On the power of the t-test and some rank tests when outliers may be present

The power of some rank tests, used for testing the hypothesis of shift, is found when the underlying distributions contain outliers. The outliers are assumed to occur as the result of mixing two normal distributions with common variance. A small sample case shows how the scores for the rank tests are found and the exact power is computed for each of these rank tests. A Monte Carlo study provides an estimate of the power of the usual two sample t-test.     

A control chart for variance based on squared ranks

A nonparametric control chart for variance is proposed. The chart is constructed following the change-point approach through the recursive use of the squared ranks test for variance. It is capable of detecting changes in the behaviour of individual observations with performance similar to a self-starting CUSUM chart for scale when normality is assumed, and a relatively better power when assessing nonnormal observations. A comparison is also made with two equivalent nonparametric charts based on Mood and Ansari-Bradley statistics. When dealing with symmetrical distributions, the proposed chart shows smaller (better) out-of-control average run length (ARL), and a competing performance otherwise. In addition, sensitivity to changes in mean and variance at the same time was tested. Extensive Monte Carlo simulation was used to measure performance, and a practical example is provided to illustrate how the proposed control chart can be implemented in practice.     

Hormone profiles,body mass index and aging male symptoms: results of the Androx Vienna Municipality study

Aging in the male is accompanied by steroid hormonal decline, and men may develop symptoms associated with hypogonadism. Increased awareness of ‘andropause’ in recent years has led to greater demand for hormonal assessments, resulting in a rising burden for health economics. We conducted a cross-sectional study to define men at risk for hypogonadism, in whom further hormonal investigation should be performed.

We examined 664 blue-collar workers aged 40–60 years at their workplace and determined hormonal status and body mass index (BMI). Men with an abnormal urogenital status and those on medication that might affect endocrine status were excluded from the study. All participants completed the validated Aging Male Symptom (AMS) questionnaire and obtained scores for psychological symptoms, somatovegetative symptoms, and sexual symptoms.

Multiple logistic regression analyses revealed a significantly increased risk (represented by the odds ratio) of psychological symptoms for men with low levels of testosterone and/or bioavailable testosterone (BAT). Increased BMI as well as low testosterone levels and/or low BAT levels raised the risk of somatovegetative symptoms. Each decrease of BAT by 1?ng/ml caused an approximately 1.8-fold increase of the risk (odds ratio?=?1.832, p?=?0.005). Additional independent risk factors were increased age and low luteinizing hormone (LH) level. Men aged 55 years with BMI >?28?kg/m² and with somatovegetative symptoms and moderate or severe psychological symptoms had a 7.2-fold increase in the risk of a BAT level <?1.5?ng/ml compared to men without these risk factors (p <?0.001). Sensitivity and specificity were 75% and 71%, respectively.

The AMS score combined with age and BMI provides an easy and convenient method to identify men with probable androgen deficiency who require hormonal assessment.     

Step-Up: Promoting Youth Mental Health and Development in Inner-City High Schools

African American and Latino youth who reside in inner-city communities are at heightened risk for compromised mental health, as their neighborhoods are too often associated with serious stressors, including elevated rates of poverty, substance abuse, community violence, as well as scarce youth-supportive resources, and mental health care options. Many aspects of disadvantaged urban contexts have the potential to thwart successful youth development. Adolescents with elevated mental health needs may experience impaired judgment, poor problem-solving skills, and conflictual interpersonal relationships, resulting in unsafe sexual behavior and drug use. However, mental health services are frequently avoided by urban adolescents who could gain substantial benefit from care. Thus, the development of culturally sensitive, contextually relevant and effective services for urban, low-income African American and Latino adolescents is critical. Given the complexity of the mental health and social needs of urban youth, novel approaches to service delivery may need to consider individual (i.e., motivation to succeed in the future), family (i.e., adult support within and outside of the family), and community-level (i.e., work and school opportunities) clinical components. Step-Up, a high school-based mental health service delivery model has been developed to bolster key family, youth and school processes related to youth mental health and positive youth development. Step-Up (1) intervenes with urban minority adolescents across inner-city ecological domains; (2) addresses multiple levels (school, family and community) in order to target youth mental health difficulties; and (3) provides opportunities for increasing youth social problem-solving and life skills. Further, Step-Up integrates existing theory-driven, evidence-based interventions. This article describes Step-Up clinical goals, theoretical influences, as well as components and key features, and presents preliminary data on youth engagement for two cohorts of students.     

