The fisher-yates exact test and unequal sample sizes

Psychometrika ◽  
1972 ◽  
Vol 37 (1) ◽  
pp. 103-106 ◽  
Author(s):  
Edgar M. Johnson
Keyword(s):  
Sample Sizes ◽  
Exact Test ◽  
Unequal Sample Sizes

Approximating the Probability of Selecting the Best Treatment With A Heteroscedastic Procedure When The First Stage Has Unequal Sample Sizes

1983 ◽  
Vol 8 (1) ◽  
pp. 45-58
Author(s):  
Rand R. Wilcox
Keyword(s):  
Sample Sizes ◽  
Two Stage ◽  
Normal Distributions ◽  
The One ◽  
Unequal Sample Sizes

Consider k normal distributions having means μ1,..., μk and variances σ21,..., σ2 k. Let μ[1]≥...≥ μ[ k] be the means written in ascending order. Dudewicz and Dalai proposed a two-stage procedure for selecting the population having the largest mean μ[ k] where the variances are assumed to be unknown and unequal. This paper considers an approximate but conservative solution for situations where unequal sample sizes are used in the first stage. The paper also considers how to estimate the actual probability of selecting the “best” treatment; that is, the one having mean μ[ k], after a heteroscedastic ANOVA has been performed.

scholarly journals A correction to the exact test based on the Ewens sampling distribution

1996 ◽  
Vol 68 (3) ◽  
pp. 259-260 ◽  
Author(s):  
Montgomery Slatkin
Keyword(s):  
Small Sample ◽  
Sampling Distribution ◽  
Sample Sizes ◽  
Exact Test ◽  
Small Sample Sizes ◽  
Larger Sample

SummaryThe exact test for neutrality based on the Ewens sampling distribution described previously (Slatkin, 1994) is not correct. The problem is that the test as described is based on the probability of the ordered configuration of numbers of alleles, while it should be based on the probability of the unordered configuration. The correctly implemented exact test leads to results that are similar to those from the homozygosity test proposed by Watterson (1977) for relatively small sample sizes but can still differ substantially for larger sample sizes. Programs to perform the exact test are available from the author.

scholarly journals High-Low Level Support Vector Regression Prediction Approach (HL-SVR) for Data Modeling with Input Parameters of Unequal Sample Sizes

2021 ◽  
pp. 2150029
Author(s):  
Maolin Shi ◽  
Liye Lv ◽  
Zhenggang Guo ◽  
Wei Sun ◽  
Xueguan Song ◽  
...  
Keyword(s):  
Support Vector Regression ◽  
Data Modeling ◽  
Support Vector ◽  
Sample Sizes ◽  
Low Level ◽  
Input Parameters ◽  
High Level ◽  
Prediction Approach ◽  
Larger Sample ◽  
Unequal Sample Sizes

Support vector regression (SVR) has been widely used to reduce the high computational cost of computer simulation. SVR assumes the input parameters have equal sample sizes, but unequal sample sizes are often encountered in engineering practices. To solve this issue, a new prediction approach based on SVR, namely as high-low level SVR approach (HL-SVR) is proposed for data modeling of input parameters of unequal sample sizes in this paper. The proposed approach consists of low-level SVR models for the input parameters of larger sample sizes and high-level SVR model for the input parameters of smaller sample sizes. For each training point of the input parameters of smaller sample sizes, one low-level SVR model is built based on its corresponding input parameters of larger sample sizes and their responses of interest. The high-level SVR model is built based on the obtained responses from the low-level SVR models and the input parameters of smaller sample sizes. A number of numerical examples are used to validate the performance of HL-SVR. The experimental results indicate that HL-SVR can produce more accurate prediction results than SVR. The proposed approach is applied to the stress analysis of dental implant, in which the structural parameters have massive samples but the material of implant can only be selected from Ti and its alloys. The obtained prediction results of the HL-SVR approach are much better than SVR. The proposed approach can be used for the design, optimization, and analysis of engineering systems with input parameters of unequal sample sizes.

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