NAME:  Foot measurements for fourth grade children
TYPE:  Convenience Sample 
SIZE:  39 observations, 6 variables

ABSTRACT:  From a very young age, shoes for boys tend to be wider than shoes for 
girls.  Is this because boys have wider feet, or because it is assumed that 
girls, even in elementary school, are willing to sacrifice comfort for fashion?  
To assess the former, a statistician measures kids' feet.  Methods for analysis include 
t-tests, ANCOVA, and least-squares model building.  This data set is useful for 
discussion of covariates, confounding, and conclusions in the context of the problem.

SOURCES:  Collected by the author in a fourth grade classroom in Ann Arbor, MI.

VARIABLE DESCRIPTIONS:

1. Birthdate: month and year  (data were collected in October 1997)
2. Length of longer foot (cm)
3. Width of longer foot (cm), measured at widest part of foot
4. Sex: boy or girl
5. Foot measured (right or left)
6. Right- or left-handedness

STORY BEHIND THE DATA:  

When my daughter was in fourth grade, I took her shopping for dress shoes. I was 
disappointed in the quality of girls' shoes at every store in the mall.  The shoes for 
boys were sturdy and had plenty of room in the toes.  On the other hand, shoes for girls 
were flimsy, narrow, and had pointed toes.  In spite of the better construction 
for boys, the costs of the shoes were similar!  For children the same age, boys 
had shoes they could run around in, while girls' shoes were clearly for style 
and not comfort.    

Upon complaining about this state of affairs, I was told by sales 
representatives in two stores that boys actually had wider feet than girls, so 
needed wider shoes.  Being very skeptical, I thought I would test this claim.

Around the same time, my daughter's teacher sent home requests to parents. She 
asked if we could schedule a day to come to the fourth grade classroom, to tell the children 
about our jobs.  I gave a talk on statistical studies, and posed the problem.  I asked the 
children to design a study to see if boys had wider feet than girls, and requested that 
they get their feet measured in the process.

PEDAGOGICAL NOTES:  

A t-test comparing widths gives (one-sided) p=0.0055, but perhaps the boys in that class 
were larger, on average, than the girls.  We need to account for foot length in the model. 
An ANCOVA gives (one-sided) p=0.040.  More advanced classes can be given the entire 
data set to analyze, making the point that the age and left/right variables are red 
herrings.  We do not wish to find reasons for boys' and girls' feet having different 
average widths, we merely wish to determine if shoe manufacturers are justified in their 
decision to make boys' shoes wider than girls' shoes, for the same length feet.  


SUBMITTED BY:

Mary C. Meyer
Department of Statistics
University of Georgia
Athens, GA 30602-1952
mmeyer@stat.uga.edu