Nonconservative exact small-sample inference for discrete data

Agresti, Alan; Gottard, Anna

doi:10.1016/j.csda.2007.02.024

Cited by 31 publications

(13 citation statements)

References 34 publications

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“…These results for conditional p-values do not extend to unconditional p-values computed by (13). For example, the results in Table I [34].…”

Section: Choice Of Test Statisticmentioning

confidence: 96%

“…and the null hypothesis is rejected if midp-value . The midp procedure was proposed by Lancaster [12] and recently has gained wider acceptance, see [4,13,14] and references therein. Barnard [15] recommends reporting both the p-value and the midp-value, arguing that the pvalue measures the significance when the data are judged alone and the midp-value is suited for combining evidence from several studies.…”

Section: The Mid-p-valuementioning

confidence: 99%

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Recommended tests for association in 2×2 tables

Lydersen

Fagerland

Laake

2009

Statistics in Medicine

262

210

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The asymptotic Pearson's chi-squared test and Fisher's exact test have long been the most used for testing association in 2x2 tables. Unconditional tests preserve the significance level and generally are more powerful than Fisher's exact test for moderate to small samples, but previously were disadvantaged by being computationally demanding. This disadvantage is now moot, as software to facilitate unconditional tests has been available for years. Moreover, Fisher's exact test with mid-p adjustment gives about the same results as an unconditional test. Consequently, several better tests are available, and the choice of a test should depend only on its merits for the application involved. Unconditional tests and the mid-p approach ought to be used more than they now are. The traditional Fisher's exact test should practically never be used.

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“…These results for conditional p-values do not extend to unconditional p-values computed by (13). For example, the results in Table I [34].…”

Section: Choice Of Test Statisticmentioning

confidence: 96%

Section: The Mid-p-valuementioning

confidence: 99%

Recommended tests for association in 2×2 tables

Lydersen

Fagerland

Laake

2009

Statistics in Medicine

262

210

View full text Add to dashboard Cite

show abstract

“…The Clopper-Pearson interval, in contrast, often has a true confidence coefficient that exceeds the nominal level (Agresti and Coull 1998). As a result, researchers such as Casella (1986), Agresti and Coull (1998), Blaker (2000), and Agresti and Gottard (2007) have developed refined methods, both exact and approximate, that offer a better match between nominal and true confidence coefficients. Any of these methods could be used here to obtain alternate stopping rules.…”

Section: Stopping Rulesmentioning

confidence: 93%

Fixed-Width Sequential Confidence Intervals for a Proportion

Frey

2010

The American Statistician

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Fixed-sample-size confidence intervals for a proportion p have widths that vary depending on the observed number of successes. In this article, we develop sequential methods for obtaining fixed-width confidence intervals for p. These methods are exact, and the confidence intervals have the simple form [max(0,p −h), min(1,p + h)], wherep is the observed proportion and h is a user-chosen half-width. We consider four possible stopping rules for obtaining the intervals, and we find that a rule based on estimating the variance ofp seems to perform best in terms of average run length and coverage probability. The new sequential confidence interval methods provide a valid way to obtain the desired accuracy in sample surveys and Monte Carlo simulation studies without doing excessively many runs. Supplementary material is available online.

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“…Using this construction with binomial probabilities and (1/2) replaced by 1.0 yields the standard Clopper and Pearson (1934) exact (conservative) CI. Considering this method and the mid P-based CI over all the possible parameter values between 0 and 1, Figure 1 from Agresti and Gottard (2007) shows the quartiles of nominal 95% coverage probabilities as a function of n. The median coverage probability (represented in each case by the middle of the three curves) is much closer to the nominal level for the mid-P-based CI. It would be useful if statistical software could provide mid-P-based smallsample CIs for cases with a single parameter, such as the binomial and Poisson parameters, and for cases in which nuisance parameters are eliminated, such as odds ratios and logistic regression parameters.…”

Section: Small-sample Score Confidence Intervalsmentioning

confidence: 99%

Score and Pseudo-Score Confidence Intervals for Categorical Data Analysis

Agresti¹

2011

Statistics in Biopharmaceutical Research

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This article reviews methods for constructing confidence intervals for analyzing categorical data. A considerable literature indicates that the method of inverting score tests performs well for a variety of cases. When the sample size is small or the parameter is near the parameter space boundary, this method usually performs much better than inverting Wald tests and sometimes better than inverting likelihood-ratio tests. For small samples, exact methods are also available. Although these methods can be quite conservative, inverting a score test using the mid P-value provides a sensible compromise that uses the small-sample distribution while reducing the conservatism and only slightly sacrificing the lower bound for the desired confidence level. For some models, scoretest-based inferences are impractical, such as when the likelihood function is not an explicit function of the model parameters. For such cases, pseudo-score inference can be based on a Pearson-type chi-squared statistic that compares fitted values for a working model with fitted values when the parameter of interest takes a fixed value. For some simple cases involving proportions and their differences, a different pseudo-score approach that adds artificial observations before forming Wald confidence intervals provides a simple way of approximating score confidence intervals.

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Nonconservative exact small-sample inference for discrete data

Cited by 31 publications

References 34 publications

Recommended tests for association in 2×2 tables

Recommended tests for association in 2×2 tables

Fixed-Width Sequential Confidence Intervals for a Proportion

Score and Pseudo-Score Confidence Intervals for Categorical Data Analysis

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