You may be interested in performing your own analysis on the data from this study. In it, IQ scores are recorded for boys (1) and girls(2) in 37 primary schools.

Here is a description of the variables in that data:

Gender

Boys=1
Girls=2

IQ - values between 60 and 144

Father's profession

1=Unskilled labour
2=Schooled labour
3=Lower white collar
4=Shopkeepers
5=Middle white collar
6=Professional, Managers

Teacher's advice

1=No further education
2=Extended primary education
3=Manual, including housekeeping
4=Agricultural
5=General
6=Secondary school for girls
7=Pre-University

School - numbers 1 - 37

The 'Advice' variable shows the type of advice given the student concerning realistic educational goals. The distribution for students that were given the most ambitious advice is shown in the following graphs.

The box plots show that the distributions for boys and girls are close to symmetric. Note the outliers in the box plot for the boys' IQ.
Box Plot for IQ: Gender = 1 (Boys)

Box Plot for IQ: Gender = 2 (Girls)

The relative frequency graphs for IQ appear to be close to normal. Of course, the means for boys and girls are not exactly equal. Do you think the means for girls and boys are statistically different?
Distribution for IQ: Gender = 1 (Boys)

Distribution for IQ: Gender = 2 (Girls)

The probability plots for the two distributions follow. They seem to follow a normal distribution.

Probability Plot for IQ: Gender = 1 (Boys)

Probability Plot for IQ: Gender = 2 (Girls)

Assignment

• See this article for more information on whether brain size matters.

• Explore this data set on brain size and IQ to help you answer the brain size question yourself.
  1. Determine first whether the (full scale) IQ scores are normally distributed.
  2. What about the distribution for the MRI (the measure of brain size)?
  3. Do these distributions appear the same for both sexes?