Summary Using the Lagrange multiplier procedure or score test on the Pearson family of distributions we obtain tests for normality of observations and regression disturbances. The tests suggested have optimum asymptotic power properties and good finite sample performance. Due to their simplicity they should prove to be useful tools in statistical analysis.

A test for normality of observations and regression residuals

The Analysis of Variance.

Guidelines for Canadian Drinking Water Quality

Statistical design and analysis of experiments , Statistical design and analysis of experiments , کتابخانه دیجیتال جندی شاپور اهواز

http://centlib.ajums.ac.ir//multiMediaFile/2224724-4-1.pdf

Statistical design and analysis of experiments

One of the most vexing of problems in data analysis is the determination of whether or not to discard some observations because they are inconsistent with the rest of the observations and/or the probability distribution assumed to be the underlying distribution of the data. One direction of research activity related to this problem is that of the study of robust statistical procedures (cf. Huber [1981]), primarily procedures for estimating population parameters which are insensitive to the effect of “outliers”, i.e., observations inconsistent with the assumed model of the random process generating the observations. Typically, the robust procedure involves some “trimming” or down-weighting procedure, wherein some fraction of the extreme observations are automatically eliminated or given less weight to guard against the potential effect of outliers.

Identification of Outliers

Several widely used tests for outlying observations are reviewed. Problems of repeated application and “masking” are described. Suggested as appropriate to over-come these problems are two new statistics: Lk which is based on the k largest (observed) values and Ek which is based on the k largest (in absolute value) residuals. Tables of approximate critical values for these statistics are given for 0.01, .025,0.05, and 0.10 levels of significance and for sample size n = 3 (1) 20 (5) 50.

Some Grubbs-Type Statistics for the Detection of Several Outliers

Mortality among 5,413 white males who were employed for at least two years at a plutonium weapons facility was investigated to measure risks from exposures to low levels of plutonium and external radiation. When compared with US death rates, fewer deaths than expected were found for all causes of death, all cancers, and lung cancer. No bone cancer was observed. An excess of brain tumors was found for the cohort in general. Elevated rate ratios for all causes of death and all lymphopoietic neoplasms were found when employees with plutonium body burdens greater than or equal to 2 nCi were compared with those with body burdens less than 2 nCi, while accounting for age, calendar period, and induction time. Increased rate ratios were also found for esophageal, stomach, colon, and prostate cancers, and for lymphosarcomas and reticulum cell sarcomas. No elevated rate ratios were noted for bone and liver cancers. When employees with cumulative exposures greater than or equal to 1 rem were compared with those with exposures less than 1 rem, elevated rate ratios were found for myeloid leukemia, lymphosarcoma and reticulum cell sarcoma, liver neoplasms, and unspecified brain tumors. No overall dose-response relationships were found for plutonium or external radiation exposures. Standardized rate ratios increased, however, as plutonium body burden levels increased for all causes, all cancers, and digestive cancers at five years induction time. Standardized rate ratios also increased as external radiation exposure categories increased for all lymphopoietic cancers and unspecified brain tumors for a two-year induction period. With the exception of analyses of combined categories of death, and perhaps of lung cancer, confidence limits were wide, indicating limited precision. Nevertheless, these findings suggest that increased risks for several types of cancers cannot be ruled out at this time for individuals with plutonium body burdens of greater than or equal to 2 nCi. Plutonium-burdened individuals should continue to be studied in future years.

Mortality among plutonium ani) other radiation workers at a plutonium weapons facility

A procedure of studentizing or standardizing the residuals by dividing them by their estimated standard deviations is proposed for testing for outliers in simple linear regression. A simulation study yielded the critical values of the test statistic, and it is shown that these values are extremely close to the values in Grubbs' (1950) Table IA and independent of the values taken for the independent variable.

Testing for a Single Outlier in Simple Linear Regression

Retention kinetics for insoluble particles that deposit in the lung oftentimes resemble a multicomponent process during alveolar clearance, with each component appearing to follow simple first-order kinetics. Inasmuch as alveolar macrophages (AM) are thought to play an important role in particle removal from the lung, a study was undertaken to examine particle-AM relationships during the clearance of particles to obtain information on potential AM mechanisms that could provide the underlying bases for the lung retention kinetics of the particles. Adult, Fischer 344 rats were intratracheally instilled with 1.6 × 107 (∼86 µg) polystyrene microspheres (∼2 µm diam). On Days 7, 14, 57, 85, and 176 thereafter, subgroups were killed, their lungs were lavaged, recovered cells (>95% AM) were counted, the frequency distribution of the particles among the AM was determined (e.g., zero, 1 to 2, 3 to 4 particles/AM), and the total numbers of particles lavaged were estimated. The lavaged lungs were solubilized, and unl...

Alveolar macrophage-particle relationships during lung clearance.

SUMMARY A table of percentiles of b2, the fourth standardized sample moment, applicable for samples of size 50 or less is given. The table was constructed by means of simulations. It can be used for testing the hypothesis of normality against alternatives of nonnormality due to kurtosis.

Gary L. Tietjen

Papers

Some Grubbs-Type Statistics for the Detection of Several Outliers

Mortality among plutonium ani) other radiation workers at a plutonium weapons facility

Testing for a Single Outlier in Simple Linear Regression

Alveolar macrophage-particle relationships during lung clearance.

Simulation probability points of b2 for small samples