Abstracts for Published Methodological Works

To describe circadian blood pressure (BP) patterns and linear interdialytic changes, a model was developed to describe
simultaneously both the straight line change and oscillatory variation in BP and heart rate over an interdialytic interval in 
hemodialysis patients. Using this trended cosinor model, we simultaneously compared the impact of mean level of BP, 
linear changes over the interdialytic interval, and oscillatory changes in BP and its relationship with antihypertensive drug 
use. Neither a straight-line change model nor the cosinor model adequately described the BP variability in 12 750 BP 
measurements from 136 chronic stable hemodialysis patients. A combination of the 2 models that allowed for the oscillatory 
rhythmic pattern in BP variation to have an upward trend in the interdialytic period most accurately described the data. Time 
elapsed since the end of dialysis demonstrated a better model fit compared with the less meaningful clock time. More 
antihypertensive medication use was associated with increasing mean systolic, diastolic, and pulse pressure. Although the 
rate of change was blunted with increasing antihypertensive drug use, the impact on oscillatory change was U-shaped for 
systolic BP, direct for diastolic BP, and inverse for pulse pressure. A trended cosinor model better describes the change in 
BP in the interdialytic interval in hemodialysis patients, especially when time elapsed is measured from the end of dialysis. 
Antihypertensive drugs, though associated with higher average BP, are associated with blunted rate of change in BP over time.

The behavioral, educational, and social sciences are undergoing a paradigmatic shift in methodology, from disciplines 
that focus on the dichotomous outcome of null hypothesis significance tests to disciplines that report and interpret 
effect sizes and their corresponding confidence intervals. Due to the arbitrariness of many measurement instruments 
used in the behavioral, educational, and social sciences, some of the most widely reported effect sizes are
standardized. Although forming confidence intervals for standardized effect sizes can be very beneficial, such confidence
interval procedures are generally difficult to implement because they depend on noncentral  t, F, and chi-square distributions. 
At present, no main-stream statistical package provides exact confidence intervals for standardized effects without the use 
of specialized programming scripts. Methods for the Behavioral, Educational, and Social Sciences (MBESS) is an R package 
that has routines for calculating confidence intervals for noncentral t, F, and chi-square distributions, which are then used in
the calculation of exact confidence intervals for standardized effect sizes by using the confidence interval transformation and
inversion principles. The present article discusses the way in which confidence intervals are formed for standardized effect
sizes and illustrates how such confidence intervals can be easily formed using MBESS in R.

Methods for planning sample size (SS) for the standardized mean difference so that a narrow confidence interval (CI)
can be obtained via the accuracy in parameter estimation (AIPE) approach are developed. One method plans SS so 
that the expected width of the CI is sufficiently narrow. A modification adjusts the SS so that the obtained CI is no wider
than desired with some specified degree of certainty (e.g., 99% certain the 95% CI will be no wider than omega). The
rationale of the AIPE approach to SS planning is given, as is a discussion of the analytic approach to CI formation for
the population standardized mean difference. Tables with values of necessary SS are provided. The freely available
Methods for the Behavioral, Educational, and Social Sciences (K. Kelley, 2006a) R (R Development Core Team, 2006)
software package easily implements the methods discussed.

The standardized group mean difference, Cohen’s d, is among the most commonly used and intuitively appealing
effect sizes for group comparisons. However, reporting this point estimate alone does not reflect the extent to which
sampling error may have led to an obtained value. A confidence interval expresses the uncertainty that exists between
d and the population value, , it represents. A set of Monte Carlo simulations was conducted to examine the integrity
of a noncentral approach analogous to that given by Steiger and Fouladi, as well as two bootstrap approaches in
situations in which the normality assumption is violated. Because d is positively biased, a procedure given by Hedges
and Olkin is outlined, such that an unbiased estimate of can be obtained. The bias-corrected and accelerated bootstrap
confidence interval using the unbiased estimate of is proposed and recommended for general use, especially in cases
in which the assumption of normality may be violated.

Applications of multidimensional scaling often make the assumption of symmetry for the population matrix of proximity
measures. Although the likelihood of such an assumption holding true varies from one area of research to another, formal
assessment of such an assumption has received little attention. The present article develops a nonparametric procedure
that can be used in a confirmatory fashion or in an exploratory fashion in order to probabilistically assess the assumption
of population symmetry for the proximity measures in a multidimensional scaling context. The proposed procedure makes
use of the bootstrap technique and alleviates the assumptions of parametric statistical procedures. Computer code for R
and S-Plus is included in an appendix.

Sample size for multiple regression: Obtaining regression coefficients that are 
accurate, not simply significant (Kelley & Maxwell, 2003)

An approach to sample size planning for multiple regression is presented that emphasizes accuracy in parameter
estimation (AIPE). The AIPE approach yields precise estimates of population parameters by providing necessary
sample sizes in order for the likely widths of confidence intervals to be sufficiently narrow. One AIPE method yields
a sample size such that the expected width of the confidence interval around the standardized population regression
coefficient is equal to the width specified. An enhanced formulation ensures, with some stipulated probability, that the
width of the confidence interval will be no larger than the width specified. Issues involving standardized regression
coefficients and random predictors are discussed, as are the philosophical differences between AIPE and the power
analytic approaches to sample size planning.

Obtaining Power or Obtaining Precision: Delineating Methods of Sample-Size 
Planning Kelley, Maxwell, & Rausch (2003)

Sample-size planning historically has been approached from a power analytic perspective in order to have some
reasonable probability of correctly rejecting the null hypothesis. Another approach that is not as well-known is one
that emphasizes accuracy in parameter estimation (AIPE). From the AIPE perspective, sample size is chosen such
that the expected width of a confidence interval will be sufficiently narrow. The rationales of both approaches are delineated
and two procedures are given for estimating the sample size from the AIPE perspective for a two-group mean comparison.
One method yields the required sample size, such that the expected width of the computed confidence interval will be the 
value specified. A modification allows for a defined degree of probabilistic assurance that the width of the computed
confidence interval will be no larger than specified. The authors emphasize that the correct conceptualization of sample-size
planning depends on the research questions and particular goals of the study.

Analytic methods for questions pertaining to a randomized pretest, posttest, 
follow-up design (Rausch, Maxwell, & Kelley, 2003)

Delineates 5 questions regarding group differences that are likely to be of interest to researchers within the framework
of a randomized pretest, posttest, follow-up (PPF) design. These 5 questions are examined from a methodological
perspective by comparing and discussing analysis of variance (ANOVA) and analysis of covariance (ANCOVA) methods
and briefly discussing hierarchical linear modeling (HLM) for these questions. This article demonstrates that the pretest
should be utilized as a covariate in the model rather than as a level of the time factor or as part of the dependent variable
within the analysis of group differences. It is also demonstrated that how the posttest and the follow-up are utilized in the
analysis of group differences is determined by the specific question asked by the researcher.