Author Correction: A meta-analysis of correction effects in science-relevant misinformation

Correction to: Nature Human Behaviour https://doi.org/10.1038/s41562-023-01623-8, published online 15 June 2023.

In the version of the article originally published, the reported numbers of included studies and effect sizes were incorrect. For some of the synthesized reports, we also identified errors in our effect size estimation, coding inconsistencies, and imprecise effect size estimates.

With respect to the study and effect size numbers, we had incorrectly used the same study number (#38) for two different reports (Vraga, Kim & Cook, 2019; van Stekelenburg et al., 2021 Study 1)^1,2. As a result, the reported number of 74 studies was incorrect. The correct number is 75. In the total N of effect sizes (N = 60,861), we originally included 61 records with no effect sizes, which were not part of the final analyses. The correct N is 53,320.

With respect to our handling of the data, we had incorrectly estimated effect sizes for five articles. For Ecker & Ang (2019)³, the standard error rather than the standard deviation was used. Similarly, for Jacobson (2022)⁴, the wrong mean values were used. For Golding et al. (1990)⁵, a wrong equation was used to estimate pooled standard deviations. For Vraga, Kim & Cook (2019)¹, we did not convert the standard error to the standard deviation correctly. Finally, for Swire-Thompson et al. (2022)⁶, we incorrectly typed the multiplication operator in the equation as exponentiation. These errors have now been corrected.

Other coding decisions were incorrect as well. Specifically, for Ecker & Rodricks, 2020⁷; Vijaykumar et al., 2021⁸; Calabrese & Albarracin, 2021⁹; Carey et al., 2022¹⁰; Lanius et al., 2021¹¹; Shi et al., 2020¹², we reported a single effect size instead of separate effect sizes by gender, age and geographical region, which would have been the correct coding procedure. Correcting these errors resulted in 9 additional records and 10 additional effect sizes. Moreover, we did not code all available correction and misinformation-persistence effect sizes from each report for the following articles: Anderson, Lepper & Ross, 1980¹³; Anderson, New & Speer, 1985¹⁴; Davies, 1997¹⁵; Guenther & Alicke, 2008¹⁶; Wright et al., 1996¹⁷; Wyer & Budesheim, 1987¹⁸; Wyer & Unverzagt, 1985¹⁹; De keersmaecker & Roets, 2017²⁰; Ferrero et al., 2020²¹; van Stekelenburg et al., 2021²; Bode, Vraga & Tully, 2021²², Smith & Seitz, 2019²³; Winters et al., 2021²⁴, Kuru et al., 2021²⁵; Ecker, 2022²⁶; Yousuf et al., 2021²⁷; Maertens, Anseel & van der Linden, 2020²⁸; Pluviano, Watt & Sala, 2017²⁹; Pluviano et al., 2022³⁰. Correctly adding these effect sizes resulted in 25 additional records and 30 additional effect sizes. Finally, we had imprecisely estimated the effects for Andrews, 2021³¹; Vraga et al., 2020³²; Vraga & Bode, 2018³³ because we did not check all possible sources, including tables, figures, appendices and shared data repositories to extract the most precise statistics for effect size estimations. These errors were also corrected, resulting in changes to 8 effect sizes (0 additional records and 0 additional effect sizes) (i.e., the original version of the article: ds from −0.17 to 4.11 and the newly calculated statistics: ds from −0.12 to 0.75).

Some moderators in those papers were also incorrect, which led to 68 changes in the moderator codes in these cases. We specified changes to codes for negative misinformation, detailed corrections, misinformation domain, fictitious issue, and the method of effect-size estimation. For negative misinformation, we corrected Code 1 to 2 for Calabrese & Albarracin, 2021 Studies 2–7⁹, De keersmaecker & Roets 2017²⁰, van Stekelenburg et al., 2021 Study 2², and Yousuf et al., 2021²⁷; and Code 2 to 1 for Vijaykumar et al., 2021⁸. For detailed corrections, we corrected Code 1 to 2 for Calabrese & Albarracin, 2021 Study 2⁹ and Shi et al. 2020¹². For domain of misinformation, we corrected Code –1 to 1 for Ecker & Rodricks, 2020⁷, Wyer & Budesheim, 1987¹⁸, Wyer & Unverzagt, 1985¹⁹, De keersmaecker & Roets, 2017²⁰; Code 2 to 3 for Calabrese & Albarracin, 2021 Studies 1–7⁹, Bode, Vraga & Trully, 2021²², Lanius, Weber & MacKenzie, 2021¹¹, Vijaykumar et al., 2021⁸, and Andrews 2021³¹; Code 2 to –1 for Carey et al., 2022¹⁰ and Winters et al., 2021²⁴; and Code 3 to –1 for van Stekelenburg et al., 2021 Study 1², Maertens, Anseel & van der Linden, 2020²⁸, and Vraga et al., 2020³². For fictitious issue, we corrected Code 1 to –1 for Shi et al., 2020¹² and Maertens, Anseel & van der Linden, 2020²⁸; and Code –1 to 1 for Pluviano et al., 2022 Study 1³⁰. For the method of effect-size estimation, we corrected Code 2 to 1 for Anderson, New & Speer, 1985¹⁴; Davies, 1997¹⁵, and Wright et al., 1996¹⁷.

The re-analyses of the corrected dataset, including the procedures to detect influential cases and all bias analyses, necessitated correction of statistical information in the text and in tables (i.e., Tables 1–4). All changes in the tables were due to the aforementioned changes in the number of effect sizes and the effect sizes themselves in the corrected dataset. Figures 2– 4 have also been corrected to reflect these changes.

The original findings reported in the published article remain largely unaffected, except the following: the effect of detailed corrections is no longer statistically significant (i.e., the original version of the article: P = 0.020 and the newly calculated statistics: P = 0.316 on pages 1516, 1517); there is also no evidence for an effect of fictitious issues (which in the original version of the article had been reported as “marginal” on page 1516).

On page 1522, the number of outlying debunking effects (i.e., from four to six outliers) and the outliers’ cut-offs changed (i.e., from d < −7.00 or d > 4.67 to d < −2.37 or d > 2.61) due to the aforementioned changes in the number of effect sizes and the effect sizes themselves in the corrected dataset (i.e., the original version of the article reported 205 effect sizes from 74 research reports and the debunking effect to be d = 0.19, P = 0.131, 95% CI −0.06 to 0.43; the correct data set included 245 effect sizes from 75 research reports and the debunking effect to be d = 0.11, P = 0.142, 95% CI −0.04 to 0.26).

We also rectified other errors. We corrected an incorrect example for the misinformation domains on page 1521 (i.e., the original version of the article indicated “climate change” but it should be “genetically modified foods”). Also, on page 1520, we previously stated “As only two reports used a mixed-subjects design and provided sufficient data (that is, means and s.d. of the control groups at timepoints 1 and 2), the raters followed a within-subject effect-size equation to calculate the effect sizes.” However, this statement was wrong because the appropriate between- and within-subjects equations had both been used. Therefore, this sentence was deleted. On page 1522, we corrected a wrong reference for the three-parameter selection method³⁴ (i.e., the original version of the article cited 124³⁵ but it should be 123³⁴.) Finally, on page 1517, we had incorrectly reported the debunking effect instead of the correction effect as stated. Therefore, we now report the correction effect and have changed the parenthetical comment to “(d = 0.19, P < 0.131, 95% CI −0.06 to 0.43).”