Statistical methodology (45)
Chair: Wilco Emons, Thursday 23rd July, 11.30 - 12.50, Uppercroft, School of Pythagoras.
Luisa Canal, Department of Cognitive and Educational Sciences, Rovereto, Italy. Statistical analysis of interval data. Tuning up the uncertainty. (121)
Michael Smithson, Department of Psychology, The Australian National University, Canberra, Australia. Heterogeneity of variance distorts moderator effects. (013)
Gerard van Breukelen, Department of Methodology and Statistics, Maastricht University, The Netherlands. ANCOVA versus change from baseline in non-randomized studies: The true difference. (073)
Hao Luo, Department of Information Science, Division of Statistics, Uppsala University, Sweden. A simulation study of Fleishman’s power method for generating non-normal samples. (064) ♥
ABSTRACTS
Statistical analysis of interval data: Tuning up the uncertainty. (121)
Luisa Canal
Information collected in behavioral sciences usually consists of single-valued numerical variables. However many phenomena are measured by intervals. Such interval-data naturally arise in different circumstances. Sometimes intervals are generated in the framework of repeated measurements when one variable can be coded in an interval using the lowest and the highest registered measure (for example in stock markets or in air pollution data). In other cases intervals arise from a couple of variables complementary with respect to a given concept (expected and perceived safety). Imprecise measurements also generate interval data through the error associated with a physical measure or the uncertainty associated with sampling from a given population. Historically, an arithmetic for interval data was introduced to deal with computer representation of real numbers with floating point numbers and more recently some statistical approaches to deal with interval data have been proposed. An alternative approach will be presented, based on a numerical structure X = (x,e) where x is the centre and e is the spread. Two scalar indices are associated with X, both involving a free parameter for fine-tuning of the uncertainty. Statistical methods for this kind of intervals will be presented and discussed.
Heterogeneity of variance distorts moderator effects. (013)
Michael Smithson
Under homogeneity of variance, moderation of correlation implies moderation of both the covariance and regression coefficients (or means, in ANOVA), and vice versa. Heterogeneity of variance (HeV), however, can distort moderator effects so that neither covariance, correlation, nor regression coefficients provide an accurate picture of moderation. We may have apparent moderation of slopes, for instance, without moderation of correlations or covariances, apparent moderation of covariances with no moderation of slopes or correlations, or even apparent moderation of regression coefficients in opposite directions. Conventional methods of dealing with HeV are not generally effective, especially if there is HeV in predictors as well as the dependent variable. A framework is presented for understanding the impact of HeV on moderator effects, and for analyzing moderators in relatively simple models under HeV. A structural equations model approach for categorical moderators is presented that enables researchers to simultaneously model apparent moderation of slopes, correlations, and covariances. This is followed by a GLM that decomposes apparent moderator effects into false moderation due to HeV and actual moderation. Continuous moderators require a more complex approach, and two partial solutions for them are presented: A nonparametric exploratory data analysis via smoothed regression, and an extension of the GLM.
ANCOVA versus change from baseline in non-randomized studies: The true difference. (073)
Gerard van Breukelen
A treatment effect is inferred from the mean outcome difference between a treated and a control group. Data can be analyzed with ANCOVA or ANOVA of change from baseline. Other methods are equivalent to one of these two. In nonrandomized studies the two methods can give contradictory results (Lord’s ANCOVA paradox). Building on statistical literature, this paper shows why ANCOVA is best if treatment assignment is based on randomization or on the pretest, and worst for studies of pre-existing groups. By writing ANCOVA as a repeated measures model, ANCOVA is shown to assume absence of a group difference at pretest. Adjusting for measurement error leads back to unadjusted ANCOVA or ANOVA of change, depending on the assumed absence or presence of a true group difference at pretest. Both methods are the opposite extremes of a multilevel approach that treats groups as random instead of fixed, and so agreement between both methods is informative about the treatment effect. The difference between the methods is illustrated by two nonrandomized studies in which Lord’s paradox occurred. Practical advice is given for the design and analysis of nonrandomized studies.
A simulation study of Fleishman’s power method for generating non-normal samples. (064)
Hao Luo
Fleishman’s power method is one of the traditional methods used for generating non-normal random numbers. In this paper, we use Monte Carlo simulation to test the applicability of this method. Specially, we assess the performance of the method under different conditions. The power of the normality test statistics proposed by D’Agostino (1986) is studied based on the generated samples. The results suggest that Fleishman’s method has difficulties on generating non-normal samples with higher levels of skewness/kurtosis. The effect of sample size is found to be significant on the reliability of the data generation. When it comes to the power study, a considerable impact of sample size is also observed on obtaining a trustworthy test decision.