A note on the statistical properties of animal locations

A statistical model of the successive locations of an animal in the plane induces a statistical model of the relative positions of successive locations. A common locational model is that the Cartesian coordinates of successive locations in the plane are independent bivariate normal random variables. This note gives the statistical properties of the direction and length of the vector joining successive locations.     

Robustness of Sequential Tests for Means

Three sequential tests of the null hypothesis, μ = μ₀, versus an alternative of the form (μ ? μ₀)²= =σ²d² are compared for different forms of violation of the underlying normal assumption. 10000 samples were simulated for d=0.6; 1.0 and 1.6 (σ² = 1), four (α, β)-combinations and seven alternative distributions. The results show that for small d-values one test is robust for α and another for β. For large d all tests can be used.     

Further Study on the Statistical Test to Detect Spatial Pattern

In the study of spatial patterns, the statistic I' = (n — 1)s²/x was commonly used. In this paper, we found that x — s² has an approximated normal distribution with zero mean if the x_i's (i = 1 to n) are independent identically distributed Poisson variables. Based on this conclusion, the hypothesis that a point pattern is completely random can be tested directly. And a method for the test of spatial patterns was proposed which can be sued as an alternative to the Chi-square based dispersion index test.     

On Errors of Measurement

When any process of measuring is considered, one of the basic questions is how to assess the precision of measurement methods and/or instruments. In this paper, this question is formulated and solved as a problem of tolerance regions for absolute and relative normaly distributed errors of measurements.     

Using a Normal Approximation to Test for the Binomial Distribution

The commonly used method to test for the binomial distribution is the x²-test. In this paper, we introduce an alternative method to test for the binomial distribution. Suppose N is the number of sample groups with n individuals each, x_ij is the jth sample in ith group, a Bernoulli variable with parameter and VVI=s²/[m(1 - m)/n]. Then it is well know that the asymptotic distribution of the statistic (N - 1) VVI is x²(N - 1) under the hypothesis p₁ = p₂ = … = p_N. Here we find that VVI has an asymptotic normal distribution N(1, 2(1 - 1/n)/(N - 1)). Unlike the x²-statistic, the variance of the normal test statistic is a function of n. This method is convenient in detecting spatial patterns and dispersion in the study of diseased organisms (e.g., plants) in field samples.     

On Parametric Confidence Intervals for the Cost‐Effectiveness Ratio

When comparing two competing interventions, confidence intervals for cost‐effectiveness ratios (CERs) provide information on the uncertainty in their point estimates. Techniques for constructing these confidence intervals are much debated. We provide a formal comparison of the Fieller, symmetric and Bonferroni methods for constructing confidence intervals for the CER using only the joint asymptotic distribution of the incremental cost and incremental effectiveness of the two interventions being compared. We prove the existence of a finite interval under the Fieller method when the incremental effectiveness is statistically significant. When this difference is not significant the Fieller method yields an unbounded confidence interval. The Fieller interval is always wider than the symmetric interval, but the latter is an approximation to the Fieller interval when the incremental effectiveness is highly significant. The Bonferroni method is shown to produce the widest interval. Because it accounts for the likely correlation between cost and effectiveness measures, and the intuitively appealing relationship between the existence of a bounded interval and the significance of the incremental effectiveness, the Fieller interval is to be preferred in reporting a confidence interval for the CER.