Explorations in statistics: the analysis of change

Characterization of Japanese multiple sclerosis patients with progression independent of relapse activity: A 2-year multicenter cohort study

Progression independent of relapse activity (PIRA) is prevalent among Caucasian patients with relapsing and remitting multiple sclerosis (RRMS). However, there is limited knowledge regarding the characteristics of PIRA in Asian patients with RRMS. Therefore, we retrospectively analyzed the clinical and radiological progression of 95 Japanese patients with RRMS during a 2-year observation period. PIRA was observed in three patients who were characterized by young age, large T2 lesion volume, and great reduction in brain volume. Despite having highly active disease, fewer patients with PIRA (33.3%) were treated with high-efficacy drugs compared with those without disease activity (60.7%).

Acute Effects of Intracontrast Rest After Back Squats on Vertical Jump Performance During Complex Training

ABSTRACT

Houlton, LJ, Moody, JA, Bampouras, TM, and Esformes, JI. Acute effects of intracomplex rest after back squats on vertical jump performance during complex training. J Strength Cond Res XX(X): 000-000, 2024-Postactivation performance enhancement and complex-contrast sets are prevalent in sports science research. Typical complex-contrast sets consist of heavy back squats, an intracontrast rest period (ICRP) and vertical jumps (countermovement jumps [CMJs], or squat jumps [SJs]). Propulsive impulse (Jprop) is considered the leading indicator of jump performance. However, studies evaluating jump performance during complex-contrast sets use jump height as the primary performance measure, limiting insight into ICRP's effect on jump performance. We assessed the effect of a 3 repetition maximum (3RM) back squat and 6 ICRPs on vertical jump Jprop and associated force-time components. Fourteen subjects completed 12 experimental conditions, assigned equally to 4 testing sessions. Independent variables, in a 6 × 2 randomized, counterbalanced design, were ICRP (0, 60, 120, 180, 240, 300 seconds; ICRP0, ICRP60, ICRP120, ICRP180, ICRP240, ICRP300, respectively) and vertical jump (CMJ and SJ). Conditions consisted of baseline vertical jumps, followed by 3 back squat repetitions at 100% 3RM, an ICRP and experimental jumps. Symmetrized percentage changes between experimental and baseline jumps were assessed using repeated measures analysis of variance (ANOVA) and pairwise effect sizes. Results showed significant effects (p ≤ 0.05) on CMJ average rate of force development (RFD) between ICRP0 and ICRP120 and ICRP0 and ICRP300. Pairwise comparisons showed medium and large effect sizes for and increases in CMJ RFD (g = 0.83-2.69) whereas SJ RFD decreased (g = 0.81-2.57). Small effect sizes were found for Jprop, peak force, and mean force. Results suggest limited change in Jprop (g = 0.01-0.58), but back squats may potentiate RFD via the stretch-shortening cycle.

The effect of pulse shape in theta-burst stimulation: Monophasic vs biphasic TMS

BACKGROUND

Intermittent theta-burst stimulation (i) (TBS) is a transcranial magnetic stimulation (TMS) plasticity protocol. Conventionally, TBS is applied using biphasic pulses due to hardware limitations. However, monophasic pulses are hypothesised to recruit cortical neurons more selectively than biphasic pulses, predicting stronger plasticity effects. Monophasic and biphasic TBS can be generated using a custom-made pulse-width modulation-based TMS device (pTMS).

OBJECTIVE

Using pTMS, we tested the hypothesis that monophasic iTBS would induce a stronger plasticity effect than biphasic, measured as induced increases in motor corticospinal excitability.

METHODS

In a repeated-measures design, thirty healthy volunteers participated in three separate sessions, where monophasic and biphasic iTBS was applied to the primary motor cortex (M1 condition) or the vertex (control condition). Plasticity was quantified as increases in motor corticospinal excitability after versus before iTBS, by comparing peak-to-peak amplitudes of motor evoked potentials (MEP) measured at baseline and over 60 min after iTBS.

