Statistically controlling for confounding constructs is hard (2016)
Mindblowing. No wonder so much science doesn&#x27;t replicate.<p>I read scientific papers fairly often compared to the average person, and this is probably the most important I&#x27;ve read in years. It feels like a similar problem to Spectre in the CPU design space: a problem nobody noticed for decades, that breaks fundamental assumptions in ways that appear nearly impossible to fix. Except this is way bigger and more important than Spectre.<p>Here&#x27;s a quick summary of the paper and its conclusions:<p>1. Virtually all claims of the form &quot;We have found X is an important factor when controlling for other factors&quot; are wrong, because they ignore the possibility of measurement error, which has unintuitive and enormous effects.<p>2. As a consequence, vast swathes of so-called findings in medical and social sciences are spurious to an even greater extent than previously realised. The paper cites Google Scholar searches to show that hundreds of thousands of papers contain trigger phrases like &quot;after controlling for&quot;.<p>3. The problem is fundamental and can&#x27;t be fixed.<p>For (3) I should explain, because the paper does propose what initially looks like a fix: an improved form of statistical modelling that incorporates measurement error into the outcomes (SEM). This can restore statistical validity.<p>Unfortunately as we study this idea closer it becomes clear that there&#x27;s no way scientists are going to adopt it:<p>• It explodes the sample sizes and therefore cost.<p>• Frequently we have no idea what the measurement error actually is.<p>• Therefore it becomes impossible to say with any confidence whether a claim is true or false.<p>Even very small amounts of measurement error can push the confidence level of the outcome under the already arbitrary and probably too lax 95% threshold. To detect a weak effect size of 0.1, handling realistic error rates could easily take you from needing hundreds of samples (grad student populations) to tens of thousands.<p>To clarify the term &quot;measurement error&quot; here, what the paper gets at is that in social sciences they are often trying to measure things indirectly via e.g. surveys which have some inherent noisiness due to people lying, not understanding the question, not being sure of the answer but being unwilling to admit it etc.  And then on top of that they are often trying to measure something ill-defined to begin with, e.g. mood, intelligence, wealth.<p>But as noise rates go up, the chances of spuriously detecting correlations that don&#x27;t exist reaches <i>100%</i>. The paper does various simulations to show that this can easily happen with 
sample sizes, p values and error rates that are standard.<p>The part that really nailed it for me was where they use a hypothetical example of a correlation between ice cream sales and swimming pool deaths. Common sense tells us ice cream doesn&#x27;t cause people to die in pools, but rather, on hot days more people go swimming and buy ice cream: it&#x27;s a confounding variable. In the case where the confounding variable is accurately measured with a thermometer, measurement errors are zero and the typical sort of regression analysis scientists use shows no correlation as expected. But if temperature is measured using a survey where people self report perceived body temperatures on the Likert scale, then you get an error rate of about 0.4. At that point a regression analysis shows a strong direct correlation between eating ice cream and dying in a pool with p &lt; 0.001 - much lower than the p &lt; 0.05 threshold needed to trigger publishing.<p>A big question is what does this mean for science and the academy? I can see nothing happening in the short run: it seems this paper wasn&#x27;t picked up by journalists, or at least I&#x27;ve not seen any mention of it even in discussions of the replication crisis. Scientists themselves can&#x27;t really pay attention to it without breaking the entire funding model of non-STEM sciences.<p>In the long run this could possibly lead to a major breakdown in society&#x27;s notions of expertise, trustworthiness of scientists and the value of government funded academia (corporate funding of social sciences is close to zero). How many decades have people been reading stories of the form &quot;$foo causes $bar&quot; or &quot;$baz (good thing) is highly correlated with $zap (bad thing)&quot;? Many people have already clocked that this kind of science is unreliable - now we seem to know precisely why.