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As in other social sciences, published findings in consumer research tend to overestimate the size of the effect being investigated, due to both file drawer effects and abuse of researcher degrees of freedom, including opportunistic analysis decisions. Given that most effect sizes are substantially smaller than would be apparent from published research, there has been a widespread call to increase power by increasing sample size. We propose that, aside from increasing sample size, researchers can also increase power by boosting the effect size. If done correctly, removing participants, using covariates, and optimizing experimental designs, stimuli, and measures can boost effect size without inflating researcher degrees of freedom. In fact, careful planning of studies and analyses to maximize effect size is essential to be able to study many psychologically interesting phenomena when massive sample sizes are not feasible.

Background Randomized pre-post designs, with outcomes measured at baseline and after treatment, have been commonly used to compare the clinical effectiveness of two competing treatments. There are vast, but often conflicting, amount of information in current literature about the best analytic methods for pre-post designs. It is challenging for applied researchers to make an informed choice. Methods We discuss six methods commonly used in literature: one way analysis of variance (“ ANOVA” ) , analysis of covariance main effect and interaction models on the post-treatment score (“ ANCOVA I ” and “ ANCOVA II ”), ANOVA on the change score between the baseline and post-treatment scores (“ ANOVA-Change ”), repeated measures (“ RM” ) and constrained repeated measures (“ cRM” ) models on the baseline and post-treatment scores as joint outcomes. We review a number of study endpoints in randomized pre-post designs and identify the mean difference in the post-treatment score as the common treatment effect that all six methods target. We delineate the underlying differences and connections between these competing methods in homogeneous and heterogeneous study populations. Results ANCOVA and cRM outperform other alternative methods because their treatment effect estimators have the smallest variances. cRM has comparable performance to ANCOVA I in the homogeneous scenario and to ANCOVA II in the heterogeneous scenario. In spite of that, ANCOVA has several advantages over cRM: i) the baseline score is adjusted as covariate because it is not an outcome by definition; ii) it is very convenient to incorporate other baseline variables and easy to handle complex heteroscedasticity patterns in a linear regression framework. Conclusions ANCOVA is a simple and the most efficient approach for analyzing pre-post randomized designs.

The stepped wedge design is increasingly being used in cluster randomized trials (CRTs). However, there is not much information available about the design and analysis strategies for these kinds of trials. Approaches to sample size and power calculations have been provided, but a simple sample size formula is lacking. Therefore, our aim is to provide a sample size formula for cluster randomized stepped wedge designs. We derived a design effect (sample size correction factor) that can be used to estimate the required sample size for stepped wedge designs. Furthermore, we compared the required sample size for the stepped wedge design with a parallel group and analysis of covariance (ANCOVA) design. Our formula corrects for clustering as well as for the design. Apart from the cluster size and intracluster correlation, the design effect depends on choices of the number of steps, the number of baseline measurements, and the number of measurements between steps. The stepped wedge design requires a substantial smaller sample size than a parallel group and ANCOVA design. For CRTs, the stepped wedge design is far more efficient than the parallel group and ANCOVA design in terms of sample size.

Normal log lengths in Norway are 3–6 m (NL), but occasionally there is a demand for short timber with a 2.5 m log length (ST). There are concerns that ST could reduce the forwarders' productivity. Six type stands were created based on harvester data. Different assortment distributions, conditions, and forwarders were simulated in each type stand. It was found that an additional ST assortment almost always decreased productivity (from –15.5 to +4%). Increased forwarding distance (m), more difficult driving conditions, and increased log concentration [m3·(100 m strip road)–1] decreased the productivity difference between sites with ST and NL and sites with only NL. Increased forwarder size increased the productivity difference between sites with ST and NL and sites with only NL. It is possible to load two stacks of ST on some forwarders. Such loading was more productive than loading one stack on longer forwarding distances, while the opposite was the case on short distances. However, loading two stacks of ST can lead to overloading.

Background Hypertension is one of the major causes of many diseases, such as heart attack, strokes, kidney failure, and many internal disorders. This presentresearch study aimed to investigate the impact of educational programs based on the health belief model to promote hypertension prevention behavior of Iran University of Medical Sciences staff. Methods This study has incorporated pretest-posttest quasi-experimental based on 128 staff members and randomly assigned the recruited and involved participants to an intervention ( n  = 64) and a control group (n = 64). The data collection tool was based on a questionnaire related to health belief model constructs based on 42 questions. The study interpreted the results using ANCOVA and robust ANCOVA as suitable approaches. Results ANCOVA showed improvement in the cues to participants’ action following educational interventional ( p  = 0.011). the robust ANCOVA specified that the intervention was successful for participants with low to moderate initial levels of knowledge, perceived susceptibility, perceived severity, perceived barriers, and self-efficacy scores. The levels of these components did not change in participants with very high baseline scores. Compared to a control group, regardless of baseline score, the perceived benefits and practice (behavior) of participants at the intervention group were improved significantly ( P  <  0.05). Conclusion This current study specified that the education-based health belief model effectively promotes hypertension preventive behaviors among Iran University of Medical Sciences staff.

Phylogenetic generalized least squares (PGLS) has become one of the most commonly used phylogenetic comparative methods. Despite its common use, descriptions, and applications of methods to test for species' deviations from allometric predictions using phylogenetic regression have been piecemeal. We simplify previous computational descriptions of PGLS standard errors in a manner that can be easily generalized toward more complex general linear models. We focus on the implementation of phylogenetic analysis of covariance, which provides a direct test for the equality of intercepts and slopes. Our computational descriptions allow testing whether individual species, or a group of species, deviate significantly from allometric predictions. The use of PGLS confidence and prediction intervals and phylogenetic analysis of covariance is exemplified in an analysis of brain structure volumes in primates.

