A New Test for 2 × 2 Tables

@article{Fisher1945ANT,
  title={A New Test for 2 × 2 Tables},
  author={Rory A. Fisher},
  journal={Nature},
  year={1945},
  volume={156},
  pages={388-388}
}
  • R. Fisher
  • Published 1 September 1945
  • Psychology
  • Nature
UNDER this heading, G. A. Barnard1 puts forward a test which, in language adopted from Neyman and Pearson, “is more powerful than Fisher's”. This means in practice that the test advocated passes as significant certain classes of experimental result which, by the test I had put forward2, would have been judged insignificant; and that, as judged by Barnard's method, my test is thought to be too stringent. However one may choose to express it, the cause of the difference in these calculations is… 

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References

SHOWING 1-4 OF 4 REFERENCES

THE INTERPRETATION OF EXPERIMENTAL FOUR-FOLD TABLES

In advocating the particular method he chooses for the interpretation of data of this important class he has, I believe, overlooked a difficulty which the approach based on, and giving the exact solution for, the classical view-point of x2 and the four-fold table was expressly devised to obviate.

On Contingency Tables.

  • E. B. Wilson
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1942
This worksheet focuses on constructing, understanding and using contingency tables.

A New Test for 2 × 2 Tables

IF an experiment yields results in the form of a 2 × 2 table: