Steve Verrill

Confidence Bounds and Hypothesis Tests for Normal Distribution Coefficients of Variation

For normally distributed populations, we obtain confidence bounds on a ratio of two coefficients of variation, provide a test for the equality of k coefficients of variation, and provide confidence bounds on a coefficient of variation shared by k populations.

Tables and Large-Sample Distribution Theory for Censored-Data Correlation Statistics for Testing Normality

Abstract Plotting order statistics versus some variant of the normal scores is a standard graphical technique for assessing the assumption of normality. To obtain an objective evaluation of the normal assumption, it is customary to calculate the correlation coefficient associated with this plot. The Shapiro—Francia statistic is the square of the correlation between the observed order statistics and the expected values of standard normal order statistics, whereas the Shapiro—Wilk statistic also involves the covariances of the standard normal order statistics. In a wide variety of applications, an investigation of the plausibility of the normal (or lognormal) model is needed when the observations on strength or life length are right-censored. The plotting procedure still applies if the observations are censored at a fixed order statistic or a fixed time. Here, the corresponding distribution theory for some modified versions of the Shapiro—Wilk correlation statistic is investigated. Because the asymptotic th...

The Decline and Fall of Type II Error Rates

For general linear models with normally distributed random errors, the probability of a Type II error decreases exponentially as a function of sample size. This potentially rapid decline reemphasizes the importance of performing power calculations.

Material Variability and Repetitive Member Factors for the Allowable Properties of Engineered Wood Products

It has been argued that repetitive member allowable property adjustments should be larger for high-variability materials than for low-variability materials. We report analytic calculations and simulations that suggest that the order of such adjustments should be reversed, that is, given the manner in which allowable properties are currently calculated, as the coefficient of variation of the strength distribution of individual elements increases, the upward repetitive member adjustments (if any) of assemblies constructed from these elements should decrease.

Predictor sort sampling, tight T's, and the analysis of covariance

In this article we revisit a method of sample allocation that has long been known to statisticians and has recently been “discovered” by wood strength researchers. The method allocates experimental units to blocks on the basis of the values of a variable, x, that is known to be correlated with the response, y We call this allocation method “predictor sort sampling.” We demonstrate that the associated paired T analysis recommended in statistical texts is deficient if the sample size is small and the correlation between x and y is high. We temper this criticism of standard statistical intuition with a proof that the approach is asymptotically correct. In a related development we show that a modified pooled T approach can be taken to this data with a resultant increase in power. We compare these approaches to an analysis of covariance approach and discuss the advantages of each. Finally, we warn against the intuitively attractive but incorrect power calculations that are likely to be performed in association...

We've Got the Positive Correlation BLUEs

Abstract Intuition suggests that combinations of positively correlated estimates of a quantity have greater variances than combinations of independent estimates of the quantity. In this note we identify circumstances under which best linear unbiased estimators (BLUEs) based on positively correlated measurements are superior to BLUEs based on independent measures.

When Good Confidence Intervals Go Bad: Predictor Sort Experiments and ANOVA

Abstract A predictor sort experiment is one in which experimental units are allocated on the basis of the values of a predictor variable that is correlated with the response. Standard ANOVA analyses of predictor sort experiments can lead to confidence intervals whose actual coverages are poor matches to nominal coverages. Correct coverages can be obtained by adjusting confidence interval lengths by appropriate factors, or by performing analyses of covariance.

Asymptotic distributions for quadratic forms with applications to censored data tests of fit

We obtain the asymptotic distributions of certain forms in observations that are possible Type I and Type II censored. This result is directly applicable to the study of asympototic distributions for censored data versions of the Shapiro- wilk test for normality. Moreove, it applies more generally than just to the null hypothesis of normality.

The large sample distribution of the Shapiro--Wilk statistic and its variants under Type I or Type II censoring

The original Shapiro--Wilk statistic is extended for testing normality when the observations are Type I or Type II censored. We determine its large sample limit distribution under Type I or Type II censoring. This censored data limit distribution has an interesting relation to the complete sample solution and is obtained from it by replacing each Hermite polynomial with a censored data form. The same limit distribution also applies to several variants of the Shapiro--Wilk statistic which are related to the correlation coefficient associated with a normal probability plot.

Sources of Confusion in the Determination of ASTM Repetitive Member Factors for the Allowable Properties of Wood Products

Confusion in the literature about the definition and calculation of repetitive member factors is identified. This confusion casts some doubt on the validity of the 1.15 repetitive member factor permitted in ASTM standards D245 and D1990. DOI: 10.1061/(ASCE)ST .1943-541X.0000413.