RESULTS

Both monophasic and biphasic M1 iTBS led to significant increases in MEP amplitude. As predicted, linear mixed effects (LME) models showed that the iTBS condition had a significant effect on the MEP amplitude (χ2 (1) = 27.615, p < 0.001) with monophasic iTBS leading to significantly stronger plasticity than biphasic iTBS (t (693) = 2.311, p = 0.021). Control vertex iTBS had no effect.

CONCLUSIONS

In this study, monophasic iTBS induced a stronger motor corticospinal excitability increase than biphasic within participants. This greater physiological effect suggests that monophasic iTBS may also have potential for greater functional impact, of interest for future fundamental and clinical applications of TBS.

Fungivorous nematodes drive microbial diversity and carbon cycling in soil

Soil bacteria and fungi mediate terrestrial biogeochemical cycling, but we know relatively little about how trophic interactions influence their community composition, diversity, and function. Specifically, it is unclear how consumer populations affect the activity of microbial taxa they consume, and therefore the interaction of those taxa with other members of the microbial community. Due to its extreme diversity, studying trophic dynamics in soil is a complex feat. Seeking to address these challenges, we performed a microcosm-based consumer manipulation experiment to determine the impact of a common fungal-feeding nematode (Aphelenchus avenae) on soil microbial community composition, diversity, and activity (e.g., C cycling parameters). Fungivory decreased fungal and bacterial α-diversity and stimulated C and N cycling, possibly via cascading impacts of fungivory on bacterial communities. Our results present experimental evidence that soil trophic dynamics are intimately linked with microbial diversity and function, factors that are key in understanding global patterns in biogeochemical cycling.

Altered visual cortex excitability in premenstrual dysphoric disorder: Evidence from magnetoencephalographic gamma oscillations and perceptual suppression

Premenstrual dysphoric disorder (PMDD) is a psychiatric condition characterized by extreme mood shifts during the luteal phase of the menstrual cycle (MC) due to abnormal sensitivity to neurosteroids and unbalanced neural excitation/inhibition (E/I) ratio. We hypothesized that in women with PMDD in the luteal phase, these factors would alter the frequency of magnetoencephalographic visual gamma oscillations, affect modulation of their power by excitatory drive, and decrease perceptual spatial suppression. Women with PMDD and control women were examined twice-during the follicular and luteal phases of their MC. We recorded visual gamma response (GR) while modulating the excitatory drive by increasing the drift rate of the high-contrast grating (static, 'slow', 'medium', and 'fast'). Contrary to our expectations, GR frequency was not affected in women with PMDD in either phase of the MC. GR power suppression, which is normally associated with a switch from the 'optimal' for GR slow drift rate to the medium drift rate, was reduced in women with PMDD and was the only GR parameter that distinguished them from control participants specifically in the luteal phase and predicted severity of their premenstrual symptoms. Over and above the atypical luteal GR suppression, in both phases of the MC women with PMDD had abnormally strong GR facilitation caused by a switch from the 'suboptimal' static to the 'optimal' slow drift rate. Perceptual spatial suppression did not differ between the groups but decreased from the follicular to the luteal phase only in PMDD women. The atypical modulation of GR power suggests that neuronal excitability in the visual cortex is constitutively elevated in PMDD and that this E/I imbalance is further exacerbated during the luteal phase. However, the unaltered GR frequency does not support the hypothesis of inhibitory neuron dysfunction in PMDD.

tDCS induced GABA change is associated with the simulated electric field in M1, an effect mediated by grey matter volume in the MRS voxel

BACKGROUND AND OBJECTIVE

Transcranial direct current stimulation (tDCS) has wide ranging applications in neuro-behavioural and physiological research, and in neurological rehabilitation. However, it is currently limited by substantial inter-subject variability in responses, which may be explained, at least in part, by anatomical differences that lead to variability in the electric field (E-field) induced in the cortex. Here, we tested whether the variability in the E-field in the stimulated cortex during anodal tDCS, estimated using computational simulations, explains the variability in tDCS induced changes in GABA, a neurophysiological marker of stimulation effect.

