Increasing physicians' awareness of the impact of statistics on research outcomes: comparative power of the t-test and and Wilcoxon Rank-Sum test in small samples applied research.

To effectively evaluate medical literature, practicing physicians and medical researchers must understand the impact of statistical tests on research outcomes. Applying inefficient statistics not only increases the need for resources, but more importantly increases the probability of committing a Type I or Type II error. The t-test is one of the most prevalent tests used in the medical field and is the uniformally most powerful unbiased test (UMPU) under normal curve theory. But does it maintain its UMPU properties when assumptions of normality are violated? A Monte Carlo investigation evaluates the comparative power of the independent samples t-test and its nonparametric counterpart, the Wilcoxon Rank-Sum (WRS) test, to violations from population normality, using three commonly occurring distributions and small sample sizes. The t-test was more powerful under relatively symmetric distributions, although the magnitude of the differences was moderate. Under distributions with extreme skews, the WRS held large power advantages. When distributions consist of heavier tails or extreme skews, the WRS should be the test of choice. In turn, when population characteristics are unknown, the WRS is recommended, based on the magnitude of these power differences in extreme skews, and the modest variation in symmetric distributions.

Power of the independent samples t test under a prevalent psychometric measure distribution.

Studies in psychology often have low power because of inadequate sample size. Thus, recent articles in this journal have suggested making sample size determinations through readily available tables that are based on population normality. Questions have been raised on the use of these power tables because prevalent psychometric distributions, such as the discrete mass at zero with gap that occurs with first use or onset variables, are radically nonnormal. In addition to demonstrating the robustness of the independent samples t test with respect to type I error, the major finding of this study shows that researchers may use these power tables without modification for this radically nonnormal distribution.

Maternal employment and early adolescent substance use.

Research stimulated by increases in maternal employment has focused primarily on children, even though mothers of adolescents are more likely to be employed. It is adolescents who experience developmental changes that promote participation in adult behaviors in advance of their abilities. This study investigated the effects of maternal employment on the use of alcohol, cigarettes, marijuana, and other substances by early adolescents. A sample of ninth-grade students responded to a 48-item survey about their substance use behavior. A comparison of maternal employment patterns (full-time vs. part-time/not employed outside the home) indicated no significant differences in substance use behavior. These results confirmed and extended the growing literature regarding the nonharmful effects of maternal employment on adolescent adjustment and behavior.

Locus of control, self-concept, and self-esteem among at-risk African-American adolescents.

The purpose of this study was to add to the sparse but growing descriptive data on at-risk African-American adolescents along the dimensions of locus of control, self-concept, and self-esteem. This study will assist professionals in better understanding the boundaries between normal and abnormal psychological profiles among adolescents, particularly on instruments which are widely used in psychology research and clinical and educational practice. Participants were 117 students from a large, urban Midwestern city in an ongoing intervention program with adolescents who were at-risk of dropping out of school because of academic underachievement and whose family's incomes were below the poverty line. Descriptive results and comparisons with data on other at-risk samples are presented, along with multivariate analyses on the three constructs on the basis of gender. This study provides benchmarks for practitioners and researchers in interpreting the results of assessments using these instruments.

Review of the rank transform in designed experiments.

Despite a plethora of asymptotic and small samples Monte Carlo studies on the failure of the rank transform in designed experiments, Choi in 1998 published a paper praising the technique. The purpose of this reaction is to (a) examine Choi's literature review on the rank transform, (b) provide some "new" results on the rank transform, and (c) summarize the failures of the rank transform.

Perceived importance of self-determination factors by consumers in substance-abuse treatment.

40 consumers (20 from 1993 and 20 from 1994) were randomly selected from about 450 residents of a midwestern urban free-standing residential substance-abuse treatment facility to participate in a study on factors relating to self-determination. Self-confidence, positive attitude, listening skills, and assuming responsibility were identified in both years as the most important factors. Role models, however, were not reported as being important.

Multidimensional differences between adolescent substance abusers and users.

High-school-aged adolescents responded to a 48-item survey about their substance use. From an original sample of 190 respondents, groups were created through consequence variables (e.g., school, family, medical, and legal problems) into abuse (n = 41) and use (n = 115) categories. Variables were organized along multidimensional lines: stimulus (e.g., frequency of substance use, use in school), organismic (e.g., age, grade), and response (e.g., driving a car while under the influence). From 27 comparisons of the abuse and use groups 16 significant differences emerged.

Externalization as a self-protective mechanism in a stigmatized group.

The Nowicki-Strickland measure of internal-external locus of control was administered to 110 African-American adolescents. Analysis indicated high externalization, even though these students had a higher than average self-concept.

Comparison of self-esteem scores: American and Indian adolescents.

The Coopersmith Self-esteem Inventory was administered to 112 African American adolescents who were academically at-risk for dropping out of high school. Results were similar to those of a previous study comparing a heterogeneous group of 100 American adolescents with 100 youths from India. Differences on scores of self-esteem for the two international groups were noted.

Comparison of two tests useful in situations where treatment is expected to increase variability relative to controls.

The type I error and power characteristics of the modified t test were compared with those of the generalized t test. Results suggested that, in contrast to the generalized t test, the modified t test can be seriously non-robust to departures from population normality, with such departures often producing anti-conservative results. Neither test held an absolute power advantage over the other when responses were from normal distributions, but the modified t test was generally more powerful for these conditions. In comparison with the pooled samples t test, both tests were usually much more efficient when treatment caused increases both in mean response and between-subject variance, and suffered only small disadvantages when between-subject variance was unchanged by treatment. Given these results and other considerations, recommendations for use of these recently devised tests are given.

A note on the operating characteristics of the modified F test.

Brownie, Boos, and Hughes-Oliver (1990, Biometrics 46, 259-266) suggested a modification to the fixed-effects analysis of variance (ANOVA) F test for use in situations where treatments are likely to affect mean response while simultaneously increasing between-subject variability. These authors suggest that the modified test (1) is robust against departures from population normality, (2) is more powerful than its classical counterpart when the expected alternative form is encountered, and (3) will suffer only minor power losses relative to the usual test when alternatives are in the form of simple shifts in location. This study shows that the modified test is not generally robust when sampling is from nonnormal distributions and is likely to produce unacceptably high Type I error inflations when sampling is from heavy-tailed or skewed distributions. Some power results are also provided for the multisample situation to supplement those of Brownie et al., who generated results only for the two-sample case.