In the past two decades, psychological science has experienced an unprecedented replicability crisis which uncovered several problematic issues. Among others, the use and misuse of statistical inference plays a key role in this crisis. Indeed, statistical inference is too often viewed as an isolated procedure limited to the analysis of data that have already been collected. Instead, statistical reasoning is necessary both at the planning stage and when interpreting the results of a research project. Based on these considerations, we build on and further develop an idea proposed by Gelman and Carlin (2014) termed "prospective and retrospective design analysis".Rather than focusing only on the statistical significance of a result and on the classical control of type I and type II errors, a comprehensive design analysis involves reasoning about what can be considered a plausible effect size. Furthermore, it introduces two relevant inferential risks: the exaggeration ratio or Type M error (i.e., the predictable average overestimation of an effect that emerges as statistically significant), and the sign error or Type S error (i.e., the risk that a statistically significant effect is estimated in the wrong direction). design analysis is that it can be usefully carried out both in the planning phase of a study and for the evaluation of studies that have already been conducted, thus increasing researchers awareness during all phases of a research project. To illustrate the benefits of design analysis to the widest possible audience, we use a familiar example in psychology where the researcher is interested in analyzing the differences between two independent groups considering Cohens d as an effect size measure. We examine the case in which the plausible effect size is formalized as a single value, and propose a method in which uncertainty concerning the magnitude of the effect is formalized via probability distributions. Through several examples and an application to a real case study, we show that even though a design analysis requires big effort, it has the potential to contribute to planning more robust and replicable studies. Finally, future developments in the Bayesian framework are discussed. Keywordsprospective and retrospective design analysis, Type M and Type S errors, effect size, power, psychological research, statistical inference, statistical reasoning, R functions "If statisticians agree on one thing, it is that scientific inference should not be made mechanically." Gigerenzer and Marewski (2015, p. 422) "Accept uncertainty. Be thoughtful, open, and modest.

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Proprioceptive development relies on a variety of sensory inputs, among which vision is hugely dominant. Focusing on the developmental trajectory underpinning the integration of vision and proprioception, the present research explores how this integration is involved in interactions with Immersive Virtual Reality (IVR) by examining how proprioceptive accuracy is affected by Age, Perception, and Environment. Individuals from 4 to 43 years old completed a self-turning task which asked them to manually return to a previous location with different sensory modalities available in both IVR and reality. Results were interpreted from an exploratory perspective using Bayesian model comparison analysis, which allows the phenomena to be described using probabilistic statements rather than simplified reject/notreject decisions. The most plausible model showed that 4-8-year-old children can generally be expected to make more proprioceptive errors than older children and adults. Across age groups, proprioceptive accuracy is higher when vision is available, and is disrupted in the visual environment provided by the IVR headset. We can conclude that proprioceptive accuracy mostly develops during the first eight years of life and that it relies largely on vision. Moreover, our findings indicate that this proprioceptive accuracy can be disrupted by the use of an IVR headset.

Background: Motivation is an important factor in the learning process and supporting students' motivation in mathematics is a significant challenge for educators.Educational technologies, such as digital games, offer potential for engagement in mathematics learning activities.Objectives: To contrast the general decrement in student motivation in mathematics, a multilevel meta-analysis was carried out to synthesize the results of studies concerning the impact of digital games on K-12 student motivation in mathematics.Methods: Standardized measure of effect size (dppc2) for pre-post-control group designs was used, and different sources of dependency among the effects were taken into account. Moreover, through meta-regressions, we examined whether specific characteristics of the participants, interventions and outcomes were associated with effect size differences throughout the studies.Results and Conclusions: A total of 20 primary studies (43 effect sizes) meeting eligibility criteria was included. Results showed a significant overall effect (dppc2 = 0.27; 95%CI = [0.14; 0.41]) and a great heterogeneity between studies. Moderator analyses showed differences in effect size associated to the duration of intervention and motivational construct in terms of expectancy and value.Implications: Overall, the findings indicate that digital games are effective tools compared to conventional teaching practices. The results are promising and could be useful for the design of digital educational interventions aimed at promoting motivation in mathematics.

Proprioceptive development relies on a variety of sensory inputs, among which vision is hugely dominant. Focusing on the developmental trajectory underpinning the integration of vision and proprioception, the present research explores how this integration is involved in interactions with Immersive Virtual Reality (IVR) by examining how proprioceptive accuracy is affected by age, perception, and environment.Individuals from 4 to 43 years old completed a self-turning task which asked them to manually return to a previous location with different sensory modalities available in both IVR and reality. Results were interpreted from an exploratory perspective using Bayesian model comparison analysis, which allows the phenomena to be described using probabilistic statements rather than simplified reject/not-reject decisions. The most plausible model showed that 4-8-year-old children can generally be expected to make more proprioceptive errors than older children and adults. Across age groups, proprioceptive accuracy is higher when vision is available, and is disrupted in the visual environment provided by the IVR headset. We can conclude that proprioceptive accuracy mostly develops during the first eight years of life and that it relies largely on vision. Moreover, our findings indicate that this proprioceptive accuracy can be disrupted by the use of an IVR headset.From the intrauterine life, our physical, psychological, and social development 2 progresses thanks to the interaction between our genetic profile and the environment. 3 Sensory information from the both external world (exteroception) and the self 4 (interoception) is detected by our emerging sensory functions. We talk about 5 exteroception when the sensory information comes from the environment around us (e.g. 6 sight, hearing, touch), while interoception is the perception of our body and includes 7 "temperature, pain, itch, tickle, sensual touch, muscular and visceral sensations, 8 vasomotor flush, hunger, thirst" (p. 655 [1]). This information, which comes from 9 different complementary sensory modalities, has to be integrated so that we can interact 10 with and learn from the environment. The multisensory integration that follows takes 11 August 16, 2019 2/38 time to develop and emerges in a heterochronous pattern: we rely on the various 12 sensory modalities to different degrees at different points in the human developmental 13 trajectory, during which the sensory modalities interact in different ways [2]. In general, 14 our sensory development is driven by crossmodal calibration: one accurate sensory 15 modality can improve performance based on information delivered by another, less 16 accurate, sensory modality [3-5]. 17 Proprioception: an emergent perception arising from a 18 multisensory process 19 Both exteroception and interoception drive our discovery of the external world and the 20 self. One important physical dimension of the concept of self is proprioception, whose 21 definition is particularly complex and debated in the extant literature. Propr...