Welcome to dead salmon data

The name for this blog was inspired by a paper by Craig M. Bennett, Abigail A. Baird, Michael B. Miller, and George L. Wolford. They studied how a dead salmon placed in a functional magnetic resonance imaging (fMRI) machine “responded” to pictures of people in emotional situations.  The salmon was not entirely forthcoming with its judgments, but Bennett and his colleagues did record some of the dead salmon’s “brain activity.” 

fMRI images are organized into tiny cubes, called “voxels.”  In flat, 2-D images, each tiny region in the image is represented by a pixel.  With the 3-D images derived using fMRI, each small 3-D region is called a voxel.  Just as the signal in a pixel represents how much light there was at that small region, the fMRI voxel represents how much biological activity there was in the corresponding 3-D region. In living brains, that activity usually represents the level of neural activity in the region.  Of the available voxels, Bennett and his colleagues found significant activity in 16 voxels, about 0.01% of the total volume. 

Based on these findings and using statistical analyses that were commonly used at the time, the authors might have concluded that they had identified the part of the fish’s brain that was responsible for making judgments about the emotional state of human beings depicted in photographs.  Before Bennett’s study was available.  About 25 – 30% of studies using fMRI published in journals used the same simple techniques as did about 80% of the papers presented at a neuroscience conference.

Obviously, there is something wrong here.  The idea of a dead fish responding to human emotion does not pass the “smell test.”  It would be remarkable enough for a live fish to identify human emotion, but it is utterly beyond reason to think that a dead one could, or that the authors were measuring brain activity in a dead fish. On top of that, we have no evidence that the fish actually engaged in the task it was assigned, as it never revealed its decisions about the emotional valence of the pictures it “observed.”

The measures of brain activity obtained using functional magnetic resonance imaging, like most other measures of just about any phenomenon include some random variation in the measured quantity. Standard statistical measures were designed to take this random variability into account.  Two measures may be numerically different without being reliable different from one another when both measures include some level of randomness. Statisticians have evolved the notion of statistical significance to indicate that an observed numerical difference is unlikely to have occurred by chance. 

But these assessments of statistical significance also involve some degree of random variability. Statisticians recognize that there are two kinds of errors that can occur.  Type I errors occur when we find a difference, when there is no actual difference (“false positive”), Type II errors occur when we fail to find a difference when there actually is one (“false negative”). 

fMRI studies compare the measured activity in each voxel during the task, with its measured level of activity during a control interval.  The more brain activity there is, the stronger the signal measured by the fMRI machine. If we were to compare the activity levels of 130,000 voxels under these two conditions, some of them would show high levels of activity just by chance because our measure is imperfect.  We would expect some percentage of these comparisons to result in false positive errors.  The specific percentage we would expect is determined by our standard of significance, often called the “p value.” It was pretty common in fMRI studies to set this value to 0.001, meaning that we would expect about 130 of the 130,000 voxels to show what appears to be a real difference, when there really is nothing but random measurement error. Multiple comparisons raise opportunities for multiple false positive errors.

There are statistical techniques for dealing with large numbers of comparisons.  In summary, these methods modify the significance standard so that differences relative to control have to be greater before one accepts that they are due to anything but chance.  When those adjustments are applied to the dead salmon fMRI data, it turns out that there are no significant areas of brain activity in the fish, as we really should expect.  When the same techniques were applied by Bennett to 11 published fMRI studies, three of them had no significant results to report at all.  If these corrections for multiple comparisons are not properly applied, researchers can come to false conclusions about the validity of their data, which can lead to wasted research effort and dead ends.

The importance of these findings extends far beyond one dead salmon, far beyond fMRI.  Spurious correlations are common throughout big-data data science.  For example, annual US spending on space, science and technology correlates over the years 1999 to 2009 with the annual incidence of suicides by hanging, strangulation, and suffocation.  http://www.tylervigen.com/spurious-correlations  If there is some kind of causal relationship here, it completely escapes me. If you have enough data and look hard enough you can find any number of correlations, but that is no guarantee that those correlations are at all meaningful.  People have a way of finding patterns, even when there are none.  Sometimes the statistics help.

Traditional statistics were developed for a time when the expensive part of research was collecting data.  Now data are plentiful, but extracting meaning from those data is still a challenge.  Simple methods are often the best, but they can also be too simple. In later posts we will consider other potential hazards of data science and what we can do to avoid them.  Unless we are careful with our data and our analyses, it is easy to get seduced into believing that we understand something when really we do not.  On the other hand, it is also easy to get seduced by approaches and methods that are popular, but may not be the best approach for the questions at hand.

In future posts, I hope to consider many of the ways in which data science, machine learning, and artificial intelligence can go wrong, but also some of the ways it can go right.  Data science is of growing importance to our businesses and even to our culture, but it is also easily misunderstood. In the same way that we see animals and faces in clouds, we may attribute to data science, particularly to artificial intelligence, properties that are not really there.  I hope to address some of these tendencies and make data science stronger and more useful as a result.

Craig Bennett,  Abigail A. Baird, Michael B. Miller, George L. Wolford (2009).  15th Annual Meeting of the Organization for Human Brain Mapping. San Francisco, CA: 2009. Neural correlates of interspecies perspective taking in the post-mortem atlantic salmon: an argument for proper multiple comparisons correction.

Craig M. Bennett, Abigail A. Baird, Michael B. Miller, George L. Wolford. (2010). Neural correlates of interspecies perspective taking in the post-mortem Atlantic Salmon: An argument for multiple comparisons correction. Journal of Serendipitous and Unexpected Results.