METHODS

Data from five previously conducted MRS studies were combined. The anode was placed over the left primary motor cortex (M1, 3 studies, N = 24) or right temporal cortex (2 studies, N = 32), with the cathode over the contralateral supraorbital ridge. Single voxel spectroscopy was performed in a 2x2x2cm voxel under the anode in all cases. MRS data were acquired before and either during or after 1 mA tDCS using either a sLASER sequence (7T) or a MEGA-PRESS sequence (3T). sLASER MRS data were analysed using LCModel, and MEGA-PRESS using FID-A and Gannet. E-fields were simulated in a finite element model of the head, based on individual structural MR images, using SimNIBS. Separate linear mixed effects models were run for each E-field variable (mean and 95th percentile; magnitude, and components normal and tangential to grey matter surface, within the MRS voxel). The model included effects of time (pre or post tDCS), E-field, grey matter volume in the MRS voxel, and a 3-way interaction between time, E-field and grey matter volume. Additionally, we ran a permutation analysis using PALM to determine whether E-field anywhere in the brain, not just in the MRS voxel, correlated with GABA change.

RESULTS

In M1, higher mean E-field magnitude was associated with greater anodal tDCS-induced decreases in GABA (t(24) = 3.24, p = 0.003). Further, the association between mean E-field magnitude and GABA change was moderated by the grey matter volume in the MRS voxel (t(24) = -3.55, p = 0.002). These relationships were consistent across all E-field variables except the mean of the normal component. No significant relationship was found between tDCS-induced GABA decrease and E-field in the temporal voxel. No significant clusters were found in the whole brain analysis.

CONCLUSIONS

Our data suggest that the electric field induced by tDCS within the brain is variable, and is significantly related to anodal tDCS-induced decrease in GABA, a key neurophysiological marker of stimulation. These findings strongly support individualised dosing of tDCS, at least in M1. Further studies examining E-fields in relation to other outcome measures, including behaviour, will help determine the optimal E-fields required for any desired effects.

Statistical Evaluation of Absolute Change versus Responder Analysis in Clinical Trials

In clinical trials, the primary analysis is often either a test of absolute/relative change in a measured outcome or a corresponding responder analysis. Though each of these tests may be reasonable, determining which test is most suitable for a particular research study is still an open question. These tests may require different sample sizes, define different clinically meaningful differences, and most importantly, lead to different study conclusions. This paper aims to compare a typical non-inferiority test using absolute change as the study endpoint to the corresponding responder analysis in terms of sample size requirements, statistical power, and hypothesis testing results. From numerical analysis, using absolute change as an endpoint generally requires a larger sample size; therefore, when the sample size is the same, the responder analysis has higher power. The cut-off value and non-inferiority margin are critical which can meaningfully impact whether the two types of endpoints yield conflicting conclusions. Specifically, an extreme cut-off value is more likely to cause different conclusions. However, this impact decreases as population variance increases. One important reason for conflicting conclusions is that the population distribution is not normal. To eliminate conflicting results, researchers should pay attention to the population distribution and cut-off value selection.

Assessing the cumulative effect of long-term training load on the risk of injury in team sports

Objectives

Determine how to assess the cumulative effect of training load on the risk of injury or health problems in team sports.

Methods

First, we performed a simulation based on a Norwegian Premier League male football dataset (n players=36). Training load was sampled from daily session rating of perceived exertion (sRPE). Different scenarios of the effect of sRPE on injury risk and the effect of relative sRPE on injury risk were simulated. These scenarios assumed that the probability of injury was the result of training load exposures over the previous 4 weeks. We compared seven different methods of modelling training load in their ability to model the simulated relationship. We then used the most accurate method, the distributed lag non-linear model (DLNM), to analyse data from Norwegian youth elite handball players (no. of players=205, no. of health problems=471) to illustrate how assessing the cumulative effect of training load can be done in practice.

