This is terrifying. If this is accurate then the Bill&Melinda Foundation spend $1bn on making American high schools worse by splitting them up because they got some statistics wrong. ?
One thing I found difficult reading this is that it appears to keep using the words “variance” and “variances” to refer to standard deviation(s), but standard deviation is defined as the square root of variance.
I think that the other conclusion to take here is that it is perilous to perform statistics using averages as inputs. If you want summaries of data that you can subsequently combine, use triples (number of samples, sum of samples, sum of sample squares) instead, and extract means and variances from them.
This is terrifying. If this is accurate then the Bill&Melinda Foundation spend $1bn on making American high schools worse by splitting them up because they got some statistics wrong. ?
One thing I found difficult reading this is that it appears to keep using the words “variance” and “variances” to refer to standard deviation(s), but standard deviation is defined as the square root of variance.
I think that the other conclusion to take here is that it is perilous to perform statistics using averages as inputs. If you want summaries of data that you can subsequently combine, use triples (number of samples, sum of samples, sum of sample squares) instead, and extract means and variances from them.