Even accounting for rounding, there's no way to get those numbers. It's even worse in other places:
25% of black kids had parents who grew up in the bottom two levels and moved up at least one.
78% of black kids had parents who grew up in the top three levels and moved down at least one.
Those two groups should sum to less than 100%, certainly not 103%.
Also, except for the "Moving to Opportunity" experiment, most of this seems to ignore the distinction between correlation and causation.
This reminds me of the recent finding that 50% of papers in reputable psych journals reported mathematically impossible data. https://medium.com/@jamesheathers/the-grim-test-a-method-for... The more people start to dig in, the more the "social sciences" look unscientific.
That infographic and the text that goes with it could be made much clearer but your interpretation is not how it should be read. (as far as I can tell)
For one thing, as ASpring mentioned, the text about white kids were shortened, with the implication that the same sentence structure as for the black kids should be used. I'm assuming it was done to make the drawing easier to read (i.e. less text) but it certainly added confusion.
I.e. it reads "25% of black kids had parents who grew up in the bottom two levels and moved up at least one" and it should read "59% of white kids had parents who grew up in the bottom two levels and moved up at least one" instead of just "59% of white kids moved up".
As for "Those two groups should sum to less than 100%, certainly not 103%.", this is incorrect: the 25% refers to the kids who had parents in the bottom two levels, while the 78% refers to kids who had parents in the top three levels. Those are separate groups. (same for the number with white kids)
So, if you look at kids coming from the 40% poorest (unclear if it's overall or amongst white/black people), from 1955 to 1970, only 25% of the black kids moved up while 59% of the white kids moved up.
And if you look at kids coming from the 60% wealthiest, 78% of black kids moved down while 43% of white kids moved down.
In other words, poor black kids are more likely to grow up and stay poor than poor white kids. Rich black kids are more likely to grow up and become poorer than their parents than rich white kids.
To simplify a bit (not 100% accurate with the available data but close): regardless of poverty level when growing up, only 22 to 25% of black kids moved up (or stayed the same), while 57 to 59% of white kids did.
His interpretation is how it should be read in English. It may be not how it should have been written.
> 78% of black kids had parents who grew up in the top three levels and moved down at least one.
Let B = all black kids;
BT = black kids who had parents who grew up in the top three levels;
BD = black kids who(se parents) moved down at least one level
The only way that sentence can be interpreted in English is:
|BT ∩ BD| / |B| = 78%
If what they wanted to say was:
|BT ∩ BD| / |BT| = 78%
Then the way to say that in English would have been:
> Of the black kids whose parents grew up in the top three levels, 78% moved down at least one.
You're right. Somehow it made sense to me when reading the article, but reading your comment I see how it doesn't make sense as stated.
I probably implied the "who" since there was no way to have a group qualified by two conditions like these end up so high. (regardless of totals of the two percentages)
It really isn't clear to me whether it is the children moving up or down relative to their parents, or the parents moving up and down within their own lifetime.
Either way, children have two parents, so could be represented in both groups. Likewise, parents can have multiple children, and one sibling could move up while another moved down.
These numbers could be skewed from unequal number of children per parent in these different groups. Successful parents might have many more or fewer children.
It's poor reporting. The statements about white children should be qualified the same way the author attempted to qualify the statements about black children.
59% of white kids moved up.
43% of white kids moved down.
Even accounting for rounding, there's no way to get those numbers. It's even worse in other places:
25% of black kids had parents who grew up in the bottom two levels and moved up at least one.
78% of black kids had parents who grew up in the top three levels and moved down at least one.
Those two groups should sum to less than 100%, certainly not 103%.
Also, except for the "Moving to Opportunity" experiment, most of this seems to ignore the distinction between correlation and causation.
This reminds me of the recent finding that 50% of papers in reputable psych journals reported mathematically impossible data. https://medium.com/@jamesheathers/the-grim-test-a-method-for... The more people start to dig in, the more the "social sciences" look unscientific.