Jan 23 2008
Accuracy? We Don’t Need No Stinkin’ Accuracy
The issue of accuracy versus precision is interesting to me. In science, there is a distinct difference between the two words. Yet to everyone else, the two are synonymous. Therefore, I was slightly amused by this exchange on Anthony Watts’ blog. A commenter wrote the first part, and Anthony replied.
In an earlier entry, you said this MMTS unit is accurate to plus or minus 5 degrees. How does this compare to the MMTS units NOAA uses now? And how accurate should the unit be to replace current models?
REPLY: “you said this MMTS unit is accurate to plus or minus 5 degrees”
I never said any such thing. That level of accuracy would be useless.
The original question refers to an accuracy [sic] of plus or minus 5 degrees. This of course is not accuracy, but precision. But what if he did mean accuracy. Any accuracy-related problems with the temperature record would involve a bias in the data, and would not affect the trend. Therefore, I can only assume he meant precision, and maybe said accuracy because the original question did.
Let’s look at what a 5 degree precision instrument record might look like. Below is a graph of a made-up time series of temperature data. This represent daily maximum temperature, as might be recorded at a surface station. It has a yearly cycle with a magnitude of 20 degrees, there is a 5 degree random error associated with each point, and there is a linear trend of 0.12 degrees. (All temperature are in C.)
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This looks almost exactly like a plot of actual temperature for a year. The only thing missing is the synoptic scale weather patterns. However, we don’t really need them in this example because their effects would average out. This data has 30 years, and it’s hard to see what each year is doing, so below I’ve extracted just the first year from the plot.
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Here it is easier to see the effects of the random error associated with each point. This really doesn’t tell us much. But what if we averaged all the points for each year, and then plotted it.
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Now this is getting somewhere. When all the days are averaged, the random errors can still be seen in the yearly data because the error for each day was a significant part of the yearly cycle. But one thing is obvious from the graph. There is an upward trend in the data, that is significantly different than zero. The trend is not exactly equal to the trend I prescribed, but that is the nature of random error. There was an equal likelihood that the trend would have been less than 0.12.
So is a precision of 5 degrees worthless? No. The degree of precision in a measurement are dependent upon what you need. In the example above, 5 degrees of precision was plenty. If one needed to know the average monthly temperature to within 0.01 degrees, then a precision of 5 degrees would probably not be too good, and any bias (accuracy) would be really bad.
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2 Responses to “Accuracy? We Don’t Need No Stinkin’ Accuracy”
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Even better, get rid of the annual trend by plotting each data point against the same data point in other years.
I just noticed this post from some time ago. I wish I had seen it sooner.
You are correct in saying that I should have used the word “precision” rather than “accuracy”. That’s what I get for rattling off a response mimicking the poster’s question without taking a pause to think my writing through. Mea culpa.
It happens. Eli made a similar silly mistake in a post on my blog by saying “A solution with pH 8 is more basic than a solution with pH 9. ” When what he probably meant was “more acidic”.
Confusing the two terms (precision and accuracy) is a common mistake made by laymen, and occasionally scientists.
Your photo of the arrow and bulls-eye is often used to illustrate the difference - it’s a good choice because laypeople can often understand it better that way.
In your example above, while you can derive a trend from a +/- 5 degree measurement, that wouldn’t be all that useful for a situation where you are looking for a trend expected to be in tenths of degrees.
But thanks for your point and example, it is an inspiration for me to post an article on the difference between accuracy and precision to help many of the laymen readers that frequent my blog understand it and as a reminder to myself to be more careful when I write.