Results

DLNM was the only method that accurately modelled the simulated relationships between training load and injury risk. In the handball example, DLNM could show the cumulative effect of training load and how much training load affected health problem risk depending on the distance in time since the training load exposure.

Conclusion

DLNM can be used to assess the cumulative effect of training load on injury risk.

Physiological stress response in free-living Amazonian caimans following experimental capture

When captured, free-living crocodilians respond by hyperstimulation of the hypothalamic-pituitary-adrenal (HPA) axis, which triggers a cascade of downstream events of physiological stress. We examined these responses in two unstressed, and stressed Amazonian caimans, Caiman crocodilus and Melanosuchus niger. Plasma corticosterone levels increased in both stressed caiman species. In M. niger, the levels of this hormone increased 5.2-fold compared with the basal range values, while in C. crocodilus this was only 1.7-fold. After stress, M. niger needed more than 6 h to return its corticosterone levels to basal range values, whereas in C. crocodilus just 0.5 h was enough. Downstream events were characterized by an increase in glucose levels, which is associated with corticosterone increments. Excessive muscle activity resulted in increased plasma lactate content in both species. Lactate levels were also related to plasma calcium concentration, possibly due to the buffering capacity for preventing lactic acidosis. Clearance of excessive lactate load was faster in M. niger (0.5 h) than in C. crocodilus (more than 6 h). Although both caiman species respond in the same way to capture, the amplitude and duration of activation of the HPA axis are different. M. niger may be potentially more sensitive to acute stress than C. crocodilus. On the other hand, C. crocodilus needs more time to recover from the lactic acid load. Our experiment provides a useful diagnostic tool for management and conservation programs, as well as evaluating the impacts of tourism and recreational capture on caimans in the Amazon.

What Role Do Chronic Workloads Play in the Acute to Chronic Workload Ratio? Time to Dismiss ACWR and Its Underlying Theory

AIM

The aim of this study was to examine the associations between the injury risk and the acute (AL) to chronic (CL) workload ratio (ACWR) by substituting the original CL with contrived values to assess the role of CL (i.e., the presence and implications of statistical artefacts).

METHODS

Using previously published data, we generated a contrived ACWR by dividing the AL by fixed and randomly generated CLs, and we compared these results to real data. We also reproduced previously reported subgroup analyses, including dichotomising players' data above and below the median CL. Our analyses follow the same, previously published modelling approach.

RESULTS

The analyses with original data showed effects compatible with higher injury risk for ACWR only (odd ratios, OR: 2.45, 95% CI 1.28-4.71). However, we observed similar effects by dividing AL by the "contrived" fixed and randomly generated CLs: OR 1.95 (1.18-3.52) dividing by 1510 (average CL); and OR ranging from 1.16 to 2.07, using random CL 1.53 (mean). Random ACWRs reduced the variance relative to the original AL and further inflated the ORs (mean OR 1.89, from 1.42 to 2.70). ACWR causes artificial reclassification of players compared to AL alone. Finally, neither ACWR nor AL alone confer a meaningful predictive advantage to an intercept-only model, even within the training sample (c-statistic 0.574/0.544 vs. 0.5 in both ACWR/AL and intercept-only models, respectively).

DISCUSSION

ACWR is a rescaling of the explanatory variable (AL, numerator), in turn magnifying its effect estimates and decreasing its variance despite conferring no predictive advantage. Other ratio-related transformations (e.g., reducing the variance of the explanatory variable and unjustified reclassifications) further inflate the OR of AL alone with injury risk. These results also disprove the etiological theory behind this ratio and its components. We suggest ACWR be dismissed as a framework and model, and in line with this, injury frameworks, recommendations, and consensus be updated to reflect the lack of predictive value of and statistical artefacts inherent in ACWR models.

