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I am using R and survey package to analyse a survey that several 2xn contingency tables need to be analysed using Chi square test and Kruskal-Wallis test (for ordered variable). Some of the contingency tables give empty cell, which gives p-value way smaller than 0.05 that I think the "significant" result is actually caused by the empty cell. These empty cells are non-structural zero, and I am thinking of ways to correct that.

I have come across the "Haldane estimator" that 0.5 is added to each of the cell. This method is not applicable to me because I cannot apply the weight-adjusted chi square test or Kruskal-Wallis test by using directly the contingency table. I need to "inject" at least 1 into one of the data point of the dataset, so that the empty cell can be eliminated.

I found quite a few articles that instead of 0.5, but 1 is added into the empty cell:

(You may want to search was added to each to find out the exact sentence that mention addition of 1 into empty cell)

These articles do not provide citation, or vaguely justify why one is added to each cells

If I need to proper justification, what should I call this maneuver of adding one into each cell in order to eliminate the empty cell? Should it be called the Haldane estimator variant? Or something else?

Thank you.

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