# ADHD linked to elevation not fluoridation

Attention-Deficit Hyperactivity Disorder (ADHD) is more likely linked to residential altitude than community water fluoridation (CWF). This finding calls into question a recent paper claiming ADHD is linked to CWF. A paper that is being heavily promoted on social media at the moment by anti-fluoridation groups.

I discussed problems with that paper, (Malin & Till, 2015) in my article* More poor-quality research promoted by anti-fluoride activists.* Now I have taken my critique further by making my own exploratory investigation of likely influences on the prevalence of ADHD in US states using the approach of Malin & Till,(2015). Except I did not limit my investigation to CWF data but also included state prevalence data for other likely influences on mental health.

## ADHD linked to elevation

One of the best correlations with ADHD state prevalence I found was with elevation data for each state. It’s a negative correlation – the higher you go the lower the prevalence of ADHD This figure shows the correlation of ADHD state prevalence in 2011 with mean elevation for the 51 states. It is statistically significant with a correlation coefficient (r) of -0.5 and significance (p) of 0.00.

For comparison, the similar correlation of ADHD state prevalence in 2011 with prevalence of CWF in 2010, while significant, has a correlation coefficient of +0.32 and significance of 0.02. However, the correlation with CWF is not significant in a multiple regression with elevation – see below.

## Other factors worth considering

My exploratory statistical analysis showed a number of other factors significantly linked to ADHD with correlations similar to, or higher than, CWF. Images for the data and a table of correlation coefficients and their significance are shown below.

The correaltion of ADHD state prevalence in 2011 with home ownership and % living in poverty are better than with CWF. These correlations are positive – the prevalence increases with % home ownership and % of people living in poverty. I guess it is hardly surprising that mental health problems would increase with the amount of poverty. But perhaps in the US home ownership is also not conducive to mental health?

The correlations of ADHD state prevalence with educational attainment (Bachelors degree) 2009 and Per Capita personal income 2010 were similar to that with CWF. These correlations are negative – I guess its easy to understand that higher incomes and better education is conducive to better mental health (lower prevalence of ADHD).

The correlation of ADHD state prevalence with the proportion of the sate’s population older than 65 was also similar to that for CWF. The correlation is positive and one can only speculate on reasons for the increase of ADHD prevalence as the proportion of older people increases.

The table below summarises correlation coefficients (r) and statistical significance (p) for the figures above.

**Correlation of ADHD state prevalence with a range of factors**

State data |
Correlation coefficient (r) |
Statistical significance (p) |

Mean elevation | -0.50 | 0.009 |

CWF 2010 % | +0.32 | 0.022 |

Home ownersip % | +0.38 | 0.005 |

Poverty % | +0.37 | 0.007 |

Education (% Bachelor’s degree) | -0.35 | 0.011 |

Per capita income ($) | -0.32 | 0.022 |

Age over 65 % | +0.30 | 0.031 |

## Multiple regressions

CWF in 2010 is correlated with mean elevation – correlation coefficient r=-0.43 and significance p=0.002 – suggesting these are not independent variables. (CWF in 1992 was similarly highly correlated with mean elevation.) Perhaps Malin and Till (2015) only found a correlation of ADHD with CWF because they are both related to mean elevation.

Multiple regression analysis suggests this is the case. The statisitically significant factors were mean elevation (p=0.001), home ownership (p=0.000) and poverty (p=0.005). The contribution of CWF in 2010 was not statistically significant in this multiple regression (p=0.587) as were most of the other factors I considered.

Malin and Till (2015) use the CWF for 1992 in most of their comparisons. My analysis shows this has a better correlation with ADHD prevalence in 2011 than CWF for any other year (r=0.45 cf 0.32 for CWF in 2010). It seems strange to use 20 year old data in a model predicting ADHD prevalence for 2011 so I used more recent data for my exploratory analysis. However, in a multiple regression the contribution from CWF in 1992 was still not statistically significant (p= 0.158).

## Conclusion

We should be careful of conclusions arising from such exploratory investigations. Firstly the obvious – correlation is not causation. But secondly the choice of data is crucial.

Malin and Till (2015) chose to consider CWF prevalence as the main factor influencing ADHD prevalence. They did also include socioeconomic status (SES) as a secondary factor. However, my analysis shows a number of other factors which could equally be considered. And when they are considered in multiple regressions the contribution from CWF is not statistically significant.

The model used by Malin and Till (2015) using CWF in 1992 and SES in 1992 explained only 31% of the variance of ADHD prevalence in 2011. The corresponding firgures for ADHD prevalence in 2003 and 2007 were 24% and 22%.) But using a model for the influence of mean elevation, home ownership and poverty only (no CWF included) I was able to predict the state prevalence of ADHD in 2011 as shown in this figure. This accounts for 48% of the variance and has a significance of p= 0.000. Perhaps further exploration of the available data could produce an even better model but the key point here is that CWF does not contribute anything once mean elevation is included.

I do not think Malin and Till (2015) are justified in drawing the conclusion that CWF influences ADHD. Their mistaken conclusion has arisen from their limited choice of data considered for the exploratory analysis. That in itself seems to have resulted from a bias inherent in their hypothesis that *“fluoride is a widespread neurotoxin.”*

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## 2 Responses to “ADHD linked to elevation not fluoridation”

Hi Ken, well done. Interesting analysis. A couple of points on the stats. I’d never say an r of 0.4 is “highly” correlated – quite the contrary, this is a poor correlation. The p-value may be small, but when it comes to correlations this is very misleading. The issue is that simply by increasing the numbers of “samples” the p-value will get smaller even if “r” does not change. This can result in v small p values even with small r.

ps. Normally, if I see an “r” and not “r^2” I assume the correlation is “Spearman’s” (rank correlation) rather than “Pearson’s”. I’m not sure that is the case here as the graphs look to me as though it would be OK (& better) to use Pearson’s r^2. If so then an r of 0.4 is r^2 of 0.16 suggesting that 16% (only) of the variance in prevalence is explained by the variable.

pps. I’d also avoid calling the p-value a “significant factor” as this can be misleading to those who don’t understand the difference between the statistical convention of “significance” and the every day use of the work “significant.”

I take your point, John, about my use of superlatives. I will go through and at least insert a few “relativelys” – as I was relating the correlations I found to those reported by Malin & Till – also the reason I used r instead of r^2 as they did.

Thanks for these comments – in the past I have always worked with a statistician who would pull me up on these things. But they are not so accessible in retirement.