Statistics Abuse and Me by Jay Mathews:
the Simpson's Paradox numbers. The national average for the SAT went up only 4 points between 1981 and 2005, but the average for whites went up 10 points, for blacks 21 points, for Asians 37 points, for Mexicans 15 points, for Puerto Ricans 23 points and for American Indians 18 points.
How can that be? Is it important? First, yes it is important. Effective use of data is an important part of management improvement. Emphasis the effective, not the data. Use of data by itself is not sufficient.
To be effective you need to learn to think about not what is printed on the page but what lies behind the numbers you see. The numbers are just proxies for the real situation. Look beyond the numbers you see to what they mean and understand how the numbers presented may not fully capture the important details you need to consider.
Ok back to how the SAT numbers could seem to go up fairly significantly for all the sub groups of the total but only a little bit for the total. This numerical quirk is known as Simpson's Paradox. If the proportions of the subgroups (Asians, American Indians...) change then the overall average is effected not just by the changes of the subgroup average SAT scores but the changes of the weighting of each subgroup (so if the overall average is less than even the lowest gain for a subgroup you know that the subgroup weighting must have increased for one or more of the subgroups with lower SAT scores).
Take care when you are make decision based on your understanding of data to avoid assumptions that may not be correct.
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