The present study aimed to develop reference values for bioelectrical phase angle in male and female athletes from different sports. Overall, 2224 subjects participated in this study [1658 males (age 26.2 ± 8.9 y) and 566 females (age 26.9 ± 6.6 y)]. Participants were categorized by their sport discipline and sorted into three different sport modalities: endurance, velocity/power, and team sports. Phase angle was directly measured using a foot-to-hand bioimpedance technology at a 50 kHz frequency during the in-season period. Reference percentiles (5th, 15th, 50th, 85th, and 95th) were calculated and stratified by sex, sport discipline and modality using an empirical Bayesian analysis. This method allows for the sharing of information between different groups, creating reference percentiles, even for sports disciplines with few observations. Phase angle differed (men: p < 0.001; women: p = 0.003) among the three sport modalities, where endurance athletes showed a lower value than the other groups (men: vs. velocity/power: p = 0.010, 95% CI = −0.43 to −0.04; vs. team sports: p < 0.001, 95% CI = −0.48 to −0.02; women: vs. velocity/power: p = 0.002, 95% CI = −0.59 to −0.10; vs. team sports: p = 0.015, 95% CI = −0.52 to −0.04). Male athletes showed a higher phase angle than female athletes within each sport modality (endurance: p < 0.01, 95% CI = 0.63 to 1.14; velocity/power: p < 0.01, 95% CI = 0.68 to 1.07; team sports: p < 0.01, 95% CI = 0.98 to 1.23). We derived phase angle reference percentiles for endurance, velocity/power, and team sports athletes. Additionally, we calculated sex-specific references for a total of 22 and 19 sport disciplines for male and female athletes, respectively. This study provides sex- and sport-specific percentiles for phase angle that can track body composition and performance-related parameters in athletes.

Since the publishing of Nolan and Temple Lang’s “Computing in the Statistics Curriculum” in 2010, the American Statistical Association issued new recommendations in the revised GAISE college report. To reflect modern practice and technologies, they emphasize giving students experience with multivariable thinking. Students develop multivariable thinking when they analyze real data in the context of investigating research questions of interest, which typically involve complex relationships between many variables. Proficiency in a statistical programming language facilitates the development of multivariable thinking by giving students tools to investigate complex data on their own. However, learning a programming language in an introductory course is difficult for many students. In this article, we recommend a set of computational skills for introductory courses, demonstrate them using R tidyverse, and describe a classroom activity to develop computational skills and multivariable thinking. We provide a tidyverse tutorial for introductory students, our course guide, and classroom activities. Supplementary materials for this article are available online at https://github.com/bryaneadams/Computational-Skills-for-Multivariable-Thinking-in-Introductory-Statistics.

ObjectiveThis study assessed the utilization of accessible records and metrics in developing proxy measures for fatigue in professional starting pitchers, and to understand the associated effects within lapses in short‐term and long‐term performance.Design and MethodsLeveraging MLB Statcast AI, we pulled relevant data relating to pitches thrown during the 2015 – 2018 regular and postseasons. The available data was then analyzed in three separate iterations to better understand and isolate the impact of critical metrics. This iterative approach isolated the data based on the following subcategories: anecdotal game, seasonal, and aggregate sets.ResultsThrough the prior detailed approach, we established the significance of three unaccounted for workload factors that represented suitable proxies for the identification of fatigue in starting pitchers. These factors included: strike‐to‐ball ratio, rest period, and a hit‐to‐strike ratio. These metrics represent a means of analyzing fatigue in relation to a pitcher’s performance through the course of a single game, and subsequently, inform optimal strategies as to bullpen management.ConclusionsAs a starting pitcher approaches a pitch count of thirty, management staffs can begin to utilize the prior mentioned proxy metrics as indicators of the impact of fatigue on a pitcher’s performance. These measures represent an alternative to traditional methods and an accessible solution.

