The random effects ANOVA model plays an important role in many psychological studies, but the usual model suffers from at least two serious problems. The first is that even under normality, violating the assumption of equal variances can have serious consequences in terms of Type I errors or significance levels, and it can affect power as well. The second and perhaps more serious concern is that even slight departures from normality can result in a substantial loss of power when testing hypotheses. Jeyaratnam and Othman (1985) proposed a method for handling unequal variances, under the assumption of normality, but no results were given on how their procedure performs when distributions are nonnormal. A secondary goal in this paper is to address this issue via simulations. As will be seen, problems arise with both Type I errors and power. Another secondary goal is to provide new simulation results on the Rust-Fligner modification of the Kruskal-Wallis test. The primary goal is to propose a generalization of the usual random effects model based on trimmed means. The resulting test of no differences among J randomly sampled groups has certain advantages in terms of Type I errors, and it can yield substantial gains in power when distributions have heavy tails and outliers. This last feature is very important in applied work because recent investigations indicate that heavy-tailed distributions are common. Included is a suggestion for a heteroscedastic Winsorized analog of the usual intraclass correlation coefficient.

The intraclass correlation, ρ, is a parameter featured in much psychological research. Two commonly used estimators of ρ, the maximum likelihood and least squares estimators, are known to be negatively biased. Olkin and Pratt (1958) derived the minimum variance unbiased estimator of the intraclass correlation, but use of this estimator has apparently been impeded by the lack of a closed form solution. This note briefly reviews the unbiased estimator and gives a FORTRAN 77 subroutine to calculate it.

A family of coefficients of relational agreement for numerical scales is proposed. The theory is a generalization to multiple judges of the Zegers and ten Berge theory of association coefficients for two variables and is based on the premise that the choice of a coefficient depends on the scale type of the variables, defined by the class of admissible transformations. Coefficients of relational agreement that denote agreement with respect to empirically meaningful relationships are derived for absolute, ratio, interval, and additive scales. The proposed theory is compared to intraclass correlation, and it is shown that the coefficient of additivity is identical to one measure of intraclass correlation.

When the underlying distribution is discrete with a limited number of categories, methods for interval estimation of the intraclass correlation which assume normality are theoretically inadequate for use. On the basis of large sample theory, this paper develops an asymptotic closed-form interval estimate of the intraclass correlation for the case where there is a natural score associated with each category. This paper employs Monte Carlo simulation to demonstrate that when the underlying intraclass correlation is large, the traditional interval estimator which assumes normality can be misleading. We find that when the number of classes is ≥ 20, the interval estimator proposed here can generally perform reasonably well in a variety of situations. This paper further notes that the proposed interval estimator is invariant with respect to a linear transformation. When the data are on a nominal scale, an extension of the proposed method to account for this case, as well as a discussion on the relationship between the intraclass correlation and a kappa-type measure defined here and on the limitation of the corresponding kappa-type estimator are given.

In a recent article, Fagot proposed a generalized family of coefficients of relational agreement for multiple judges, focusing on the concept of empirically meaningful relationships. In this paper an ordinal coefficient of relational agreement, based on ranking data, is presented as a special case of the generalized family. It is shown that the proposed ordinal coefficient encompasses other ordinal coefficients, such as the Kendall coefficient of concordance, the average Spearman rank-order coefficient, and intraclass correlation based on ranks. It is also shown that the Kendall coefficient of concordance, corrected for chance agreement, is equivalent to the ordinal coefficient proposed in this paper.

Recent studies have focused on habitual intake without addressing meal-specific intakes. We aimed to identify meal-specific dietary patterns and their contribution to habitual dietary patterns. This cross-sectional study was conducted on 838 adults, both sexes who attended the health centres in Tehran. Dietary data were recorded by three 24-h dietary recalls (24hDR). Dietary patterns were identified by using principal component analysis on meal-specific and overall food intakes. Intraclass correlation (ICC) was used as a measurement of consistency across meals and days. Correlation analysis and linear regression (partial R 2) were used for meals contribution. Four habitual dietary patterns were derived from average dietary intake of 3-d 24hDR labelled as ‘Western’, ‘Healthy’, ‘Traditional’ and ‘Legume and broth’. Also, we identified two major dietary patterns on each meal level (factor 1 and 2 for breakfast, lunch, afternoon snack and dinner). The highest contribution of energy intake was observed in lunch (25·7 %), followed by dinner (20·81 %). Consistency of food groups was the highest across days (ICC tea = 0·58) and breakfasts (ICC tea = 0·60). Dinner had a strong correlation coefficient with the ‘Western’ habitual dietary pattern then followed by lunch. Similarly, dinner and lunch contributed the most (r and partial R 2) to the ‘Western’ habitual dietary pattern. Our results suggest that habitual dietary patterns to several extents are formed at meal levels, and dinner has a greater contribution to the habitual dietary patterns in Iranian people. This may help planning for local dietary guidelines according to the time of eating to promote public health.

Reliable and valid assessment of sports nutrition knowledge can inform athlete nutrition education to address knowledge gaps. This study aimed to test the reliability and validity of an electronically administered sports nutrition knowledge tool – Platform to Evaluate Athlete Knowledge of Sports Nutrition Questionnaire (PEAKS-NQ). A 94-item PEAKS-NQ was piloted to 149 developmental athletes (DA) in New Zealand, with a subset invited to complete the PEAKS-NQ again to assess reliability. Reliability was evaluated using sign test, intraclass correlation and Cronbach’s α. Accredited sports dietitians (ASD; n 255) completed the PEAKS-NQ to establish construct validity via known-groups methodology and provided relevance scores to determine the scale content validity index (S-CVI). Rasch analysis was conducted to identify potentially problematic items and test reliability. Score differences between DA and ASD were analysed using independent t or non-parametric tests. DA (n 88) were 17·8 (sd 1·4) years, 61·4 % female and mostly in high school (94·3 %). ASD (n 45) were 37·8 (sd 7·6) years, 82·2 % female, with >5 years of dietetic experience (59·1 %). ASD scored higher than DA in all sections and overall (91·5 (sd 3·4) v. 67·1 (sd 10·5) %) (P < 0·001). There were no differences between retests (n 18; P = 0·14). Cronbach’s α was 0·86. S-CVI indicated good content validity (0·88). Rasch analysis resulted in a fifty-item PEAKS-NQ with high item (0·91) and person (0·92) reliability. The PEAKS-NQ is reliable and valid for assessing sports nutrition knowledge which could assist practitioners effectively tailor and evaluate nutrition education.