The contrast-coefficient table is a convenient way to check that the proper weights were given to the groups.

If the mean assessments of the DVD player for the 32-38 and 39-45 age groups are equal, then you would expect the observed difference in the mean assessment for these groups to be near 0. By specifying -1 and 1 as the contrast coefficients for these groups, the first contrast tests whether the observed difference is statistically significant.

- Similarly, if the mean assessments of the under-32 age groups and over-45 age groups are equal, you would expect the sum of the first two groups to be equal to the sum of the last two groups, and the difference of these sums to be near 0.