# Meta-analytic interval estimation for bivariate correlations.

@article{Bonett2008MetaanalyticIE, title={Meta-analytic interval estimation for bivariate correlations.}, author={Douglas G. Bonett}, journal={Psychological methods}, year={2008}, volume={13 3}, pages={ 173-81 } }

The currently available meta-analytic methods for correlations have restrictive assumptions. The fixed-effects methods assume equal population correlations and exhibit poor performance under correlation heterogeneity. The random-effects methods do not assume correlation homogeneity but are based on an equally unrealistic assumption that the selected studies are a random sample from a well-defined superpopulation of study populations. The random-effects methods can accommodate correlation…

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## References

SHOWING 1-10 OF 31 REFERENCES

### Confidence intervals for the amount of heterogeneity in meta‐analysis

- MathematicsStatistics in medicine
- 2007

A novel method for constructing confidence intervals for the amount of heterogeneity in the effect sizes is proposed that guarantees nominal coverage probabilities even in small samples when model assumptions are satisfied and yields the most accurate coverage probabilities under conditions more analogous to practice.

### Is the meta-analysis of correlation coefficients accurate when population correlations vary?

- BiologyPsychological methods
- 2005

A Monte Carlo study compared the efficacy of Hedges and Vevea's random-effects methods of meta-analysis with Hunter and Schmidt's, over a wide range of conditions, as the variability in population correlations increases.

### Fixed- and random-effects models in meta-analysis.

- Mathematics
- 1998

There are 2 families of statistical procedures in meta-analysis: fixed- and randomeffects procedures. They were developed for somewhat different inference goals: making inferences about the effect…

### Fixed Effects vs. Random Effects Meta‐Analysis Models: Implications for Cumulative Research Knowledge

- Psychology
- 2000

Research conclusions in the social sciences are increasingly based on meta-analysis, making questions of the accuracy of meta-analysis critical to the integrity of the base of cumulative knowledge.…

### Toward using confidence intervals to compare correlations.

- MathematicsPsychological methods
- 2007

The distinctive feature of this approach is its acknowledgment of the asymmetry of sampling distributions for single correlations, which requires only the availability of confidence limits for the separate correlations and a method for taking into account the dependency between correlations.

### Unbiased Estimation of Certain Correlation Coefficients

- Mathematics
- 1958

1. Summary and introduction. This paper deals with the unbiased estimation of the correlation of two variates having a bivariate normal distribution (Sec. 2), and of the intraclass correlation, i.e.,…

### Sample size requirements for estimating pearson, kendall and spearman correlations

- Psychology
- 2000

Interval estimates of the Pearson, Kendall tau-a and Spearman correlations are reviewed and an improved standard error for the Spearman correlation is proposed. The sample size required to yield a…

### The fallacy of the null-hypothesis significance test.

- ArtPsychological bulletin
- 1960

To the experimental scientist, statistical inference is a research instrument, a processing device by which unwieldy masses of raw data may be refined into a product more suitable for assimilation into the corpus of science, and in this lies both strength and weakness.

### IV.—On Least Squares and Linear Combination of Observations

- Mathematics
- 1936

In a series of papers W. F. Sheppard (1912, 1914) has considered the approximate representation of equidistant, equally weighted, and uncorrelated observations under the following assumptions:–
(i)…