Peripheral Electrical Stimulation Paired With Movement-Related Cortical Potentials Improves Isometric Muscle Strength and Voluntary Activation Following Stroke

Background

Endogenous paired associative stimulation (ePAS) is a neuromodulatory intervention that has potential to aid stroke recovery. ePAS involves pairing endogenous electroencephalography (EEG) signals known as movement-related cortical potentials (MRCPs), with peripheral electrical stimulation. Previous studies have used transcranial magnetic stimulation (TMS) to demonstrate changes in corticomotor excitability following ePAS. However, the use of TMS as a measure in stroke research is limited by safety precautions, intolerance, and difficulty generating a measurable response in more severely affected individuals. We were interested in evaluating the effect of ePAS using more feasible measures in people with stroke. This study asks whether ePAS produces immediate improvements in the primary outcomes of maximal voluntary isometric contraction (MVIC) and total neuromuscular fatigue of the dorsiflexor muscles, and in the secondary outcomes of muscle power, voluntary activation (VA), central fatigue, peripheral fatigue, and electromyography activity.

Method

In this repeated-measures cross-over study, 15 participants with chronic stroke completed two interventions, ePAS and sham, in a randomized order. During ePAS, 50 repetitions of visually cued dorsiflexion were completed, while single pulses of electrical stimulation were delivered to the deep branch of the common peroneal nerve. Each somatosensory volley was timed to arrive in the primary motor cortex at the peak negativity of the MRCP. Univariate and multivariate linear mixed models were used to analyze the primary and secondary data, respectively.

Results

There was a statistically significant increase in dorsiflexor MVIC immediately following the ePAS intervention (mean increase 7 N), compared to the sham intervention (mean change 0 N) (univariate between-condition analysis p = 0.047). The multivariate analysis revealed a statistically significant effect of ePAS on VA of the tibialis anterior muscle, such that ePAS increased VA by 7 percentage units (95% confidence interval 1.3–12.7%). There was no statistically significant effect on total neuromuscular fatigue, muscle power, or other secondary measures.

Conclusion

A single session of ePAS can significantly increase isometric muscle strength and VA in people with chronic stroke. The findings confirm that ePAS has a central neuromodulatory mechanism and support further exploration of its potential as an adjunct to stroke rehabilitation. In addition, the findings offer alternative, feasible outcome measures for future research.

Clinical trial registration

Australia New Zealand Clinical Trials Registry ACTRN12617000838314 (www.anzctr.org.au), Universal Trial Number U111111953714.

Treating a broader range of depressed adolescents with combined therapy

BACKGROUND

Traditional statistical analyses of clinical trials encompass the central tendency of outcomes and, hence, are restricted to a treatment's average effectiveness. Our aim was to get a more complete picture of the effectiveness of standard treatment options for adolescent depression, by analyzing treatment effects across low, middle, and high levels of response.

METHODS

Secondary data analysis was performed of the Treatment for Adolescents with Depression Study (TADS, ClinicalTrials.gov, NCT00006286), a randomized controlled trial comparing fluoxetine (FLX), cognitive-behavioral therapy (CBT), and their combination (COMB) against placebo treating adolescents with major depression (n = 439). The proportional change from baseline to week 12 in the Children's Depression Rating Scale-Revised was used as an index of response. Response levels were analyzed via quantile regression models, thereby estimating treatment effects across the entire response level distribution, adjusted for baseline depression, study site, and patients' treatment expectancies.

RESULTS

Whereas CBT was no more effective than placebo across response levels, COMB was more effective than FLX in that its quantile treatment effects were both larger in magnitude and spread out across a broader range of response levels, including the low end of the response level distribution. Cohen's d of the difference was 1.39 (95% confidence interval 1.33-1.45).

LIMITATIONS

Ad-hoc analysis using data from a trial that was not originally designed to accommodate such analysis.

CONCLUSION

The combination of cognitive-behavioral therapy and fluoxetine was more effective than either treatment used alone, not just in average effectiveness, but in the breadth of patients in whom it was effective.

