Transcript Critical analysis of the statistics in “The Bell Curve”

Critical analysis of the
statistics in “The Bell Curve”
Cinnamon Hillyard
Quantitative Skills Center
University of Washington, Bothell
February 28, 2005
What is a “Bell Curve”?
DeVoire, in the 1600s, observed that many data sets turn out to follow this
pattern:
It is offically called the normal curve, but has been nicknamed “bell curve.
More about
normal
distributions …
When we say something is normally distributed, we are really just talking
about the shape of the distribution. In fact, it can be fat or skinny.
However, normal distributions all have the following properties:
•
Normal distributions are symmetric around their mean.
•
The area under the normal curve is equal to 1.0.
•
Normal distributions are denser in the center and less dense in the tails. 68% of
the area of a normal distribution is within one standard deviation of the mean
•
NO REAL DATA SET IS PERFECTLY BELL SHAPED!
Example 1:
Distributions of IQ scores for blacks
and whites
On page 279, we see the graph below and are told “throughout
the upper half of the range, the disproportions between the
number of whites and blacks at any given IQ level are huge
… the social consequences are potentially huge as well”
Example 1, continued
•Structurally, the areas of each distribution cannot equal 1. What
do they mean when the say they are proportional to the
composition of the population … why would you do that?
•Standardized test scores are often “massaged” to fit the normal
distribution.
•Finally, this is just giving us a spread of the SAMPLE … not the
population it’s representing –
•What is the population it can be generalized to? Where did the
data come from?
•We expect there to be differences just from sampling
differences … but this book fails to go to the powerful statistical
methods of inference.
Example 2: IQ and Poverty
Throughout the text we are given graphs like
the one below relating IQ to something.
What you need to remember about
regression analysis
• GOOD regression analysis should tell the FORM and the STRENGTH
of your data. This example only gives form which can be calculated
for ANY data set!
• Strength of this data is only given for a few variables in the appendix.
Most of the numbers are very small … i.e., there is not a strong
relationship between variables.
• Any GOOD regression analysis should factor out confounding factors.
This book does that sporadically, (accounting for poverty for example),
but then does some weird reasoning to put the factors back in.
• Also, you should always ask yourself about other possible confounding
factors that weren’t measured.
Finally, even if their analysis was
right (which it wasn’t) … the BIG
flaws are:
• The authors claim that one number, namely the IQ, can
measure intelligence.
• Consequently, how can we measure race with one number?
Data may be objective, but the
who, why, when, and how we get the data
is subjective.