5 ms·

https://twitter.com/benmschmidt/status/1562489422503120896 https://twitter.com/benmschmidt/status/1562489422503120896 It's a log scale centered on 100%, so t

by tedd4u 4y ago

https://twitter.com/benmschmidt/status/1562489422503120896 https://twitter.com/benmschmidt/status/1562489422503120896 It's a log scale centered on 100%, so that the relative positions of dots accurately shows their proportions relative to each other. E.g. "doubled" is the same distance from "stayed the same" as is "halved." A weird hills I choose to die on is that log scales are often better.

josephg 4y ago
Yep; I agree. The original has some layout issues (the 0 line should be highlighted). But the scale is better. In the "fixed" chart the scale goes from -130% (meaningless - implies negative degrees were awarded) to about +130%. A course dropping its graduation rate to 0 would be a big deal - but this chart implies it wouldn't be as shocking as the CS graduate rate doubling. The top entry is at 130% - meaning the number of graduates approximately doubled (2.3x). The lowest entry looks to be about -48%, so the number of graduates approximately halved. These are similar changes, so they should look like similar magnitudes in the chart's scale. But in the "corrected" chart, they look very different. In a geometric / logarithmic scale, they would look like they'd drifted a similar distance from the middle ("unchanged"). If I were going to improve this even more, I'd draw lines from each data point back to the centre point ("0") implying movement from the centre (which is what the chart is showing). Nitpicking mode: I'd also label the centre as "unchanged from 2011" and I'd add the absolute numerical values to the chart. (There's plenty of room!). I also find the title a bit vague. "% change in undergraduate degrees 2011-21" made me wonder if it was talking about the enrollment or graduation rate. I'd mention that its counting undergraduate degrees awarded, and that the data set is for the USA. (As opposed to a particular college, or the whole world or something). As it is, both variants seem a little underwhelming to me. Original: https://statmodeling.stat.columbia.edu/wp-content/uploads/2023/01/harvardmag_humanitiesmajors.jpg https://statmodeling.stat.columbia.edu/wp-content/uploads/20... "Fixed": https://statmodeling.stat.columbia.edu/wp-content/uploads/2023/01/redo_harvardmagazine_humanitiesmajors.png https://statmodeling.stat.columbia.edu/wp-content/uploads/20...
rcme 4y ago
Log scales are impossible to reason about unless you're dealing with exponential data. Otherwise, the transform is meaningless because log is literally an exponent, so not having an exponent in the data is equivalent to garbage in, garbage out, more or less.
- nerdponx 4y ago
  The quote literally explains how to reason about it.
  - rcme 4y ago
    > "doubled" is the same distance from "stayed the same" as is "halved." What's more natural: looking at a change relative to 0, or looking at a change relative to all the other points? Personally, I think looking at a change relative to 0 makes much more sense. Trying to figure out the meaning of the points by looking at relative values is garbage, because there is no underlying exponent to justify the use of the logarithm.
    - rssoconnor 4y ago
      If the number of students enrolled in my course goes up by 25% one year, and then the next year the number of students enrolled in my course drops by 20%, how many students are now in enrolled in my course compared to the beginning? What if it were reversed: what if the number of students dropped by 20% one year, and then when up by 25% the following year. How many students are now enrolled in my course compared to the beginning in this scenario?
      - rcme 4y ago
        In any scenario like that, where a quantity X changes by Y% and then that new quantity changes by Z%, I almost always think about it like (1 + Z) * ((1 + Y) * X). That is, I compute the new size after adjusting by Y% first, and then take Z% of that. To me, this is still treating values as magnitudes from 0 and the Y% change is totally independent from the Z% change. I guess you can multiply Y and Z first, but that’s not how I think about it.
kurthr 4y ago
Coming out really strong on the quadratic fit is pretty weird. People aren't going to judge you for keeping your mouth shut, but not recognizing a log scale? I mean over this short a range (and I do which he'd plotted -50% -30% 0 +40% +100% +140%) a linear interpolation is easy and pretty accurate. You'll probably notice the sqrt2 in there, if you look.
Spivak 4y ago
I think the original graph maker is 99% the way there in the followup. This data makes no sense at all in a graph like this, a table sorted by percentage would have been more illustrative, as well as something histogram flavored based on the absolute counts. Log graphs might be better but without a log unit that people can actually grok I think it’s pointless. We’re looking at percent change. What does the difference in the distance between +25% to +15% vs +25% to -10% even tell you? Ahh yes the relative difference of the relative change.

