In their article, Hutchins et al. (1) claim that, referring to Table 2, there were no significant differences in total, energy or carbohydrate intake between the control and the 10-g flaxseed feeding period. This is based on the ANOVA, which they used to compare the means.
The difficulty with the ANOVA is that it assumes that the variances of the normal distributions of the means being compared are equal, though unknown. Because there is no reason why unknown variances should be homogeneous, this is a source of error with the ANOVA. The SD are not equal, giving no reason why the variances should be expected to be equal. Thus, the ANOVA is not a generally valid method of comparing normal means with unknown variances. This has already been pointed out (2).
The problem of comparing the means of normal populations at exact significance levels (in the frequent sense) when their variances are unknown is the well-known Behrens-Fisher problem, and this has been solved by Tsakok (3). Using the software General Statistical Package, which implements the Tsakok technique, it is found that, between the control and the 10-g flaxseed feeding periods, there are significant differences in the intakes of energy (kcal) and carbohydrate (CHO, g) at 0.02 significance level (2 d.p.).
Another cause for suspicion arises from the use of a logarithmic scale to correct for non-normality in urinary lignan excretion analyses (1). No justification is given, and it is not generally true that a logarithmic scale can correct for non-normality. It is known that a multiplicative model can be transformed to a linear model through a logarithmic transformation, but that does not necessarily make it normally distributed. The original data should be made available for a correct analysis, using the article by Tsakok (4), which enable exact UMPU tests to be constructed to investigate non-normal data.
Thus, the conclusions of Hutchins et al. (1) need to be reassessed.
The Tsakok techniques are reprinted (5) with additional results.
Reply
We appreciate the comments by A. D. Tsakok on our paper in Cancer Epidemiology, Biomarkers & Prevention, 2000, 9: 1113–1118. This study used a crossover design, and so the ANOVA used repeated measures, not a two-sample comparison as in the Behrens-Fisher problem. Although the variances were unknown, they were quite close in size, and the ANOVA is known to be robust to minor differences in group SD. To answer the second question, several variables with skewed distributions were analyzed on the logarithmic scale, where the sample distributions were closer to the normal curve.
RSS Feeds