A Measure of 2 x 2 Association with Stable Variance and Approximately Normal Small-Sample Distribution: Planning Cost-Effective Studies

Biometrics ◽  
1986 ◽  
Vol 42 (2) ◽  
pp. 359 ◽  
Author(s):  
Helena Chmura Kraemer
Keyword(s):  
Cost Effective ◽  
Small Sample ◽  
Sample Distribution ◽  
Distribution Planning ◽  
Small Sample Distribution

The Exact Distribution of Moran's I

1995 ◽  
Vol 27 (6) ◽  
pp. 985-999 ◽  
Author(s):  
M Tiefelsdorf ◽  
B Boots
Keyword(s):  
Exact Distribution ◽  
Small Sample ◽  
Moran’S I ◽  
Moran's I ◽  
Sample Distribution ◽  
Explanatory Variables ◽  
Regression Residuals ◽  
Exact Power ◽  
Exact Distribution Function ◽  
Small Sample Distribution

In analogy to the exact distribution of the Durbin—Watson d statistic for serial autocorrelation of regression residuals, the exact small sample distribution of Moran's I statistic (or alternatively Geary's c) can be derived. Use of algebraic results by Koerts and Abrahamse and theoretical results by Imhof, allows the authors to determine by numerical integration the exact distribution function of Moran's I for normally distributed variables. For the case in which the explanatory variables have been neglected, an upper and a lower bound can be given within which the exact distribution of Moran's I for regression residuals will lie. Furthermore, the proposed methodology is flexible enough to investigate related topics such as the characteristics of the exact distribution for distinct spatial structures as well as their different specifications, the exact power function under different spatial autocorrelation levels, and the distribution of Moran's I for nonnormal random variables.

Relationship between noise-induced annoyance and age based on data of previous literatures

2021 ◽  
Vol 263 (3) ◽  
pp. 3769-3778
Author(s):  
Ke Ni ◽  
Yu Huang
Keyword(s):  
Rating Scales ◽  
Age Groups ◽  
Quantitative Model ◽  
Small Sample ◽  
Small Samples ◽  
Sample Distribution ◽  
Year 2000 ◽  
Small Sample Distribution ◽  
The Relationship ◽  
Distribution Assumption

Many studies have investigated subjective responses to noise, but few concerned about the influence of age on the annoyance (discomfort) caused by noise. It is difficult to get a quantitative model featuring the relationship between noise-induced annoyance and age from one or several laboratory studies due to relatively small samples and limited age groups. This paper investigated recent studies (published after the year 2000) on noise-induced annoyance by the literature review method. We classified the studies according to their employed noise types and summarized the quantified subjective values and the ranges of age. The quantitative values of annoyance obtained from variable rating scales were transferred to a uniform scale and normalized. A probability density function then figured out the corresponding annoyance of a certain age under the small sample -distribution assumption. A predicting model of noise-induced annoyance from the age of 7-55 was proposed, which fitted previous data well.

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