Let’s say you were plotting some temperature data. You take the temperature every day and record it for a month. When you go to plot the data, the normal thing to do is decide on the scale for the y-axis and then plot each temperature point according to where it fits on that scale. This allows you to see any trends in your data (perhaps it’s spring and the temperature is trending upwards over the month).
What you don’t do is sort your temperature data and then put the lowest temperature at the very bottom and the highest temperature at the top, with every other point spaced evenly between those extremes according to their rank. This completely obscures the relative temperature differences between the points!
Well this is what was done with the number words data we’re discussing. Look at the plot for English. Notice that zero is in the top left (because z is last in sequence), followed by one halfway up, which is also okay. But then look at two and three. You would expect two and three to be very close together because they both start with t, but they’re not. Words starting with t should be around 76% of the way up the y-axis (because t is the 20th letter of the alphabet) but two is at 99% of the way up and three is 77% of the way up.
This is problematic if you’re hoping to use the plots to spot trends. For example, with German (as another commenter pointed out) all 2-digit number words read the ones place before the tens place. If the data were plotted by cardinality (treating each word as a rational number between 0 and 1) then you’d easily spot this trend in German number words because all the points would fall on roughly horizontal lines.
Is there a good way to do this? I am thinking one could (taking English as an example) treat each word as a base-26 number (o.ne, t.wo, t.hree, …) and divide them by 26 to normalize values between 0 and 1.
Let’s say you were plotting some temperature data. You take the temperature every day and record it for a month. When you go to plot the data, the normal thing to do is decide on the scale for the y-axis and then plot each temperature point according to where it fits on that scale. This allows you to see any trends in your data (perhaps it’s spring and the temperature is trending upwards over the month).
What you don’t do is sort your temperature data and then put the lowest temperature at the very bottom and the highest temperature at the top, with every other point spaced evenly between those extremes according to their rank. This completely obscures the relative temperature differences between the points!
Well this is what was done with the number words data we’re discussing. Look at the plot for English. Notice that zero is in the top left (because z is last in sequence), followed by one halfway up, which is also okay. But then look at two and three. You would expect two and three to be very close together because they both start with t, but they’re not. Words starting with t should be around 76% of the way up the y-axis (because t is the 20th letter of the alphabet) but two is at 99% of the way up and three is 77% of the way up.
This is problematic if you’re hoping to use the plots to spot trends. For example, with German (as another commenter pointed out) all 2-digit number words read the ones place before the tens place. If the data were plotted by cardinality (treating each word as a rational number between 0 and 1) then you’d easily spot this trend in German number words because all the points would fall on roughly horizontal lines.
Is there a good way to do this? I am thinking one could (taking English as an example) treat each word as a base-26 number (o.ne, t.wo, t.hree, …) and divide them by 26 to normalize values between 0 and 1.
Yes, that’s exactly the way to do it!
Oh now I finally see it. I thought all just gad their limits from A to Z, but they are all different. That’s just… wrong