A Nonrandomized Unconditional Test for Comparing Two Proportions in 2×2 Contingency Tables

McDonald, Lyman L.; Davis, B. M.; Milliken, George A.

doi:10.1080/00401706.1977.10489522

Cited by 32 publications

(23 citation statements)

References 5 publications

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“…However, when P is small the Fisher-Irwin test is quite conservative, as can be seen in Table 3. Because of this conservatism, alternative tests for 2 X 2 tables have recently been proposed (McDonald, Davis and Milliken 1977), but a discussion of these procedures is beyond the scope of this paper.…”

Section: Resultsmentioning

confidence: 99%

Exact Sample Sizes for Use with the Fisher-Irwin Test for 2 x 2 Tables

Haseman¹

1978

Biometrics

102

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Section: Resultsmentioning

confidence: 99%

Exact Sample Sizes for Use with the Fisher-Irwin Test for 2 x 2 Tables

Haseman¹

1978

Biometrics

102

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“…When fewer than 50% of the ponds had non-zero values for a taxon, we constructed 2Â2 contingency tables with presence and absence data for each of the categories. We performed tests of homogeneity of the proportion 'present' by category with methods of McDonald et al (1977).…”

Section: Analyses Of Datamentioning

confidence: 99%

“…We assumed equal variances because most variance comparisons did not suggest differences at the 1% level. If fewer than 50% of the samples were non-zero, but at least 4 non-zero values were available, we constructed a contingency table(McDonald et al, 1977) with presence and absence data and reported observed significant levels (OSL).…”

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confidence: 99%

Macroinvertebrate abundance, water chemistry, and wetland characteristics affect use of wetlands by avian species in Maine

et al. 2006

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Our objective was to determine use by avian species (e.g., piscivores, marsh birds, waterfowl, selected passerines) of 29 wetlands in areas with low (<200 leq l )1 ) acid-neutralizing capacity (ANC) in southeastern Maine. We documented bird, pair, and brood use during 1982-1984 and in 1982 we sampled 10 wetlands with a sweep net to collect invertebrates. We related mean numbers of invertebrates per wetland to water chemistry, basin characteristics, and avian use of different wetland types. Shallow, beaver (Castor canadensis)-created wetlands with the highest phosphorus levels and abundant and varied macrophyte assemblages supported greater densities of macroinvertebrates and numbers of duck broods (88.3% of all broods) in contrast to deep, glacial type wetlands with sparse vegetation and lower invertebrate densities that supported fewer broods (11.7%). Low pH may have affected some acid-intolerant invertebrate taxa (i.e., Ephemeroptera), but high mean numbers of Insecta per wetland were recorded from wetlands with a pH of 5.51. Other Classes and Orders of invertebrates were more abundant on wetlands with pH > 5.51. All years combined use of wetlands by broods was greater on wetlands with pH £ 5.51 (77.4%) in contract to wetlands with pH>5.51 that supported 21.8% of the broods. High mean brood density was associated with mean number of Insecta per wetland. For lentic wetlands created by beaver, those habitats contained vegetative structure and nutrients necessary to provide cover to support invertebrate populations that are prey of omnivore and insectivore species. The fishless status of a few wetlands may have affected use by some waterfowl species and obligate piscivores.

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“…This test was also proposed by McDonald, Davis, and Milliken (1977). The p-value from Fisher's conditional test is used as the test statistic in this unconditional test.…”

Section: Boschloo's (1970) Exact Unconditional Test (B)mentioning

confidence: 99%

A Cautionary Note on Exact Unconditional Inference for a Difference between Two Independent Binomial Proportions

2003

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Fisher's exact test for comparing response proportions in a randomized experiment can be overly conservative when the group sizes are small or when the response proportions are close to zero or one. This is primarily because the null distribution of the test statistic becomes too discrete, a partial consequence of the inference being conditional on the total number of responders. Accordingly, exact unconditional procedures have gained in popularity, on the premise that power will increase because the null distribution of the test statistic will presumably be less discrete. However, we caution researchers that a poor choice of test statistic for exact unconditional inference can actually result in a substantially less powerful analysis than Fisher's conditional test. To illustrate, we study a real example and provide exact test size and power results for several competing tests, for both balanced and unbalanced designs. Our results reveal that Fisher's test generally outperforms exact unconditional tests based on using as the test statistic either the observed difference in proportions, or the observed difference divided by its estimated standard error under the alternative hypothesis, the latter for unbalanced designs only. On the other hand, the exact unconditional test based on the observed difference divided by its estimated standard error under the null hypothesis (score statistic) outperforms Fisher's test, and is recommended. Boschloo's test, in which the p-value from Fisher's test is used as the test statistic in an exact unconditional test, is uniformly more powerful than Fisher's test, and is also recommended.

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A Nonrandomized Unconditional Test for Comparing Two Proportions in 2×2 Contingency Tables

Cited by 32 publications

References 5 publications

Exact Sample Sizes for Use with the Fisher-Irwin Test for 2 x 2 Tables

Exact Sample Sizes for Use with the Fisher-Irwin Test for 2 x 2 Tables

Macroinvertebrate abundance, water chemistry, and wetland characteristics affect use of wetlands by avian species in Maine

A Cautionary Note on Exact Unconditional Inference for a Difference between Two Independent Binomial Proportions

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