A p-value offers little insight into the data. It may indicate that there is an
association, but does not identify the nature of the relationship. A mosaic plot expresses
the deviations from independence.
The mosaic plot represents the counts in a contingency table by tiles whose area is
proportional to the cell count. Column widths show the marginal proportions of hair
colors. The heights of the tiles show the conditional frequency of eye color given
hair color. Under the null hypothesis of independence, the heights of the tiles in
each row should be the same.
(click to enlarge)
It is easier to see the deviation from independence by coloring and shading the tiles
by the residuals from the Pearson test. Positive deviations are blue, negative red.
The absolute value of the residual is shown by the shading; cells with residuals
less than 2 are unfilled; cells >= 2 are filled; those >= 4 are filled with a
darker pattern. Under the assumption of independence, these values roughly
correspond to two-tailed probabilities p < .05 and p < .0001 that a given
value of exceeds 2 or 4.
You can see from the mosaic plot that Black/Brown and Blond/Blue are
over-represented, while Blond/Brown is under-represented.