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BACKGROUND AND PURPOSE The role of apparent diffusion coefficient (ADC) for preoperative grading and treatment planning of high-grade gliomas (HGG) is still debated since the assumption of inverse correlation between ADC and cellularity is not completely coherent with the results of some studies. It has been recently hypothesized that restricted diffusivity in HGG may be related to hypoxic/ischemic changes inside the tumor. We therefore investigated the differences of ADC values between areas with magnetic resonance spectroscopy (MRS) markers of hypoxia and necrosis (lactate and lipid compounds) and regions with lack of both metabolites. METHODS The MRS datasets and the corresponding ADC maps of 28 patients with HGG were retrospectively reviewed. Circular regions of interest (ROIs) were placed on ADC maps by means of spectral characteristics, considering the solid portions of gliomas. One-way ANOVA or Welch test were performed for multiple comparison of the Mean ADC, minimum ADC (minADC), and standard deviation of pixel-by-pixel ADC measurements (ADC SD) values among the groups of ROIs with lactate, lipids, and lack of both metabolites (LAC, LIP, and NEG group, respectively). RESULTS The minADC values in LAC group (908 ± 161 × 10−6 mm2s−1) were found to be significantly (P = .03) higher than in NEG group (792 ± 122 × 10−6 mm2s−1). We did not find other significant differences by the multiple comparison tests. CONCLUSIONS HGG areas with MRS markers of hypoxia and necrosis are not associated with restricted diffusivity. To explain the trend to diffusion facilitation in HGG lactate-expressing regions, we hypothesize a possible hypoxia-induced volume reduction of glioma cells with extracellular shift of cytoplasmic water.

Recently, CRESSIE and WHITFORD (1986) showed that Welch's test of H0 :μ1 = μ2 can be biased, under nonnormality, where μ1 and μ2 are the means of two independent treatment groups. They suggested, therefore, that a two-sample analog of Johnson's test be used instead. One goal in this paper is to examine the extent to which a two-sample analog of Johnson's test improves upon Welch's technique in terms of Type I errors and power when sample sizes are small or moderately large. Several alternative procedures are also considered including an additional modification of Johnson's procedure, a procedure suggested by DUNNETT (1982) that uses Tiku's modified maximum likelihood estimate with 10% trimming, two versions of Efron's bootstrap, and a test recently proposed by WILCOX (1989). The paper also describes situations where Welch's procedure is not robust in terms of Type I errors. This is important because based on results currently available, Welch's procedure is thought to be nonrobust in terms of power, but robust in terms of Type I errors.

Guenther derived a simple formula for the accurate computation of equal sample sizes when the two-sample t-test with pooled variance estimate is used. In the present paper, the Guenther formula is generalized to the case of unequal sample sizes. In addition, the case of unequal variances is considered.

The comparison of the unknown means of two populations with unknown variances is called the Behrens-Fisher problem, if the populations are assumed to be normal and the ratio of the variances is not known. In this paper a summary of recipes is given to solve this problem in practice, as published in the past 35 years by Banerjee, Fisher and Behrens, Pagurova, Wald and Hajek, Welch, Welch and Aspin, together with two large sample solutions and one solution often used as an approximate one without justification. The solutions are presented mainly in terms of confidence intervals for the difference of the population means. Some remarks are made concerning the lengths of these intervals and the power of the corresponding tests. The solutions in this paper are dependent on the means and the variances of samples drawn from the two populations only. All solutions discussed, except the disqualified approximate one, are robust against violations of the normality assumptions with respect to the populations and they provide, at least asymptotically, good measures for the difference of the population means if the samples are drawn from populations whatsoever with finite second moment.

By using Monte Carlo studies, this paper compares the Welch test, the James test and the Brown-Forsythe test for comparing several means under heteroscedasticity. It appears that all the tests are quite robust with respect to departure from normality. The Brown-Forsythe test is at least as good as the James test and the Welch test; but the differences are so small that the choice is immaterial for practical purposes.