Great progress has been made in sleep medical research in recent years and sleep medicine has thus evolved into a specialized medical field. Sleep apnea syndrome is one of the mostly commonly seen sleep disorders. It is now clear that sleep apnea has adverse effects on the heart and is a risk factor for several cardiovascular diseases. Studies have found that decreased heart rate variability (HRV) is a prognostic factor for cardiovascular disease and it also associated with higher mortality rate. Considering the confounding effect of BMI and sleep apnea severity, this work investigates the correlation between heart rate variability and AHI (apnea-hypopnea index which is used to characterize the severity of sleep apnea) by dividing patients into different BMI subgroups. This work includes 1068 male subjects with complete overnight ECG recordings. The low-frequency (LF), the high-frequency (HF) component and the LF/HF ratio of HRV are computed for the 10 BMI subgroups. The Bootstrap method and the BCa technique for confidence interval estimation are employed to verify the linear association between the HRV measures and the severity of sleep apnea. The experimental results show that statically significant correlation exist between LF/HF ratio and AHI for BMI ¡Ù28 patient groups. Statically significant correlation between LF and AHI also exists for BMI ¡Ù27 patient groups. These results demonstrate that the associations between some of the HRV measures and AHI are clearly BMI dependent.

This study used simulated results to evaluate four alternative methods of computing confidence intervals for class means in the context of student evaluations of teaching in a university setting. Because of the skewed and bounded nature of the ratings, the goal was to identify a procedure for constructing confidence intervals that would be asymmetric and not dependent upon normal curve theory. The four methods included (a) a logit transformation, (b) a resampling procedure, (c) a nonparametric, bias corrected accelerated Bootstrapping procedure, and (d) a Bayesian bootstrap procedure. The methods were compared against four criteria including (a) coverage probability, (b) coverage error, (c) average interval width, and (d) the lower and upper error probability. The results of each method were also compared with a classical procedure for computing the confidence interval based on normal curve theory. In addition, Student evaluations of teaching effectiveness (SET) ratings from all courses taught during one semester at Brigham Young University were analyzed using multilevel generalizability theory to estimate variance components and to estimate the reliability of the class means as a function of the number of respondents in each class. The results showed that the logit transformation procedure outperformed the alternative methods. The results also showed that the reliability of the class means exceeded .80 for classes averaging 15 respondents or more. The study demonstrates the need to routinely report a margin of error associated with the mean SET rating for each class and recommends that a confidence interval based on the logit transformation procedure be used for this purpose.