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Meta-analysis is a quantitative method for summarizing single studies. In a meta-analysis, one tries to quantify the treatment effect, assigning more weight to large studies than to small studies. A much used method for weighting is the inverse variance method. If all studies have measured the results in the same way, the results can be used directly in the meta-analysis, but if the same outcome is measured in different ways across different studies, one has to use a standardized effect size where results are converted to a common scale. If it is believed that the effect is consistent across various populations and settings, one can employ a fixed-effect model. If systematic differences in effect can be expected, a random-effects model is used. Meta-analyses are often depicted as forest plots. Each line represents one study where the effect estimate is marked as a point on a line, with each end of the line representing the confidence interval around it. The meta-analysis is shown as a diamond where the width illustrates the uncertainty around the estimate. If all study results point in the same direction, the meta-analysis is considered "homogeneous". But if the studies vary in their effect size and direction, the findings are "heterogeneous". The strength of meta-analysis is that it can be used to summarize a large body of information in one number. This is also its limitation. One number cannot describe the variation that exists across different studies. [ABSTRACT FROM AUTHOR]

Introduction: Literally hundreds of methods for hypothesis tests and confidence intervals for contingency tables are described in the literature. This is the case even for the seemingly simple 2 × 2 table. The Pearson chi squared test, the Fisher exact test, and the Wald confidence interval are widely used methods. Unfortunately, these methods are also commonly used in situations when they perform poorly, and better alternatives exist. Aims: To show how to evaluate and choose appropriate methods for hypothesis testing and confidence interval estimation for 2x2 tables. Methods: Important properties of a hypothesis test are the actual significance level and power. Important properties for a confidence interval are coverage probability, expected interval width, and symmetry. We have studied these properties for alternative methods. Conclusion: For large samples, the asymptotic Pearson chi squared test performs well. Yates's continuity correction should never be used. In small samples, the traditional advice is the Fisher exact test. But unconditional tests are generally more powerful than Fisher's exact test for small samples. Unconditional tests also preserve the significance level. That is, the actual significance level does not exceed the nominal significance level, which is often 5%. Unconditional tests were but previously disadvantaged by being computationally demanding. Alternatively, Fisher's exact test with mid-p adjustment is easy to compute, and gives approximately the same results as an unconditional test. The Wald confidence interval is a traditional choice for the difference between two proportions. But its coverage can dip substantially below the nominal coverage, which is usually 95%. The Agresti-Caffo interval and the Newcombe hybrid score interval are also easy to compute with closed form expressions. They have better coverage, and also narrower expected interval width, and better symmetry than the Wald interval. [ABSTRACT FROM AUTHOR]