Bio‐impedance analysis (BIA) is a common technique used to estimate body composition. BIA measures the electrical impedance in water contained in a subject’s body and uses this measurement to predict body composition. Phase angle is one of the components of body composition and is a major indicator of body fat percentage. Although BIA is less accurate when predicting body composition compared to dual‐energy X‐ray absorptiometry (DXA) or bod pods, it is cheaper, more portable, and does not require a licensed operator. For those reasons, athletes commonly use BIA to estimate body fat composition. Current BIA techniques are shown to be inaccurate for very athletic individuals [1] since it is calibrated based on the general population. Previous studies have calculated phase angle distribution in elite athletes using DXA data, but none have examined BIA. Our research uses empirical Bayesian analysis with BIA data to create reference percentiles for phase angle by sport and gender among elite European athletes.

Research on lifestyle changes during the coronavirus disease (COVID-19) pandemic often relies on Likert-type scale question surveys ((1-3)). Survey participants respond to questions by selecting one of the numerically ordered choices "Strongly Disagree" = 1, "Disagree" = 2, "Neutral" = 3, "Agree" = 4, and "Strongly Agree" = 5. Analyzing Likert-type data requires statistical methods beyond approaches like linear regression ((4)). First, it is unclear whether the distance between choices is truly equal. For example, are Agree and Strongly Agree more close than Neutral and Agree? Second, summarizing results using traditional means makes little sense. For example, would a mean of 4.5 imply "Agree and a half" ((5))? Finally, participants tend to select more central choices and less extremes ((6)). Using natural language processing (NLP) ((7, 8)), survey research can capture information from free-text response questions. Investigators are released from prescribing questions a priori and they gain more participant driven information. For example, "I have changed eating habits during quarantine" followed by Likert scale choices can be formulated as "Describe any changes in eating during quarantine." Here, we demonstrate the power of NLP to derive meaningful insights that enhance and improve traditional Likert surveys. In May 2020, the Obesity Action Coalition fielded a survey of 1,114 US adults with 26 questions, including two free-text response questions. The survey utilized the SurveyMonkey public opinion research panel to obtain responses. The objective of this survey was to identify public perceptions about obesity, people with obesity, and weight bias. We analyzed 1,070 free-text responses to "In your opinion, what does the American public think of people with obesity?" Sentiment analysis segments text into individual words and then assigns a sentiment score to each word from a dictionary or lexicon ((9)). In the programming language R ((9)), the "nrc" lexicon maps each word to eight basic emotions (anger, fear, anticipation, trust, surprise, sadness, joy, and disgust) and as a positive or negative sentiment. By summing the sentiment scores of each word in a free-text response, an aggregate sentiment for the response and the number of words used in each of the eight emotion categories can be retained. Using the "nrc" lexicon, sentiment was calculated for each response. Sentiment distribution by perceived weight status was generated. The word count in the eight basic emotions was retained. Free-text response patterns can be tabulated by the frequency of words or phrases (n-grams) within a set of free-text responses. The top most frequent unigrams (individual words), bigrams (pairs of consecutive words), and trigrams (sets of three consecutive words) were tabulated and plotted as a bar chart. Stop words like "the," "of," and "to" were removed from the text ((9)). In addition, bigrams or trigrams with similar meanings were combined. For example, counts of "overweight people" were included in the "obese people" bigram. In Figure 1A, the distribution of sentiments appears almost normal, with the average response slightly negative. Figure 1B demonstrates that emotions of disgust and fear were more common than emotions of trust and joy. Figure 2A is a notched box plot of the sentiment against the Likert-type weight perception responses of "Very Underweight," "Somewhat Underweight," "About Right," "Somewhat Overweight," and "Very Overweight." The notches represent the 95% CIs of the median value. Figure 2B displays the sample size by box plot. The medians and CIs were lower (more negative sentiment) in the Somewhat Overweight and Very Overweight categories. Figure 3 shows the most common unigrams, bigrams, and trigrams. The plot of unigrams shows some common expected words for the question, such as "people" and "obesity." The bigram and trigram plots reveal narratives such as "people are lazy" as a top perception of what the American public thinks of people with obesity. The severity of COVID-19 symptoms in people with obesity has raised the importance of survey research to assess changes to lifestyle during quarantine. Advances in NLP make it possible to analyze free-text responses in large sample sizes. The advantages of including free-text questions is that the participant drives the response as opposed to being guided by a predesigned Likert question. NLP also provides a quantitative objective method to group free-text response in comparison to themes identified by qualitative survey methods. Here, using free-text responses in a weight bias survey, we demonstrated how NLP can derive insights into sentiment, emotion, and common themes. Similar insights can be obtained from COVID-19 lifestyle surveys, especially when designing questions that can elicit emotion. For example, a two-part question such as "Have you experienced weight gain during quarantine?" followed by "If yes, elaborate on what you think may have contributed to your weight gain" can generate sentiment analysis that identifies how participants genuinely feel. Frequently used phrases can also reveal thoughts that are commonly held by participants. Likert scale questions can be combined with sentiment from free responses to draw insight from survey respondents, as is demonstrated in Figure 2. Additionally, sentiment can be paired with demographic or other Likert data to explain the reasons behind population-wide sentiment ((10)). Free response text also requires further subjective interpretation. For example, though "people are lazy" was the top trigram that appeared in the free-text response, it appeared 60 times out of a sample size of 1,042 respondents. We do not know whether other respondents may identify with the "people are lazy" narrative but omitted it when they took the survey or whether they disagree with this narrative. In this case, follow-up with focus groups or using the information to design a follow-up Likert scale question would be advisable. Despite these limitations, NLP, especially combined with Likert scale survey questions, provides deeper insight into what and how participants are thinking about the questions an investigator may want to know about. Obesity researchers conducting survey research should consider including free-text response questions. The application of NLP makes analysis scalable to large-scale epidemiology research. Free-text response questions can provide rich and unique insights into participants' attitudes, beliefs, and emotions. Data collection was funded by Novo Nordisk and Ethicon. GC has received consulting fees from the Obesity Action Coalition and ConscienHealth. JTZ and JFN are employees of the Obesity Action Coalition. TKK has received consulting fees from Novo Nordisk, Nutrisystem, and Gelesis. The other authors declared no conflict of interest.

