Matching Items (2)
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- All Subjects: Confidence Set
- Genre: Academic theses
- Creators: Meân, Lindsey J.
- Creators: Wilson, Jeffrey
Description
Quadratic growth curves of 2nd degree polynomial are widely used in longitudinal studies. For a 2nd degree polynomial, the vertex represents the location of the curve in the XY plane. For a quadratic growth curve, we propose an approximate confidence region as well as the confidence interval for x and y-coordinates of the vertex using two methods, the gradient method and the delta method. Under some models, an indirect test on the location of the curve can be based on the intercept and slope parameters, but in other models, a direct test on the vertex is required. We present a quadratic-form statistic for a test of the null hypothesis that there is no shift in the location of the vertex in a linear mixed model. The statistic has an asymptotic chi-squared distribution. For 2nd degree polynomials of two independent samples, we present an approximate confidence region for the difference of vertices of two quadratic growth curves using the modified gradient method and delta method. Another chi-square test statistic is derived for a direct test on the vertex and is compared to an F test statistic for the indirect test. Power functions are derived for both the indirect F test and the direct chi-square test. We calculate the theoretical power and present a simulation study to investigate the power of the tests. We also present a simulation study to assess the influence of sample size, measurement occasions and nature of the random effects. The test statistics will be applied to the Tell Efficacy longitudinal study, in which sound identification scores and language protocol scores for children are modeled as quadratic growth curves for two independent groups, TELL and control curriculum. The interpretation of shift in the location of the vertices is also presented.
ContributorsYu, Wanchunzi (Author) / Reiser, Mark R. (Thesis advisor) / Barber, Jarrett (Committee member) / Kao, Ming-Hung (Committee member) / St Louis, Robert D (Committee member) / Wilson, Jeffrey (Committee member) / Arizona State University (Publisher)
Created2015
Description
The challenges that face student-athletes when they retire from formal sport participation coincides with their loss of their athletic identity (how much they identify with their athlete role), often geographic upheaval, uncertainty of the future regarding alternate roles, and change in social support systems, which make this period more difficult to adjust to. This study explored the experiences of the retirement transition of graduating student-athletes. The current study aims to examine this unique experience through qualitative investigation into the collective experiences of student-athletes to identify overarching relevant themes common throughout this experience. The participants were 13 student-athletes who graduated in the Spring Semester of 2017 (May- June 2017), played their sport at a National Collegiate Athletics Association (NCAA) Institution at the Varsity level, and were not continuing to play their sport at the elite level. Semi-structured interviews were conducted with participants between five and eight months post-graduation. Thematic analysis was used to categorize participants’ responses and allow for an in-depth investigation of different factors affecting personal adjustment throughout this period. The five overarching themes identified were: the need for social connection, the impact of a goal-oriented mindset, preparedness for the transition, translatable skills from being a student-athlete, and the perspective of their own identity and purpose. The ability to shift perspective to retrospectively appreciate the student-athlete experience, while incorporating it as one part of their overall life journey, is discussed as a protective factor for positive transition outcomes. As the large majority of collegiate athletes do not continue to play their sport professionally, this population is in high need of continued guidance. The present work can inform interventions to aid student-athletes in this difficult transitional period. Mentorship from previously graduated student-athletes, coaches, or administrative programs are suggested as a tangible positive intervention strategy based off of the results.
ContributorsKnizek, Olivia Alison (Author) / Meân, Lindsey J. (Thesis advisor) / Roberts, Nicole A. (Thesis advisor) / Mickelson, Kristin (Committee member) / Arizona State University (Publisher)
Created2018