#### Abstract

A cross-sectional observational study design was used to determine the prevalence of *Escherichia coli * 0157:H7 in wild deer feces. Samples were voluntarily submitted at a number of different locations. In order to determine if the proportions of *E. coli * 0157: H7 positive samples submitted were equal for each of the 26 locations, a 26 by 2 contingency table was analyzed. There were only four *E. coli * 0157:H7 positive samples, which resulted in a sparse table. It is possible to obtain statistically significant results in sparse tables using Fisher's exact test, whereas the chi-square test is generally unreliable in such situations. Thus, Fisher's exact test should be considered when small expected cell counts bring into question the validity of the chi-square test. However, the statistical conclusions based on either the exact test or an asymptotic chi-square test are shown to vary drastically by slight alterations in the distribution of non-empty cells. Therefore, a different statistical conclusion very easily could have been reached if a volunteer had submitted a sample at a different location. In addition, we show that the computational times for exact tests in SAS® can be an applicational limitation.

#### Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

#### Recommended Citation

Renter, D. G.; Higgins, J. J.; and Sargeant, J. M.
(2000).
"PERFORMANCE OF THE EXACT AND CHI-SQUARE TESTS ON SPARSE CONTINGENCY TABLES,"
*Annual Conference on Applied Statistics in Agriculture*.
http://newprairiepress.org/agstatconference/2000/proceedings/19

PERFORMANCE OF THE EXACT AND CHI-SQUARE TESTS ON SPARSE CONTINGENCY TABLES

A cross-sectional observational study design was used to determine the prevalence of *Escherichia coli * 0157:H7 in wild deer feces. Samples were voluntarily submitted at a number of different locations. In order to determine if the proportions of *E. coli * 0157: H7 positive samples submitted were equal for each of the 26 locations, a 26 by 2 contingency table was analyzed. There were only four *E. coli * 0157:H7 positive samples, which resulted in a sparse table. It is possible to obtain statistically significant results in sparse tables using Fisher's exact test, whereas the chi-square test is generally unreliable in such situations. Thus, Fisher's exact test should be considered when small expected cell counts bring into question the validity of the chi-square test. However, the statistical conclusions based on either the exact test or an asymptotic chi-square test are shown to vary drastically by slight alterations in the distribution of non-empty cells. Therefore, a different statistical conclusion very easily could have been reached if a volunteer had submitted a sample at a different location. In addition, we show that the computational times for exact tests in SAS® can be an applicational limitation.