From the paper I reviewed yesterday by Button, Ioannidis, et al. called “Power failure: why small sample size undermines the reliability of neuroscience.”

*All direct quotes. Original paper HERE.*

## Effect size

An effect size is a standardized measure that quantifies the size of the difference between two groups or the strength of an association between two variables. As standardized measures, effect sizes allow estimates from different studies to be compared directly and also to be combined in meta-analyses.

## Excess significance

Excess significance is the phenomenon whereby the published literature has an excess of statistically significant results that are due to biases in reporting. Several mechanisms contribute to reporting bias, including study publication bias, where the results of statistically non-significant (‘negative’) studies are left unpublished; selective outcome reporting bias, where null results are omitted; and selective analysis bias, where data are analysed with different methods that favour ‘positive’ results.

## Fixed and random effects

A fixed-effect meta-analysis assumes that the underlying effect is the same (that is, fixed) in all studies and that any variation is due to sampling errors. By contrast, a random-effect meta-analysis does not require this assumption and allows for heterogeneity between studies. A test of heterogeneity in between-study effects is often used to test the fixed-effect assumption.

## Meta-analysis

Meta-analysis refers to statistical methods for contrasting and combining results from different studies to provide more powerful estimates of the true effect size as opposed to a less precise effect size derived from a single study.

## Positive predictive value

The positive predictive value (PPV) is the probability that a ‘positive’ research finding reflects a true effect (that is, the finding is a true positive). This probability of a research finding reflecting a true effect depends on the prior probability of it being true (before doing the study), the statistical power of the study and the level of statistical significance.

## Proteus phenomenon

The Proteus phenomenon refers to the situation in which the first published study is often the most biased towards an extreme result (the winner’s curse). Subsequent replication studies tend to be less biased towards the extreme, often finding evidence of smaller effects or even contradicting the findings from the initial study.

## Statistical power

The statistical power of a test is the probability that it will correctly reject the null hypothesis when the null hypothesis is false (that is, the probability of not committing a type II error or making a false negative decision). The probability of committing a type II error is referred to as the false negative rate (β), and power is equal to 1 – β.

## Winner’s curse

The winner’s curse refers to the phenomenon whereby the ‘lucky’ scientist who makes a discovery is cursed by finding an inflated estimate of that effect. The winner’s curse occurs when thresholds, such as statistical significance, are used to determine the presence of an effect and is most severe when thresholds are stringent and studies are too small and thus have low power.

## Bonus! CAMARADES

The Collaborative Approach to Meta-Analysis and Review of Animal Data from Experimental Studies (CAMARADES) is a collaboration that aims to reduce bias and improve the quality of methods and reporting in animal research. To this end, CAMARADES provides a resource for data sharing, aims to provide a web-based stratified meta-analysis bioinformatics engine and acts as a repository for completed reviews.

*Now go lift something heavy,*

Nick Horton