glass: British social mobility data
In aylmer: A generalization of Fisher's exact test

Description Usage Details Source Examples

Classification of son-father status

1	data(glass)

Data collected by Glass: social status of son cross-classified with status of father.

Dataset glass.al includes all the original data; dataset glass has the diagonal set to NA, thus restricting the sample to those pairs where the father's status is different from that of the son's.

This dataset has ordered factors: social status is ordered from 1 (highest) to 5 (lowest).

An example of a test only possible where the factors are ordered is given below. The alternative is a function, f(), that sums the counts in the lower triangular region of the matrix: the son has higher status than the father. If f(glass) is large, then this suggests that upward social mobility occurs more often than downward mobility.

Note that, because the test is conditioned on the marginal totals, a significant result would imply that downward mobility, when it occurs, involves a more extreme fall than the (more common) upwardly mobile case.

Bishop WMV, Fienberg SE, and Holland PW 1975. Discrete multivariate analysis. MIT Press

f <- function(x){sum(x[lower.tri(x)])}


# First a toy example:
a <- matrix(0,5,5)
diag(a) <- NA
a[cbind(c(2:5,1),1:5)] <- 3

# Thus 'a' has 12 social climbers and 3 fallers.  Chance?

aylmer.test(a , alternative=f)

# No!


# Now the real dataset:
data(glass)
aylmer.test(glass , alternative=f, simulate.p.value=TRUE , B=100)

# p-value of about 0.975 means that most boards have f(random.board) >
# f(observed.board).  In this case, f() is the number of climbers.  The
# test shows that the number of climbers is less than expected: those
# who do climb, climb further than the fallers fall.

# See how one needs to be careful about one-sided and two-sided tests.