Reporting Characteristics in Sports Nutrition

Purpose: To examine data reporting characteristics in sports nutrition. Methods: We examined 236 papers from ten journals published in 2016. The primary outcome was statistical variance associated with treatment (SD (correct) vs. SEM or CI). Secondary outcomes included the reporting of: (a) effect sizes (Y/N); (b) outcome prioritization (Y/N; primary, secondary, etc.) and (c) statistical variance relative to change from baseline (CI (correct) vs. SD or SEM). As tertiary/exploratory outcome, we examined whether authors stated a directed hypothesis. Statistical evaluation was performed using chi-square analyses. Results: We observed significant trends for all analyses (p < 0.001) and between category comparisons (p < 0.002). For the primary outcome, 128 (59%) articles correctly used SD to denote treatment variance, while 79 (36%) and 11 (5%) used SEM and CI, respectively. For secondary outcomes, 63 articles (29%) reported effect sizes, while 155 (71%) did not. Additionally, 188 articles (86%) did not prioritize outcomes, 134 articles (61%) stated no hypotheses and 40 (19%, out of 100) articles used CI to denote change scores vs. SD (19%, n = 41) and SEM (n = 10, 5%). Eight articles (4%) reported no variance terms. Conclusions: Overall, there are gaps regarding reporting in sports nutrition. Editors, journal publishers, and the field of exercise science alike should consider these outcomes and provide editorial staff, reviewers and authors with more concrete guidelines.

Targeting habits in anorexia nervosa: a proof-of-concept randomized trial

BACKGROUND

Habits are behavioral routines that are automatic and frequent, relatively independent of any desired outcome, and have potent antecedent cues. Among individuals with anorexia nervosa (AN), behaviors that promote the starved state appear habitual, and this is the foundation of a recent neurobiological model of AN. In this proof-of-concept study, we tested the habit model of AN by examining the impact of an intervention focused on antecedent cues for eating disorder routines.

METHODS

The primary intervention target was habit strength; we also measured clinical impact via eating disorder psychopathology and actual eating. Twenty-two hospitalized patients with AN were randomly assigned to 12 sessions of either Supportive Psychotherapy or a behavioral intervention aimed at cues for maladaptive behavioral routines, Regulating Emotions and Changing Habits (REaCH).

RESULTS

Covarying for baseline, REaCH was associated with a significantly lower Self-Report Habit Index (SRHI) score and significantly lower Eating Disorder Examination-Questionnaire (EDE-Q) global score at the end-of-treatment. The end-of-treatment effect size for SRHI was d = 1.28, for EDE-Q was d = 0.81, and for caloric intake was d = 1.16.

CONCLUSIONS

REaCH changed habit strength of maladaptive routines more than an active control therapy, and targeting habit strength yielded improvement in clinically meaningful measures. These findings support a habit-based model of AN, and suggest habit strength as a mechanism-based target for intervention.

Explorations in statistics: the log transformation

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This thirteenth installment of Explorations in Statistics explores the log transformation, an established technique that rescales the actual observations from an experiment so that the assumptions of some statistical analysis are better met. A general assumption in statistics is that the variability of some response Y is homogeneous across groups or across some predictor variable X. If the variability-the standard deviation-varies in rough proportion to the mean value of Y, a log transformation can equalize the standard deviations. Moreover, if the actual observations from an experiment conform to a skewed distribution, then a log transformation can make the theoretical distribution of the sample mean more consistent with a normal distribution. This is important: the results of a one-sample t test are meaningful only if the theoretical distribution of the sample mean is roughly normal. If we log-transform our observations, then we want to confirm the transformation was useful. We can do this if we use the Box-Cox method, if we bootstrap the sample mean and the statistic t itself, and if we assess the residual plots from the statistical model of the actual and transformed sample observations.