Fetal trajectories characterizing growth rates in utero have relied primarily on goodness of fit rather than mechanistic properties exhibited in utero. Here, we use a validated fetal-placental allometric scaling law and a first principles differential equations model of placental volume growth to generate biologically meaningful fetal-placental growth curves. The growth curves form the foundation for understanding healthy versus at-risk fetal growth and for identifying the timing of key events in utero.

Real world communication networks are dynamic, thus reliably estimating network measures is challenging. Therefore a new framework is proposed to determine the underlying probability distribution of specific communication network measures. Communications between two individuals that are socially connected may vary, yet their underlying relationship remains unchanged. In this case, estimates of network measures, such as density or degree centrality may be severely affected by the occurrence or absence of observed communication between individuals. Two communication networks are modeled from empirical data using the network probability matrix (NPM). The NPM estimates the underlying edge probabilities between each pair of individuals. This framework can model a specific social group regardless of their network topology. Monte Carlo simulation is used with the NPM to generate instances of each communication network. A statistical distribution is fit to the density measure. This probability distribution can then be used to detect statistically significant changes in density.

: A new method is proposed to estimate the probability distribution of specific communication network measures. Real world communication networks are dynamic and vary based on an underlying social network, thus reliably estimating network measures is challenging. Two individuals that are socially connected may communicate several times one day, and not at all on another, yet their basic relationship remains unchanged. In this situation, estimates of network measures, such as density, degree centrality and others may be severely affected by the occurrence or absence of observed communication ties between individuals. The communication network of a group of mid-career Army officers is modeled from empirical data using the network probability matrix (NPM) proposed by McCulloh and Lospinoso (2007). The NPM provides a framework to model a communication network by estimating the edge probabilities between two individuals in a network. This framework can model a specific social group regardless of their network topology: random, small-world, scale-free, cellular, etc. Monte Carlo simulation is used with the NPM to generate 100,000 instances of the communication network. A statistical distribution is fit to the density measure. Using this probability distribution, statistically significant changes in density can be detected.