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Exact statistics

Stata 10 offers several commands for exact analysis, providing more reliable statistical inference with small-sample datasets.

• New command exlogistic fits exact logistic regression models. The dependent variable can be Bernoulli (0 or 1) or binomial (the number of successes in n trials). Exact joint hypothesis tests can be performed, and predictions with exact confidence intervals can be obtained.
• New command expoisson fits exact Poisson regression models of count outcomes. Exact joint hypothesis tests can be performed.
• Other commands for exact statistics include

Command	Description
bitest	Binomial probability test
cc	Case–control study odds ratios
ci	Centiles with confidence intervals
cs	Cohort study risk differences and ratios
ir	incidence-rate ratios and differences
istdize	Indirect standardization
ksmirnov	Two-sample Kolmogorov–Smirnov test
loneway	Large one-way analysis of variance
mcc	Matched case–control study statistics
median	Equality-of-medians test
symmetry	Symmetry and marginal homogeneity tests
tabulate2, tab2	Two-way tables with Fisher’s exact test
tetrachoric	Tetrachoric correlations

Exact logistic example

Stata’s new exact logistic regression command provides better coverage in small samples than does standard logistic regression.

It also provides parameter estimates and confidence intervals where standard asymptotic methods cannot.

Such cases include small-data problems with binary regressors for which the outcome is 1 whenever the regressor is 1.

In the example below, every treated patient exhibits a positive response. Standard logistic regression cannot estimate the treatment effect. Stata 10’s new exlogistic command can:

. exlogistic response treatment x2 x3

Parameter estimates, standard errors, and CIs are calculated on the basis of permutation without recourse to asymptotic assumptions and results.

Not only is the treatment effect estimated, but tests of significance and reported confidence intervals are based on exact methods.

Stata 10 also includes exact Poisson regression for count data.

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