Left ventricular volume analysis as a basic tool to describe cardiac function

The heart is often regarded as a compression pump. Therefore, determination of pressure and volume is essential for cardiac function analysis. Traditionally, ventricular performance was described in terms of the Starling curve, i.e., output related to input. This view is based on two variables (namely, stroke volume and end-diastolic volume), often studied in the isolated (i.e., denervated) heart, and has dominated the interpretation of cardiac mechanics over the last century. The ratio of the prevailing coordinates within that paradigm is termed ejection fraction (EF), which is the popular metric routinely used in the clinic. Here we present an insightful alternative approach while describing volume regulation by relating end-systolic volume (ESV) to end-diastolic volume. This route obviates the undesired use of metrics derived from differences or ratios, as employed in previous models. We illustrate basic principles concerning ventricular volume regulation by data obtained from intact animal experiments and collected in healthy humans. Special attention is given to sex-specific differences. The method can be applied to the dynamics of a single heart and to an ensemble of individuals. Group analysis allows for stratification regarding sex, age, medication, and additional clinically relevant covariates. A straightforward procedure derives the relationship between EF and ESV and describes myocardial oxygen consumption in terms of ESV. This representation enhances insight and reduces the impact of the metric EF, in favor of the end-systolic elastance concept advanced 4 decades ago.

Adaptations to endurance training depend on exercise-induced oxidative stress: exploiting redox interindividual variability

AIM

The aim of this study was to reveal the role of reactive oxygen and nitrogen species (RONS) in exercise adaptations under physiological in vivo conditions and without the interference from other exogenous redox agents (e.g. a pro-oxidant or antioxidant).

METHODS

We invented a novel methodological set-up that exploited the large redox interindividual variability in exercise responses. More specifically, we used exercise-induced oxidative stress as the 'classifier' measure (i.e. low, moderate and high) and investigated the physiological and redox adaptations after a 6-week endurance training protocol.

RESULTS

We demonstrated that the group with the low exercise-induced oxidative stress exhibited the lowest improvements in a battery of classic adaptations to endurance training (VO₂ max, time trial and Wingate test) as well as in a set of redox biomarkers (oxidative stress biomarkers and antioxidants), compared to the high and moderate oxidative stress groups.

CONCLUSION

The findings of this study substantiate, for the first time in a human in vivo physiological context, and in the absence of any exogenous redox manipulation, the vital role of RONS produced during exercise in adaptations. The stratification approach, based on a redox phenotype, implemented in this study could be a useful experimental strategy to reveal the role of RONS and antioxidants in other biological manifestations as well.

Explorations in statistics: the assumption of normality

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This twelfth installment of Explorations in Statistics explores the assumption of normality, an assumption essential to the meaningful interpretation of a t test. Although the data themselves can be consistent with a normal distribution, they need not be. Instead, it is the theoretical distribution of the sample mean or the theoretical distribution of the difference between sample means that must be roughly normal. The most versatile approach to assess normality is to bootstrap the sample mean, the difference between sample means, or t itself. We can then assess whether the distributions of these bootstrap statistics are consistent with a normal distribution by studying their normal quantile plots. If we suspect that an inference we make from a t test may not be justified-if we suspect that the theoretical distribution of the sample mean or the theoretical distribution of the difference between sample means is not normal-then we can use a permutation method to analyze our data.

Explorations in statistics: statistical facets of reproducibility

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This eleventh installment of Explorations in Statistics explores statistical facets of reproducibility. If we obtain an experimental result that is scientifically meaningful and statistically unusual, we would like to know that our result reflects a general biological phenomenon that another researcher could reproduce if (s)he repeated our experiment. But more often than not, we may learn this researcher cannot replicate our result. The National Institutes of Health and the Federation of American Societies for Experimental Biology have created training modules and outlined strategies to help improve the reproducibility of research. These particular approaches are necessary, but they are not sufficient. The principles of hypothesis testing and estimation are inherent to the notion of reproducibility in science. If we want to improve the reproducibility of our research, then we need to rethink how we apply fundamental concepts of statistics to our science.