When statistically significant is insignificant

I love Twitter. I got a hold of this little bit of anti-vax nonsense and just had to bring it to everyone’s attention. Check this out:

Source.

You can click on the image to see it a little larger. The original caption is what caught my eye. It reads: “Snapshot of the Verstraeten study dated 02/29/00 showing a statistically significant relationship between mercury exposure and autism.” My emphasis added in bold because this image shows no such thing. It shows a statistically insignificant relationship between mercury exposure and autism.

However, I realize that some of these terms might as well be in Chinese to some of you, unless you speak Chinese. So let’s break it down piece by piece.

Relative Risk (RR) is the ratio in the risk of developing autism given an exposure to thimerosal between a control and an intervention group. That’s the left-hand axis. The control group doesn’t get thimerosal. The intervention group does.

For example, if the RR is 10, then those exposed to thimerosal have a ten times higher risk of developing autism than those who were not exposed. An RR of 1 means that there is no difference in the risks; both exposed and unexposed have equal risks of developing autism. So, an RR of 1 means that the relationship observed is not statistically significant.

Statistical significance means that the results you observe are not due to random chance. That’s the 95% confidence interval (CI) part. That CI tells you the range of RR values you’d see 95 out of 100 times if you repeated the same experiment 100 times. The CI in this chart is represented by the error bars in each value.

At <37.5 micrograms, there was no difference between the two groups. The RR was 1. Note the lack of error bars for that value because of the low number of study subjects (n=5).

At 37.5 micrograms, the RR is still 1. Again, no difference.

At 50 micrograms, the RR is 0.93. This means that the control group is about 7% more likely to develop autism than the thimerosal group. BUT the CI includes 1, so there is a very good chance that your RR will be 1 if you repeat the experiment 100 times. As a result, this finding is not statistically significance. Certainly, I would not go out to the streets and proclaim that thimerosal protects from autism.

At 62.5 micrograms, the RR is 1.26, meaning that the group receiving thimerosal is 26% more likely to get autism than the control group. BUT look at the CI again! It still includes 1. As before, this result is statistically insignificant.

At over 62.5 micrograms, the RR rises to 2.48. The CI still includes 1. This result is statistically insignificant.

Wait! Doesn’t this show a trend whereby if the exposure is high enough, then the association will be stronger? Nope. It doesn’t. If you look at the error bars, you could hit 1.0 the whole time. Heck, with the logic shown in this article, I could make a case that thimerosal is protective against autism at certain levels.

It’s nonsense (to not use a harsher word).

But anti-vaccine advocates are not known for letting facts get in the way. The author of that piece of nonsense continues with quotes taken out of context from some meeting long used by anti-vaxers as evidence of a plot… Blah! Blah! Blah!

If you don’t know what is statistically significant and what is not, then that pretty much destroys your entire argument from the get-go. If you try to come off as a researcher, when you’re obviously not, then you lose the argument even worse.

But what about that study? Well, read all about it here, here, here, and here, and see how it has been misused to further the anti-vaccine agenda. Too bad they don’t know the difference between significant and insignificant, or they would have not used this study (or this graph).

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