danz
Registered:1348995178 Posts: 192
sfew
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Registered:1135986598 Posts: 850
Posted 1508081586
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#2
Dan, When values along an interval scale are labeled in this manner, which is common, ambiguity is created. I'll illustrate by asking a question. In the top graph, which is a dot histogram, in which column of dots would a state with 30% appear? It isn't obvious whether it belongs in the column to the left or to the right of the 30% label. To eliminate this ambiguity, I usually label ranges of values rather than specific values along the scale (>=15% & <20%, >=20% & <25%, etc.). The graphs that display marginal tax rates are not frequency distribution displays involving interval scales like the upper graphs. The scales along the X axis are ordinal (i.e., a series of discrete values that have a proper order but do not represent intervals along a continuous quantitative range). Notice that 28% appears twice along the X axis. It does so, apparently, because there are two distinct marginal tax rates of 28%, one of which is an alternative minimum tax rate. Lines should not have been used to connect these values--and certainly not curvy lines. Bar graphs or dot plots should have been used to display these discrete values.
__________________ Stephen Few

danz
Registered:1348995178 Posts: 192
Posted 1508091554
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#3
Steve,
First chart scale notation ambiguity does not bother me much. I can accept for such of design a general rule as you mentioned, AK >= 20 and AK < 25. It looks acceptable for me when a continuous range is equally divided this way. When they are not, second graph, same approach does not work for me, your notation is the only choice.
Can we focus one more time on last two charts, showing marginal tax rate? I think they raise even more questions than chart choice and curvy shape. What at first sight looks like an ordinal scale, a repeated equal value at 28 (even marked with *) invalidates the assumption. We can't have two different associated values for the same ordinal value. We can't have another measure mixed up this way either. A virtual possible situation is when the scale is nominal and two different entities having the same label are differentiated with an extra sign. The article has the link to original data. http://www.taxpolicycenter.org/model-estimates/distribution-business-income-august-2016/t16-0185-sources-flow-through-business.

sfew
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Posted 1508101777
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#4
Dan, You actually can have two items that share the same position along an ordinal scale. What makes it an ordinal scale is the fact that the items are discrete but have a proper order. In this case, a marginal tax rate of 28% and an alternative minimum tax rate of 28% share the same position in the order, so their relative order is arbitrary or established by convention. The fact that two items share the same position does not negate the ordinal nature of the scale.
__________________ Stephen Few

danz
Registered:1348995178 Posts: 192
Posted 1508150946
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#5
Steve,

Thank you for your answer. While usually "arbitrary order" term usually excludes the "intrisic order" idea, I was tempted to consider that NYTimes chart uses a nominal scale. I agree with your interpretation that "conventional order" can be assimilated to an ordinal scale. Either interval or ordinal, all NYTimes graphs mentioned in my first post were clearly designed using categorical scales.

Returning one more time to the last two graphs, the designed categorical scales (ordinal) are strongly associated to a quantitative variable (tax rate), yet they are not quantitative scales. However considering the way the article started, with a good slopegraph using the quantitative scale for tax rate, I was wondering if the intention of the author wasn't to actually use the same quantitative scale for last two graphs as well. I will start with first graph which seems to be associated with the statement "Most pass-throughs are small sole proprietorships currently paying less than a 25 percent marginal rate" . A quick makeover of curvy line graph using bars would be the following.

Above makeover does a reasonable good job, yet I would have choose another way of illustrating first statement. Below, my alternate solution making use of tax rate as quantitative scale (X variable) and cumulative frequency of number of units summarized in ascending order of the tax rate as Y variable. Even if it looks very similar, the below design should not be confused with ogive.

I think it make sense to start exploring quantitative variables using associated quantitative scales. But I also agree that interval or ordinal scales derived from quantitative variables values have their own place in data analysis, especially for variables with low cardinality (marginal tax rate).

My overall impression about NYTimes article was that the author was mostly focused on the variety of graphical displays rather than on careful design. Promoted on Twitter by

NYT Graphics , I expect nothing else than top class graphs. But they were not, not this time.

Dan