Let us have a $r \times c$ contingency table with positive frequencies. The interaction is derived which is statistically most significant. A direct proof is given that the test based on this most significant interaction is asymptotically equivalent with the common $\chi^2$-test (under the hypothesis of independence in the contingency table).
 Goodman L. A.: On Placketťs test for contingency table interactions
. J. Roy. Statist. Soc. Ser. B 25 (1963), 179-188. MR 0175232
 Goodman L. A.: Simultaneous confidence limits for cross - product ratios in contingency tables
. J. Roy. Statist. Soc. Ser. B 26 (1964), 86-102. MR 0175264
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