A distribution-free approach to inducing rank correlation among input variables

A method for inducing a desired rank correlation matrix on a multivariate input random variable for use in a simulation study is introduced in this paper. This method is simple to use, is distribution free, preserves the exact form of the marginal distributions on the input variables, and may be used with any type of sampling scheme for which correlation of input variables is a meaningful concept. A Monte Carlo study provides an estimate of the bias and variability associated with the method. Input variables used in a model for study of geologic disposal of radioactive waste provide an example of the usefulness of this procedure. A textbook example shows how the output may be affected by the method presented in this paper.     

The rank transformation as a method of discrimination with some examples

The procedure of statistical discrimination Is simple in theory but so simple in practice. An observation x₀possibly uiultivariate, is to be classified into one of several populations π₁,…,π_k which have respectively, the density functions f₁(x), ? ? ? , f_k(x). The decision procedure is to evaluate each density function at X₀ to see which function gives the largest value f_i(X₀) , and then to declare that X₀ belongs to the population corresponding to the largest value. If these den-sities can be assumed to be normal with equal covariance matricesthen the decision procedure is known as Fisher’s linear discrimi-nant function (LDF) method. In the case of unequal covariance matrices the procedure is called the quadratic discriminant func-tion (QDF) method. If the densities cannot be assumed to be nor-mal then the LDF and QDF might not perform well. Several different procedures have appeared in the literature which offer discriminant procedures for nonnormal data. However, these pro-cedures are generally difficult to use and are not readily available as canned statistical programs.

Another approach to discriminant analysis is to use some sortof mathematical trans format ion on the samples so that their distribution function is approximately normal, and then use the convenient LDF and QDF methods. One transformation that:applies to all distributions equally well is the rank transformation. The result of this transformation is that a very simple and easy to use procedure is made available. This procedure is quite robust as is evidenced by comparisons of the rank transform results with several published simulation studies.     

Small sample sensitivity analysis techniques for computer models.with an application to risk assessment

As modeling efforts expand to a broader spectrum of areas the amount of computer time required to exercise the corresponding computer codes has become quite costly (several hours for a single run is not uncommon). This costly process can be directly tied to the complexity of the modeling and to the large number of input variables (often numbering in the hundreds) Further, the complexity of the modeling (usually involving systems of differential equations) makes the relationships among the input variables not mathematically tractable. In this setting it is desired to perform sensitivity studies of the input-output relationships. Hence, a judicious selection procedure for the choic of values of input variables is required, Latin hypercube sampling has been shown to work well on this type of problem.

However, a variety of situations require that decisions and judgments be made in the face of uncertainty. The source of this uncertainty may be lack ul knowledge about probability distributions associated with input variables, or about different hypothesized future conditions, or may be present as a result of different strategies associated with a decision making process In this paper a generalization of Latin hypercube sampling is given that allows these areas to be investigated without making additional computer runs. In particular it is shown how weights associated with Latin hypercube input vectors may be rhangpd to reflect different probability distribution assumptions on key input variables and yet provide: an unbiased estimate of the cumulative distribution function of the output variable. This allows for different distribution assumptions on input variables to be studied without additional computer runs and without fitting a response surface. In addition these same weights can be used in a modified nonparametric Friedman test to compare treatments, Sample size requirements needed to apply the results of the work are also considered. The procedures presented in this paper are illustrated using a model associated with the risk assessment of geologic disposal of radioactive waste.