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I am working with a model that models water flows in a certain area. These flows can be influenced by taking certain measures, resulting in multiple water management scenarios. I would like to compare the flows and residence time per scenario using box plots.

However, the box plots based on the daily output have very many outliers, making the box plots hard to interpret. Creating a box plot of the monthly averaged flows gives a nicer, smoothed box plot (for clarity, I don't mean a box per month. I mean 1 boxplot of the full dataset for each scenario, but averaged by month). However, I am not sure if that is representative, given that I am using averaged values. Is making a boxplot of averaged values useful in any way, or is it like averaging averages, and giving a skewed view of the situation?

Thank you!

Edit: The outliers are not relevant for what we are looking into. The focus is on the "normal" situation, not the extremes. It's okay to lose information on extremes.

Also, the extremes are mainly on the high side (high flows), while there are hardly any on the low side. Uploading an image doesn't work, but on a bean plot the bottom is almost flat and very wide. Then gets slightly wider going up, and then goes up exponentially. Ending in a thin long line on top.

Nathan
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  • For some constructive ideas see https://stats.stackexchange.com/questions/13086 and the second part of https://stats.stackexchange.com/questions/74537 (concerning re-expressed values) The use of boxplots goes hand in hand with other basic tools of exploratory data analysis and visualization including re-expression and examination of residuals. – whuber Jan 30 '24 at 11:40
  • I have worked a lot with discharge data and almost always plot on logarithmic scale. For management purposes total discharge is of some importance often. For analysis purposes box plots are usually indirect at best. – Nick Cox Jan 30 '24 at 18:21

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This is up to you and what you want to find out. Are the outliers important? I could see how they could be (floods, droughts, etc) but maybe not. Or do you only want an average per month (maybe you have to allocate resources that way?)

My tendency would be toward the daily plots, but I don't know what you want.

You also might not want boxplots at all.

Peter Flom
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    +1. I dislike boxplots intensely, because they condense all the info into just 5+ pieces of information, and typically people have no visceral understanding of the fact that 50% of the observations fall outside the box. Do consider plotting the underlying data (possibly a subsample, or jittered horizontally), perhaps a beanplot. You can also overlay the beanplot and the boxplot over the actuals. (If you add a boxplot over the actuals, turn off plotting the "outliers", because otherwise these will be double-plotted.) – Stephan Kolassa Jan 30 '24 at 10:44
  • @Peter Flom Thank you for you answer! I understand what you are saying, but it's not really where my problem lies. I'm trying to find a way to phrase my question better.

    For this case, the extremes are not important. If the model output would be monthly, I would use that dataset, but it can only give daily output, which is then averaged to monthly output. Because the extremes are not important here, I would prefer to use the monthly averaged dataset. What I am unsure about is the statistical implication of doing so. Does it give any insights, or is it skewed like averaging the averages?

     – Nathan Jan 30 '24 at 12:59
  • It isn't skewed, it just obscures the data by averaging it out. If that's what you want. – Peter Flom Jan 30 '24 at 13:07
  • The focus is on the general state of the system, deliberately wanting to exclude extremes. They are not relevant for the scenario's, and make it harder to compare the "regular" situation, which is what we want to look it.

    In this case, am I correct to say that "obscuring the data" means I lose some information, like the outliers (which is acceptable, and even desired) and thus this I can use the monthly averages? Would it be similar to using a model that would give monthly output directly? Is there a better way to visualise the data, with a focus on "normal" not "extreme"?

     – Nathan Jan 30 '24 at 13:20
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    @StephanKolassa Thanks for your reply! I am experimenting with the bean plots and other suggestions now. – Nathan Jan 30 '24 at 13:24