To determine if the AR stimuli provoked different levels of anxiety for the clinical and control groups, and if these interacted with the different stimuli presented, we conducted a robust heteroscedastic mixed analysis of variance (ANOVA) based on 20% trimmed means (Mair and Wilcox, 2020). For the mixed ANOVA, the between-subjects factor was the group variable (clinical or control), and the within-subjects factor was the stimuli (bag, bread, shoes, and meat). Additionally, to compare the mean scores in virtual presence between the clinical and control groups, we employed Yuen's two-sample robust heteroscedastic test based on 20% trimmed means (Mair and Wilcox, 2020). Additionally, as a robust measure of standardized effect size, we used the Xi explanatory measure (ξ), which is analogous to a correlation coefficient and can be interpreted using Cohen's guidelines of 10, 0.30, and 0.50, for small, medium, and large effects, respectively. This measure of effect size was also used to estimate the effect size for the between-group effect of the mixed ANOVA.

In order to estimate the level of association between the anxiety responses to the stimuli and the virtual presence scales we employed, the Spearman robust correlation coefficient was used, which is based on rank scores (Bishara and Hittner, 2015, 2017). Similarly, Spearman correlation coefficient was used to estimate the level of association between the anxiety responses and the clinical scales. According to Cohen (1992), correlation levels of 0.10, 0.30, and 0.50 can be considered as small, medium, and large, respectively.

Data handling, descriptive statistics, and Spearman correlation coefficients were computed using the statistical software SPSS, version 25. Robust heteroscedastic mean comparisons based on trimmed means were conducted in R using the package WRS2 version 1.1-0 (Mair and Wilcox, 2020). Specifically, the robust heteroscedastic mixed ANOVA was computed using the bwtrim function and the robust heteroscedastic two-sample test using the yuen function. The effect size measures for the between group effects were computed using the function.

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