Parents' socioeconomic status and children's academic ... - Nova

project: an immigrant is a person whose parents are born abroad, regardless
of where that person is born. Most immigrant children in this project were
born in Norway.
3.2 Data analysis
Our analysis is based on both bivariate and multivariate methods. In the
bivariate analysis, cross tabulation with the ordinal measure of association,
gamma ‘γ’, is used to test the association between two variables. For comparisons
between scores across different groups, we use a traditional
binominal population proportion test. Multivariate analysis is conducted by
linear regression, with the sum of the marks in each of the three subjects as
the response variable.
Gamma is an ordinal measure of association between two ordinal
variables. It utilises the concepts of concordant and discordant pairs of
observations. Although gamma is both a powerful and intuitive interpretable
statistic, it is not frequently used. We therefore give a brief explanation of the
concepts of concordant and discordant pairs and the gamma measure (for a
more complete and somewhat more formal description, see Agresti and
Finlay 2009). In our description here we use pupils’ grades and parents’
education as an example. From a sample with n observations, n*(n-1)/2 pairs
can be drawn. A concordant pair is a pair of observations where the observation
with the (strictly) highest score on parental education also has the
(strictly) highest score on children’s school results. A discordant pair is a pair
of observations where the observation with the (strictly) highest value on
parental education has the (strictly) lowest value on children’s school
achievements. 3
The gamma measure is based on a count of concordant and discordant
pairs of observations. It is the standardized difference between the total
number of concordant pairs (positively associated pairs) and the total
number of discordant pairs (negatively associated pairs) in the resulting
contingency table of two variables. In other words, gamma is the difference
3
A pair that is neither concordant nor discordant is termed a tie. The incidence of ties
is not utilised in the calculation of the gamma-statistic.
– Parents’ socioeconomic status and children’s academic performance – 21