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Plotting Zero Values (Logarithmic Scatter Plot)

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    Plotting Zero Values (Logarithmic Scatter Plot)

    When I Google this problem, I only see results for the problem opposite to that which I'm having. I need to plot zero values, not get rid of them.

    I am plotting logarithmic permeability (x-axis) vs. depth (y-axis). Apparently Excel cannot plot zeros on a log scale simply because the logarithm of zero is undefined (correct?).

    Here's my problem. Not only does permeability vary over several orders of magnitude, but it often has a value of zero (or effectively zero). For the project on which I'm working, the depth intervals which have zero permeability are just as important to plot as those that have permeability values greater than zero. Some of the intervals simply have no data, and if I cannot plot the zero-value intervals, then on the graph they are not decipherable from those that don't have data.

    If I turn off the Log scale, I can plot zeros, but cannot effectively display the variability of magnitude. Ideas for solutions?

    Thanks in advance.

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    Re: Plotting Zero Values (Logarithmic Scatter Plot)

    Make the zero values #N/A, which will keep them from plotting. Nothing is totally impermeable, it's just to low to measure, and as you point out, 0 has no logarithm.
    Entia non sunt multiplicanda sine necessitate

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    Re: Plotting Zero Values (Logarithmic Scatter Plot)

    Quote Originally Posted by shg View Post
    Make the zero values #N/A, which will keep them from plotting. Nothing is totally impermeable, it's just to low to measure, and as you point out, 0 has no logarithm.
    No offense, but did you read my question? I need to plot the zeros, not "keep them from plotting."
    Last edited by aaochsner; 10-29-2013 at 08:30 PM.

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    Re: Plotting Zero Values (Logarithmic Scatter Plot)

    No offense, but did you read my answer? You can't plot zero values on a log axis.

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    Re: Plotting Zero Values (Logarithmic Scatter Plot)

    Quote Originally Posted by shg View Post
    No offense, but did you read my answer? You can't plot zero values on a log axis.
    I'm not on here for an argument. If you read my post you'll see that I already know that. I'm looking for a way to display both magnitude variability and zero values.

    If there's no way to do that in Excel, fine. Just looking for possible solutions.

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    Re: Plotting Zero Values (Logarithmic Scatter Plot)

    I'm not sure it is a question of whether Excel can do it or not -- it's more a question of what you really want Excel to do. At this point, it seems that you really don't have a good idea of what you want Excel to do. Some thoughts:

    1) 0 (zero) has no meaning on a logarithmic axis. One could put an arbitrarily small non-zero value in, but this might unduly obscure the logarithmic axis, depending on what the magnitude of the other values is. Perhaps assign a value of one or two orders of magnitude smaller than the smallest non-zero value to these zero values and plot them. Your readers will need to be smart enough to recognize that this is an arbitrary value that represents 0.

    2) Since Excel can only do linear or logarithmic axes, those are the two choices. If you decide the previous suggestion won't work, then I would suggest coming up with a different "transformation" for the axis. Perhaps a square root axis or some other transformation will work. These other axes can be plotted in Excel using variations on this "arbitrary axis" technique, such as this one used for a reciprocal (1/x) axis http://peltiertech.com/Excel/Charts/RecipAxisChart.html At that point, the hardest part will be outside of Excel, trying to decide what kind of transformation will be most useful for your data.
    Quote Originally Posted by shg
    Mathematics is the native language of the natural world. Just trying to become literate.

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    Re: Plotting Zero Values (Logarithmic Scatter Plot)

    Quote Originally Posted by MrShorty View Post
    At this point, it seems that you really don't have a good idea of what you want Excel to do.
    I had an idea of what I wanted Excel to display, but apparently did not have a grasp on how synonymous Excel's graphing limitations are with the relevant mathematical limitations (in other words, I thought I could maybe "cheat" somehow).

    I'll look into axis transformations, as you suggest. I considered option 1, but would like to avoid it if I can.

    Thanks!

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    Re: Plotting Zero Values (Logarithmic Scatter Plot)

    I don't doubt that such "cheats" can be implemented in Excel, they just won't be pre-programmed into Excel for us.

    Another thought: use a panel chart http://peltiertech.com/WordPress/bro...n-excel-chart/ One panel could show the plot you have now, not displaying the zero values. The second panel could show the same data on a linear plot to show the relationship of the other data to the 0 values.

    Out of curiosity, what kind of "permeability" is this (geologic, chemical, or other? your reference to depth might suggest geologic/earth science type data)? I have to believe that you are not the first one to encounter this issue. How have others in your field presented this kind of data?

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    Re: Plotting Zero Values (Logarithmic Scatter Plot)

    Quote Originally Posted by MrShorty View Post
    Out of curiosity, what kind of "permeability" is this (geologic, chemical, or other? your reference to depth might suggest geologic/earth science type data)? I have to believe that you are not the first one to encounter this issue. How have others in your field presented this kind of data?
    Thank you for your suggestions, sounds like I may have a few different options on how to display this.

    This is geological permeability. Modern permeability data can have precision as high as 0.001 millidarcys (mD, where 1 mD = 9.869233e-13 m2) or better. I'm not sure what the precision of the modern permeameter is, but for most groundwater modeling purposes (which I'm working on), one does not need a precision any better than that. Therefore, most publications these days that plot permeability vs. depth do not have the problem I'm having. The data I'm working with, however, is over 50 years old, and has a precision of only 0.1 mD. Anything lower than that was given a '0' value. This is why I prefer not to assign arbitrary values to the zeros. Ideally, I'd be able label my lowest x-axis tick mark as <0.1 mD, but to my knowledge that is not possible in Excel. Given that, a footnote specifying zeros as simply being <0.1 mD seems more reasonable than just giving them a value of 0.01 or 0.001, for example.

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    Re: Plotting Zero Values (Logarithmic Scatter Plot)

    Ideally, I'd be able label my lowest x-axis tick mark as <0.1 mD, but to my knowledge that is not possible in Excel.
    True, if you limit yourself strictly to built in functionality. I expect this should be fairly easy using the arbitrary axis technique I mentioned earlier (different example here http://peltiertech.com/Excel/Charts/ArbitraryAxis.html).

    1) It sounds like the minimum real value is 0.1, so assign those which are sited as 0 the plotted value 0.01.
    2) Create a dummy series to be used for the "arbitrary axis". This will need y values at each decade from 0.01 to the desired max value for the y axis. The x value should be chosen to place the axis where you want it (far left, I assume).
    3) For the axis labels, you can use the y values as plotted, except for the 0.01 mark, which will be labeled "<0.1".

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