Background When using a continuous outcome measure in a randomised controlled trial (RCT), the baseline score should be measured in addition to the post-intervention score, and it should be analysed using the appropriate statistical analysis. Methods We derive the correlation between the change score and baseline score and show that there is always a correlation (usually negative) between the change score and baseline score. We discuss the following correlations and provide the mathematical derivations in the Appendix: Correlation between change score and baseline score Correlation between change score and post score Correlation between change score and average score. The setting here is a parallel, two-arm RCT, but the method discussed in this paper is applicable for any studies or trials that have a continuous outcome measure; it is not restricted to RCTs. Results We show that using the change score as the outcome measure does not address the problem of regression to the mean, nor does it take account of the baseline imbalance. Whether the outcome is change score or post score, one should always adjust for baseline using analysis of covariance (ANCOVA); otherwise, the estimated treat effect may be biased. We show that these correlations also apply when comparing two measurement methods using Bland-Altman plots. Conclusions The correlation between baseline and post-intervention scores can be derived using the variance sum law. We can then use the derived correlation to calculate the required sample size in the design stage. Baseline imbalance may occur in RCTs, and ANCOVA should be used to adjust for baseline in the analysis stage.

Adjustment for baseline covariates in randomized trials has been shown to lead to gains in power and can protect against chance imbalances in covariates. For continuous covariates, there is a risk that the the form of the relationship between the covariate and outcome is misspecified when taking an adjusted approach. Using a simulation study focusing on individually randomized trials with small sample sizes, we explore whether a range of adjustment methods are robust to misspecification, either in the covariate–outcome relationship or through an omitted covariate–treatment interaction. Specifically, we aim to identify potential settings where G-computation, inverse probability of treatment weighting (IPTW), augmented inverse probability of treatment weighting (AIPTW) and targeted maximum likelihood estimation (TMLE) offer improvement over the commonly used analysis of covariance (ANCOVA). Our simulations show that all adjustment methods are generally robust to model misspecification if adjusting for a few covariates, sample size is 100 or larger, and there are no covariate–treatment interactions. When there is a non-linear interaction of treatment with a skewed covariate and sample size is small, all adjustment methods can suffer from bias; however, methods that allow for interactions (such as G-computation with interaction and IPTW) show improved results compared to ANCOVA. When there are a high number of covariates to adjust for, ANCOVA retains good properties while other methods suffer from under- or over-coverage. An outstanding issue for G-computation, IPTW and AIPTW in small samples is that standard errors are underestimated; they should be used with caution without the availability of small-sample corrections, development of which is needed. These findings are relevant for covariate adjustment in interim analyses of larger trials.

ObjectiveThe statistical analysis for a 2-arm randomised controlled trial (RCT) with a baseline outcome followed by a few assessments at fixed follow-up times typically invokes traditional analytic methods (eg, analysis of covariance (ANCOVA), longitudinal data analysis (LDA)). ‘Constrained’ longitudinal data analysis (cLDA) is a well-established unconditional technique that constrains means of baseline to be equal between arms. We use an analysis of fasting lipid profiles from the Group Medical Clinics (GMC) longitudinal RCT on patients with diabetes to illustrate applications of ANCOVA, LDA and cLDA to demonstrate theoretical concepts of these methods including the impact of missing data.MethodsFor the analysis of the illustrated example, all models were fit using linear mixed models to participants with only complete data and to participants using all available data.ResultsWith complete data (n=195), 95% CI coverage are equivalent for ANCOVA and cLDA with an estimated 11.2 mg/dL (95% CI −19.2 to −3.3; p=0.006) lower mean low-density lipoprotein (LDL) cholesterol in GMC compared with usual care. With all available data (n=233), applying the cLDA model yielded an LDL improvement of 8.9 mg/dL (95% CI −16.7 to −1.0; p=0.03) for GMC compared with usual care. The less efficient, LDA analysis yielded an LDL improvement of 7.2 mg/dL (95% CI −17.2 to 2.8; p=0.15) for GMC compared with usual care.ConclusionsUnder reasonable missing data assumptions, cLDA will yield efficient treatment effect estimates and robust inferential statistics. It may be regarded as the method of choice over ANCOVA and LDA.

For inferring a treatment effect from the difference between a treated and untreated group on a quantitative outcome measured before and after treatment, current methods are analysis of covariance (ANCOVA) of the outcome with the baseline as covariate, and analysis of variance (ANOVA) of change from baseline. This article compares both methods on power and bias, for randomized and nonrandomized studies. The methods are compared by writing both as a regression model and as a repeated measures model, and are applied to a nonrandomized study of preventing depression. In randomized studies both methods are unbiased, but ANCOVA has more power. If treatment assignment is based on the baseline, only ANCOVA is unbiased. In nonrandomized studies with preexisting groups differing at baseline, the two methods cannot both be unbiased, and may contradict each other. In the study of depression, ANCOVA suggests absence, but ANOVA of change suggests presence, of a treatment effect. The methods differ because ANCOVA assumes absence of a baseline difference. In randomized studies and studies with treatment assignment depending on the baseline, ANCOVA must be used. In nonrandomized studies of preexisting groups, ANOVA of change seems less biased than ANCOVA, but two control groups and two baseline measurements are recommended.