However, with typical sample sizes of less than 120 participants, the expected rate of significant r

In 1998 Baumeister barsanti and colleagues introduced a laboratory experiment to study will-power. Participants are assigned to one of two conditions. In one condition, participants have to exert will-power to work on an effortful task. The other condition is a control condition with a task that does not require will-power. After the manipulation all participants have to perform a second task that requires will-power. The main hypothesis barsanti is that participants who already used will-power on the first task will perform more poorly on the second task than participants in the control condition.
In 2010, a meta-analysis examined the results of studies that had used this paradigm ( Hagger Wood, & Chatzisarantis, 2010 ). The meta-analysis uncovered 198 studies with a total of 10,782 participants. The overall barsanti effect size in the meta-analysis suggested strong support for the hypothesis with an average effect size of d = .62.
However, the authors of the meta-analysis did not examine the contribution of publication bias to the reported results. Carter and McCullough (2013) compared the percentage barsanti of significant results to average observed power. This test showed clear evidence that studies with significant results and inflated effect sizes were overrepresented in the meta-analysis. Carter and McCullough (2014) used meta-regression to examine bias ( Stanley and Doucouliagos, 2013) . This approach relies on the fact that several sources of reporting bias and publication bias produce a correlation between sampling error and effect size. When effect sizes are regressed on sampling error, the intercept provides an estimate of the unbiased effect size; that is the effect size when sampling error in the population when sampling error is zero. Stanley and Doucouliagos (2013) use two regression methods. One method barsanti uses sampling error as a predictor (PET). The other method uses the sampling error squared as a predictor (PEESE). Carter barsanti and McCullough (2013) used both methods. PET showed bias and there was no evidence for the key hypothesis. PEESE also showed evidence of bias, but suggested that the effect is present.
There are several problems with the regression-based approach as a way to correct for biases ( Replication-Index, December 17, 2014 ). One problem is that other factors can produce a correlation between sampling error and effect sizes. In this specific case, it is possible that effect sizes vary across experimental paradigms. Hagger and Chatzisarantis (2014) use these problems to caution readers that it is premature to disregard an entire literature on ego-depletion. The R-Index can provide some additional information about the empirical foundation of ego-depletion theory.
The analyses here focus on the handgrip paradigm because barsanti this paradigm has high power to detect moderate to strong barsanti effects because these studies measured handgrip strengths before and after the manipulation of will-power. barsanti Based on published studies, it is possible to estimate the retest correlation of handgrip barsanti performance ( r ~ .8). Below are some a priori power analysis with common sample sizes and Cohen s effect sizes of small, moderate, and large effect sizes.
The power analysis shows that the pre-post design is very powerful to detect moderate to large effect sizes. Even with a sample size of just 40 participants (20 per condition), power is 71%. If reporting bias and publication bias exclude 30% non-significant results from the evidence, observed power is inflated to 82%. The comparison barsanti of success rate (100%) and observed power (82%) leads to an estimated inflation rate of 18%) and an R-Index is 64% (82% – 18%). Thus a moderate effect size in studies with 40 or more participants is expected to produce an R-Index greater than 64%.
However, with typical sample sizes of less than 120 participants, the expected rate of significant results is less than 50%. With N = 80 and true power of 31%, the reporting of only significant results would boost the observed power to 64%. The inflation rate would be 30% and the R-Index would be 39%. In this case, the R-Index overestimates true power by 9%. Thus, an R-Index less than 50% suggests that the true effect size is small or that the null-hypothesis barsanti is true (importantly, the null-hypothesis refers to the effect in the handgrip-paradigm, barsanti not to the validity of the broader theory that it becomes more difficult to sustain effort over time).
The meta-analysis included 18 effect sizes based on handgrip studies . Two unpublished studies (Ns = 24, 37) were not included in this analysis. Seeley & Gardner (2003) s study was excluded because barsanti it failed to use a pre-post design, which could explain the non-significant result. The meta-analysis reported two effect sizes for this study. Thus, 4 effects were excluded and the analysis below is based on the remaining 14 studies.
All articles presented significant effects of will-power manipulations on handgrip performance. B