by Patti Englert on September 5th, 2005

Patti Englert

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According to the Scientific Method, why is the average of three trials in an experiment more accurate than only doing it once?

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  • by n_o_u_s on September 27th, 2005

    n_o_u_s

    One of the main tools of scientific investigation is induction. So one way to answer your question is that one sample doth not inductive evidence make, and three aren't terribly good, but they are a lot better than one. In my opinion, one sample is largely useless.

    Another way is this. You collect several data points so that you might predict other data points, i.e. you might want to fit a graphical curve to the data. One important task of the statistician is to take some data and find a known probability distribution function (PDF) that the data fits well. I'm only in the middle of my first class on statistical inference, but so far it seems futile to assign a phenomenon a PDF based on a single observation. It also seems very useful to be able to assign a PDF to the phenomenon you are studying. Having at least three data points might let you do that with some confidence, but more are better.

    As an example, I work at a convience store and I often must replenish the soda water and beer coolers. From the back of the coolers (or from inside the walk-in cooler) one notices an interesting pattern. On a given shelf most spaces to the far left or right are full or nearly full, and most in the middle are empty or nearly so. this might help: 8,7,6,3,1,4,5,6,7 where 8 is the number of cokes remaining in the left most slot, and there is one coke left in the middle slot. This is especially the case when the entire shelf is all coca-cola or all regular pepsi. Some investigation yields that the cokes follow a gaussian distribution (aka a normal distribution). Also the 'curve' is shifted slightly away from the hinge on the door, because people rarely reach all the way to that side and more commonly reach for one nearer the side that door opens on.

    If you go to a large super-market where there are 10 or more check-out lines in a row, walmart is good for this, you'll notice that, for the most part, the middle few lines are the longest, while the outliers have fewer people. Again a gaussian distribution, and there will likely be some factors the make the distribution 'lean,' proximity to the exit for one.

    I saw this once several years ago, and it motivated me to pay attention to the sodas and line waiters, and I established, for myself, that these things follow a gaussian distribution only after seeing it many times, and seeing no examples to the contrary.

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