that the reported association explain only 1.2% of the IQ variance. That is a very small value.

    8: Finally, the author’s rely on p-values (in this case 0.04) and conventionally we say a relationship is “significant” if p is less than 0.05. By itself, p-values can be very misleading – and are often simply used to confirm a bias. Authors should provide all the information for their statistical analyses. In this case, an R-squared value of 0.012 (which they refused to report) would have told us that the reported association was meaningless. I do not think this is honest or objective reporting by these authors
    On the other hand, I must compliment them for at least showing us some of the data – this enables us to come to our own conclusions about the significance of their results. Of course, anti-fluoride activists will only be discussing the p-value in their misrepresentations.

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