by tedd4u 4y ago

josephg 4y ago

Yep; I agree. The original has some layout issues (the 0 line should be highlighted). But the scale is better. In the "fixed" chart the scale goes from -130% (meaningless - implies negative degrees were awarded) to about +130%. A course dropping its graduation rate to 0 would be a big deal - but this chart implies it wouldn't be as shocking as the CS graduate rate doubling. The top entry is at 130% - meaning the number of graduates approximately doubled (2.3x). The lowest entry looks to be about -48%, so the number of graduates approximately halved. These are similar changes, so they should look like similar magnitudes in the chart's scale. But in the "corrected" chart, they look very different. In a geometric / logarithmic scale, they would look like they'd drifted a similar distance from the middle ("unchanged"). If I were going to improve this even more, I'd draw lines from each data point back to the centre point ("0") implying movement from the centre (which is what the chart is showing). Nitpicking mode: I'd also label the centre as "unchanged from 2011" and I'd add the absolute numerical values to the chart. (There's plenty of room!). I also find the title a bit vague. "% change in undergraduate degrees 2011-21" made me wonder if it was talking about the enrollment or graduation rate. I'd mention that its counting undergraduate degrees awarded, and that the data set is for the USA. (As opposed to a particular college, or the whole world or something). As it is, both variants seem a little underwhelming to me. Original: https://statmodeling.stat.columbia.edu/wp-content/uploads/2023/01/harvardmag_humanitiesmajors.jpg https://statmodeling.stat.columbia.edu/wp-content/uploads/20... "Fixed": https://statmodeling.stat.columbia.edu/wp-content/uploads/2023/01/redo_harvardmagazine_humanitiesmajors.png https://statmodeling.stat.columbia.edu/wp-content/uploads/20...

rcme 4y ago

Log scales are impossible to reason about unless you're dealing with exponential data. Otherwise, the transform is meaningless because log is literally an exponent, so not having an exponent in the data is equivalent to garbage in, garbage out, more or less.

nerdponx 4y ago
The quote literally explains how to reason about it.
- rcme 4y ago
  > "doubled" is the same distance from "stayed the same" as is "halved." What's more natural: looking at a change relative to 0, or looking at a change relative to all the other points? Personally, I think looking at a change relative to 0 makes much more sense. Trying to figure out the meaning of the points by looking at relative values is garbage, because there is no underlying exponent to justify the use of the logarithm.
  - rssoconnor 4y ago
    If the number of students enrolled in my course goes up by 25% one year, and then the next year the number of students enrolled in my course drops by 20%, how many students are now in enrolled in my course compared to the beginning? What if it were reversed: what if the number of students dropped by 20% one year, and then when up by 25% the following year. How many students are now enrolled in my course compared to the beginning in this scenario?
    - rcme 4y ago
      In any scenario like that, where a quantity X changes by Y% and then that new quantity changes by Z%, I almost always think about it like (1 + Z) * ((1 + Y) * X). That is, I compute the new size after adjusting by Y% first, and then take Z% of that. To me, this is still treating values as magnitudes from 0 and the Y% change is totally independent from the Z% change. I guess you can multiply Y and Z first, but that’s not how I think about it.

kurthr 4y ago

Coming out really strong on the quadratic fit is pretty weird. People aren't going to judge you for keeping your mouth shut, but not recognizing a log scale? I mean over this short a range (and I do which he'd plotted -50% -30% 0 +40% +100% +140%) a linear interpolation is easy and pretty accurate. You'll probably notice the sqrt2 in there, if you look.

Spivak 4y ago

I think the original graph maker is 99% the way there in the followup. This data makes no sense at all in a graph like this, a table sorted by percentage would have been more illustrative, as well as something histogram flavored based on the absolute counts. Log graphs might be better but without a log unit that people can actually grok I think it’s pointless. We’re looking at percent change. What does the difference in the distance between +25% to +15% vs +25% to -10% even tell you? Ahh yes the relative difference of the relative change.