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Using Probability Distribution Plots to See Data Clearly

Bring your numbers to life

Eston Martz
Tue, 09/15/2015 - 11:41
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When we take pictures with a digital camera or smartphone, what the device really does is capture information in the form of binary code. At the most basic level, our precious photos are really just a bunch of 1s and 0s, but if we were to look at them that way, they'd be pretty unexciting.

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In its raw state, all that information the camera records is worthless. The 1s and 0s need to be converted into pictures before we can actually see what we’ve photographed.

We encounter a similar situation when we try to use statistical distributions and parameters to describe data. There’s important information there, but it can seem like a bunch of meaningless numbers without an illustration that makes them easier to interpret.

For instance, if you have data that follow a gamma distribution with a scale of 8 and a shape of 7, what does that really mean? If the distribution shifts to a shape of 10, is that good or bad? And even if you understand it, how easy would it be explain to people who are more interested in outcomes than statistics?

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Submitted by William A. Levinson on Tue, 09/15/2015 - 10:03

Always include a probability plot

A histogram and a quantile-quantile plot should ALWAYS accompany any process capability study, SPC chart, or designed experiment (for the residuals in the latter case). Otherwise there is no guarantee that the assumptions you have made are valid. The non-fit of a bell curve to Poisson data, as shown in this article, is a good example, although the Poisson will behave more normal as its mean increases. That is generally not good, though, because the Poisson distribution is a model for defects.

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