Wednesday, April 04, 2018

Errors v/s Error bars

A lot of people confuse errors with error bars.

Every measurement has sources of error in it. Another way to say this is that there is no such thing as a perfect measurement. There are two main types of error - random error (which includes errors made by the observer) and systematic errors (which are the by product of unknowable or poorly captured physics in the system of measurement).

The existence of errors in each measurement has two main consequences

1) Accuracy (how close the real value of a physical quantity the measurement is) is not a naturally available quantity in every measurement - so it has to be carefully redefined in terms of precision (how repeatable the measurement of the same physical quantity is).

2) Unless the error of the measurement is bounded (i.e. does not exceed/fall below a certain amount) - a discussion of the precision of the measurement becomes impossible.

Error bars typically report the bounds of the measurement. It is impossible to compare quantities that do not have error bars because you don't know what will happen if you measure the same thing again. The first measurement could be an accident or an experimental artifact - and unless you have a sense of what the error bars on the measurement are, you can't make any statements about the reliability of that one number you have just captured.

There are well developed techniques that allow a user to estimate the bounds on the random error in a measurement. These are often taught in high school and undergrad level sciences classes. There are more complex ways of accounting for the systematic errors - but that is a very advanced topic typically only taught to graduate students who work in measurement heavy disciplines like experimental physics and extremely high end instrumentation engineering. This is an unfortunate aspect of modern science education. Most scientists figure out the way to handle systematic errors on the job and often at cost to their careers. I wish it weren't like this and that everyone was put on the same level playing field w.r.t systematic error related education - but this is a very difficult topic to teach.

That said - in the world of professional scientists - measurements are often presented with implicit error bars. A common theme is to neglect the lower bound on the error bar as it is usually set by the instrument of measurement and only report the upper bounds. This works as long as you are communicating with your scientific peer group. Communicating outside it can be challenging if you don't discuss the error bars in detail. 

Communicating such matters with lay audiences is even more challenging.

Ordinary civilians associate error with blanket unreliability. They do not understand the key difference between bounded v/s unbounded error in measurements. The extent of understanding depends on the actual level of mental competency and agility accrued during education. There mere existence of a HS or College degree is no guarantee that they will understand what you are saying. 

A significantly adverse consequence of this kind of problem is in mass communication of healthcare related information. You can see this when you compare the number of idiotic comparisons between allopathic clinical information (which has well established scientific error bars) and homeopathic/traditional medical information (which is presented as fact without error bars). Peopl put these two things on the same footing. It is stupid and causes a major problem with public health issues especially in pandemic prone areas of the world.

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