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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:

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Critical analysis of the statistics in “The Bell Curve”

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  1. Critical analysis of the statistics in “The Bell Curve” Cinnamon Hillyard Quantitative Skills Center University of Washington, Bothell February 28, 2005

  2. 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.

  3. 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!

  4. 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”

  5. 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.

  6. Example 2: IQ and Poverty Throughout the text we are given graphs like the one below relating IQ to something.

  7. 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.

  8. 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.

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