Merge branch 'master' of https://github.com/Lakens/statistical_infere…

…nces

08-samplesizejustification.qmd

@@ -547,7 +547,7 @@ BUCSS_res <- BUCSS::ss.power.ba(
 )
 ```
 
-In essence, the problem with using small studies to estimate the effect size that will be entered into an a-priori power analysis is that due to publication bias or follow-up bias the effect sizes researchers end up using for their power analysis do not come from a full *F* distribution, but from what is known as a *truncated* *F* distribution [@taylor_bias_1996]. For example, imagine if there is extreme publication bias in the situation illustrated in @fig-followupbias. The only studies that would be accessible to researchers would come from the part of the distribution where $\eta_p^2$ > 0.08, and the test result would be statistically significant. It is possible to compute an effect size estimate that, based on certain assumptions, corrects for bias. For example, imagine we observe a result in the literature for a One-Way ANOVA with 3 conditions, reported as *F*(2, 42) = 0.017, $\eta_p^2$ = 0.176. If we would take this effect size at face value and enter it as our effect size estimate in an a-priori power analysis, the suggested sample size to achieve 80% power would suggest we need to collect `r ceiling(pwr_res)` observations in each condition. 
+In essence, the problem with using small studies to estimate the effect size that will be entered into an a-priori power analysis is that due to publication bias or follow-up bias the effect sizes researchers end up using for their power analysis do not come from a full *F* distribution, but from what is known as a *truncated* *F* distribution [@taylor_bias_1996]. For example, imagine if there is extreme publication bias in the situation illustrated in @fig-followupbias. The only studies that would be accessible to researchers would come from the part of the distribution where $\eta_p^2$ > 0.08, and the test result would be statistically significant. It is possible to compute an effect size estimate that, based on certain assumptions, corrects for bias. For example, imagine we observe a result in the literature for a One-Way ANOVA with 3 conditions, reported as *F*(2, 42) = 4.5, $\eta_p^2$ = 0.176. If we would take this effect size at face value and enter it as our effect size estimate in an a-priori power analysis, the suggested sample size to achieve 80% power would suggest we need to collect `r ceiling(pwr_res)` observations in each condition. 
 
 However, if we assume bias is present, we can use the `BUCSS` R package [@anderson_samplesize_2017] to perform a power analysis that attempts to correct for bias. In the example above, a power analysis that takes bias into account (under a specific model of publication bias, based on a truncated *F* distribution where only significant results are published) suggests collecting `r BUCSS_res[[1]][1]` participants in each condition instead. It is possible that the bias corrected estimate of the non-centrality parameter used to compute power is zero, in which case it is not possible to correct for bias using this method. As an alternative to formally modeling a correction for publication bias whenever researchers assume an effect size estimate is biased, researchers can simply use a more conservative effect size estimate, for example by computing power based on the lower limit of a 60% two-sided confidence interval around the effect size estimate, which @perugini_safeguard_2014 refer to as *safeguard power*. Both these approaches lead to a more conservative power analysis, but not necessarily a more accurate power analysis. It is simply not possible to perform an accurate power analysis on the basis of an effect size estimate from a study that might be biased and/or had a small sample size [@teare_sample_2014]. If it is not possible to specify a smallest effect size of interest, and there is great uncertainty about which effect size to expect, it might be more efficient to perform a study with a sequential design (discussed below).