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comparing weights of irregular shapes

I am trying to produce a graphic for a popular magazine showing how, through overfishing, various species of fish are now physically smaller than they were 50 years ago. My notion was to have an outline of a fish--a tuna, say--and within it a smaller outline showing the smaller modern size. In the 1950s tunas weighed an average of 163 pounds, today 82. Shrinking the larger outline by 50% is clearly wrong, but what is right? (To complicate matters further, I'd like the tuna to be proportional to other pictured fish--a 278 pound marlin, for example.)

-- Paul Rauber (email)

There are many studies examining the relationship between length and weight of just about any fish you would be interested in representing. Most contain a plot of their data with the best fitting line drawn over the data points. For example if you search the literature for "Bluefin tuna length-weight relationship", you will have little difficulty finding a study that includes a useful plot of the Bluefin tuna. Once you decide on a scale, you can use these plots to calculate how long to make an image to represent a particular fish's weight so it is proportional to other fish at different weights.

Jim Gundlach

-- Jim Gundlach (email)

If the fish were the same shape and density regardless of size, for each species, you could use the rule that volume is proportional to the cube of length.

In other words, for each species:

weight = k x length^3

where k is a different constant for each species.

If you could find even one example of a fish with weight and length given you could find k for that species and calculate the length for any given weight using it.

-- Matthew Leitch (email)

If the actual fish existed in only 2 dimensions then a 50 percent smaller outline on the page would accurately portray the size of the smaller fish. Unless you plan to show the fish in 3 dimensions, a 50 percent smaller outline is the right way to compare the smaller fish to the larger one. Let each square unit area of paper represent a given weight, 1 lb. or 10 lb., say, and scale each fish accordingly.

-- Paul Sharke (email)

Are you sure you are not creating chart junk with the pictures of fish? Would a simple table work?

-- Kent Karnofski (email)

Because the fish length and weight are not linearly related, the length of a fish picture would be a bad choice to indicate its weight, as this graph for cod shows: (link)

Perhaps skip the fish picture to indicate weight, or use the picture to show species and length but write the weight. Since we want to show the decrease, consider on page 158 of Visual Display the graph "Current Receipts of Government as a Percentage of GDP, 1970 and 1979". It is an excellent chart showing ranked data, comparison between years, and the rate of change.

If we want to demonstrate that over-fishing is the cause (instead of pollution, loss of habitat, global warming, etc.) then more information is required. Can we distinguish species, not fished or with a regulated catch, that have not decreased in size? Can we correlate the size of the global catch over the last fifty years to the decrease in size?

ET advises against dumbing down graphics. If your readers are smart enough to subscribe to the magazine and interested enough to read the article, then they shouldn't be shortchanged by a data-thin graphics.

-- David A. Nash (email)

This may be a repeat, my computer crashed as I was about to submit, if so I apologise and please skip to the next response.


By trying to represent mass (= volume) by changes in either length or area, you are in grave danger of producing a D.U.C.K. (Deceptive Uninformative Caricature of Knowledge -- cf VDQI).

A better approach would be to have a dot chart showing the catch weights in 1950 and now compared side by side. If your editor still wants "cute/flashy/catchy" you could have an illustrated fish beside/below the comparison.

For this sort of data a table is probably best but I'm assuming that your editor wants a figure.

-- John Walker (email)

I should emphasize that in the graph above, the curve of the line for cod length and weight gives us the information, not the fish pictures. The pictures are only decoration, and in this case very bad decoration, because they unfortunately draw one of the measurements, length, against the other measurement's scale, weight.

-- David A. Nash (email)

"K.I.S.S. 2 D.U.C.K." jd

-- J.D.McCubbin (email)

I would be interested in seeing such a graphic, but only if the relative size of the fish in the graphic corresponded to the relative size of the fish they are referring to. To use relative size to refer to relative weight and in doing so you exaggerate the actual sizes, you would deceive the viewer. So I agree with the previous poster about converting the weight data you have into size data, or find data about average sizes then and now, and let actual size determine the size ratio in your graphic. Of course the difference will not appear as striking between a 163 pound fish and an 82 pound fish showing stickly size diffences but below the fish you can indicate in numbers the weight.

-- mivester

To understand the theorized relationship of overfishing to physical size, I would like to see distributions of the data in histograms or curves (frequency or count versus weight). The 1950's data and 2000's data should be on the same graph for a particular species of fish or a single species in a certain region. Several such graphs could be created (small multiples) and shown on the same page. To best illustrate the theorized overfishing cause, it would help to compare populations of the same species in overfished and non-overfished areas.

If fish outlines or pictures are desireable, they could be added in any blank space in the graph, to identify the species in each graph.

-- Bruce Murden (email)

Thanks to all for your thoughtful and prompt answers! I thought you might be interested in our final decision. We went with Jim Gundlach's suggestion and found the length-weight relationships for each species. (The absence of this data was what was deviling us before, since we found that trying to use length to represent weight was clearly wrong--a DUCK, as some have pointed out.) This also allowed us to make the species proportional to each other, as mivester desired. While perhaps not as striking as some other choices, I feel that its verisimilitude more than compensated. Besides, it's interesting to learn that a tuna that weighs twice as much is only 20% larger.

-- Paul Rauber (email)

For those of us still pondering your very interesting question can you tell us "who cares?" so that a solution might be better tailored when determining the graphic? Is the audience salmon farmers, sport fishermen, or biologists, etc.? I love to salmon fish in British Columbia every year and to demonstrate the size of a fish I caught once, I placed the expired salmon next to my infant and took a photo. It was much more telling than a picture of me holding it up by my two hands and even better than a tape measure or yard stick next to the fish. See Tufte's Visual Explanations pg. 17 graphic in bottom right for another idea.

-- Michael Fink (email)

The audience in this case is a large environmental organization. While eveyone is working on this, let me introduce a new element. In addition to declining in size, the fish are also declining in frequency. The Bigeye Tuna mentioned above, for instance, was eight times more abundant in the 1950s. We experimented with having shadowy tuna shapes lined up behind the illustration to capture this, but it just loooked junky. In the end we just mentioned the fact in the text, but I am nagged by the feeling that there must have been a clever graphic way to portray it. Any ideas?

-- Paul Rauber (email)

Along with a well-made data chart (devoid of junk) you might include photographs. A 163 lb tuna next to an 82 lb tuna, etc, with a caption for each. This will provide the visual punch you're looking for without creating junk or tempting readers with visual comparisons that don't represent numerical truth (scaled oulines, shadows, etc.)

Of course this would take some effort to put together, but worth the effort perhaps.

-- LeMel (email)

Threads relevant to statistical graphics:

Sports data (along with financial and medical data) are an obvious and natural application of sparklines.