He was the first statistician that had a real impact on me. His book “Data Analysis and Regression” coauthored with John Tukey was the first time I had encountered any thinking when dealing with statistics. Until then, all of the statistics books I had read were purely mechanical. You have a normal distribution, your mean is this, your median is that. You calculate standard deviation like so. Mosteller’s book started out asking how normal was the distribution? How can you be sure of what you are measuring and how can you minimize the errors when trying to discern the central tendency of that invisible distribution underlying your data? He showed how it was easy to confuse a normal distribution with a so called “dirty” normal distribution. The dirty normal was a kind of worse case scenario for statisticians in that the data looked like a typical normal distribution, but the actual trend that you were trying to study deviated from a normal distribution in some substantial ways.
What this means is that if you took an arithmetical mean (the average) of your data, it would be significantly different than the actual center point of the underlying trend. He used a variety of trimmed means and studies of Kurtosis (how normal is your normal distribution) in order to minimize errors when trying to estimate central tendencies.
I know, I’m a big geek. But the man made statistics something worth thinking about! I admired his approach (if not his rather obtuse writing style) and his book gave me quite an insight into how statistics actually works. Turns out that he was in a nursing home right here in Falls Church! Had I known that I’m sure that I would have gone to visit him once in a while…
You can read more about him and his amazing range of research topics here.