Subtleties of Distributions
How are we to investigate causes with complex effects? The
effect of divorce and remarriage on children's academic performance
is complex, and yet more and more of a pressing reality in our
fragmenting society. What is the academic penalty suffered by
children as a result of divorce or the death of a parent? Should
society be encouraging single or widowed mothers to remarry (e.g.,
by tax incentives) in hopes of establishing a new stable family, or
should we be encouraging them to stay single, to avoid yet another
emotional trauma in the child's life?
The National Education Longitudinal Study (NELS) contains data
that is intended to throw light on this issue. One substantively
important academic indicator is reading performance. The 1988
sample of 24,599 children contains reading measures for children in
all three family conditions. Here are their summary
statistics:
| Reading Measure, 8th Grade 1988 |
Mean |
Standard Deviation |
Intact Families
Single-parent Families
Reconstituted Families |
51.93
50.44
50.39
|
9.87
9.91
9.61
|
What are we to make of this? The intact families do best - as we
would predict. Children in single-parent families perform better
than in reconstituted families. The policy-makers appear to have
their answer: tell the parent not to remarry! But what about
dispersions?
Now look at the plot. It challenges the accepted wisdom about
the affect of family status on academic performance. Are
reconstituted families just like intact families? No, the
distribution of children in intact families is to the right, but it
is not a huge effect. Are reconstituted families automatically
better than single-parent families? No, their means essentially
coincide - in fact, there is no advice to policy-makers here. The
standard deviations, however, are even more perplexing. The tails
of the single-parent distribution are slightly wider than the
reconstituted, so that the cumulative curves cross. These data are
ambiguous.
William H. Jeynes
Department of Education, University of Chicago
Subtleties of distributions. Jeynes W.H. … Rasch Measurement Transactions, 1996, 10:3 p. 515.