35
To answer the question, “Is there a significant difference between the levels of per capita
income in the CAP regions?” the Tukey-Kramer Procedure21 is used to determine whether the
average per capita income levels of the CAP regions are significantly different from each other. The
Tukey-Kramer Procedure is a single factor analysis of variance procedure to determine which means,
in a set of c means, are significantly different from each other given unequal sample sizes. Table 6
reports the average levels of per capita incomes calculated for four samples of unequal size - the core,
adjacent, periphery and periphery regions - for four different periods.
The Tukey-Kramer procedure permits a concurrent examination of comparison between all
pairs of CAP average per capita income means in a given year. The null hypothesis states that there is
no difference among the average per capita income levels in a given year. The alternative hypothesis
states that not all means are equal. For the data observations on each year, the Sum of the Squares
Within (SSW) groups was calculated. This allowed a determination of the Mean Square of the Sum
Within (MSW) given that the number of levels in each year c = 4, and the total number of regions n =
202. The upper-tail critical value QU from the Studentized range distribution with c = 4 degrees of
freedom in the numerator, and n - c = 202 - 4 = 198 degrees of freedom in the denominator is given to
be QU = 2.37.
The results of the test are given for c(c - 1)/2 = 6 pairs of means for a group-to-group
comparison for each year. The analysis shows that in all the group-to-group comparisons, the absolute
difference between the average per capita income levels exceeds their respective critical range. The
one exception is in 1995 between the means of the periphery region and the island periphery regions.
In this case, the absolute difference between the means (12.2) is marginally less than the critical range
(12.37), so that the null hypothesis cannot be rejected. This situation changes in the following years.
The conclusion of the analysis is that the null hypothesis is rejected, and the alternative hypothesis that
there is a significant difference between the average per capita levels of income in the CAP regions, is
accepted.
21
Levine, D. Berenson, M. L., and Stephan, D., (1999), ‘Statistics for Managers (2/ed)’, Prentice Hall, New Jersey.