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What Can Classical Chinese Poetry Teach Us About Graphical Analysis?

mountainsA famous classical Chinese poem from the Song dynasty describes the views of a mist-covered mountain called Lushan.

The poem was inscribed on the wall of a Buddhist monastery by Su Shi, a renowned poet, artist, and calligrapher of the 11th century.

Deceptively simple, the poem captures the illusory nature of human perception.
 

poem   Written on the Wall of West Forest Temple

                                      --Su Shi
 
  From the side, it's a mountain ridge.
  Looking up, it's a single peak.
  Far or near, high or low, it never looks the same.
  You can't know the true face of Lu Mountain
  When you're in its midst.

 

Our perception of reality, the poem suggests, is limited by our vantage point, which constantly changes.

In fact, there are probably as many interpretations of this famous poem as there are views of Mt. Lu.

Centuries after the end of the Song dynasty, imagine you are traversing a misty mountain of data using the Chinese language version of Minitab 17...

Written in the Graphs Folder in Minitab Statistical Software     

From the interval plot, you are extremely (95%) confident that the population mean is within the interval bounds.

From the individual value plot, the data may contain an outlier (which could bias the estimate the mean).

From the boxplot, the data appear to be extremely skewed (making the confidence interval and mean estimate unreliable).

From the histogram, the data are bimodal (which makes the estimate of the mean utterly ...er...meaningless)

From the time series plot, the data show an order effect, with increasing variation and downward drift.

From the individuals and moving range charts with stages, the data appear stable and in control:

These graphs are all of the same data set.

Take it from Su Shi. Don't rely on a single graphical view to capture the true reality of your data.

Image of Lushan licensed by Wikimedia Commons.

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Comments

Name: tamoghna • Wednesday, April 16, 2014

Why the outlier (Q1-1.5x IQR) is not reported in the Box plot?

How to interpret the IMR chart


Name: Patrick • Tuesday, April 22, 2014

Good questions. The point that appears as a possible outlier on the individual plot is not shown as an outlier on the boxplot because it does not meet the conditions for the outlier test used by the boxplot: it is not below the quartile 1 value by at least 1.5 times the interquarile range (the length of the box). That's why it's a good idea to look at the individual value plot as well, in case there are data points that are "close" to being outliers but that may not satisfy formal criteria for defining an outlier. Such data values might still have a strong effect on the results--depending on the sample size--or represent something unusual going on--including data entry errors.

Interpret the I-MR chart like other control charts. Out-of-control points on an I chart indicate the process center is not stable, due to the presence of special causes. Out-of-control points on the moving range chart indicate the process variation is not stable.

On the I-MR chart with stages shown above in the post, the process appears to be in control. That's because the chart uses stages to identify two distinct groups in the data (you can see the two groups clearly on the bimodal histogram). If you displayed an I-MR chart without stages, without accounting for these two groups in the data, the I-MR chart would show out-of-control points and you'd reach the opposite conclusion: your process i unstable. You always have to be on the look out for those sneaky lurking variables!

For more information on interpreting the I-MR chart choose Minitab > Stat Guide. Under Contents, expand Control Charts. Expand Variables Charts for Individuals/. Click I-MR.

Thanks for your questions!


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