Small-sample tests for homogeneity of response probabilities in 2 × 2 contingency tables.

1987 ◽  
Vol 102 (2) ◽  
pp. 307-314 ◽  
Author(s):  
John E. Overall ◽  
Howard M. Rhoades ◽  
Robert R. Starbuck
Keyword(s):  
Contingency Tables ◽  
Small Sample

scholarly journals A discussion on significance indices for contingency tables under small sample sizes

PLoS ONE ◽  
2018 ◽  
Vol 13 (8) ◽  
pp. e0199102 ◽  
Author(s):  
Natalia L. Oliveira ◽  
Carlos A. de B. Pereira ◽  
Marcio A. Diniz ◽  
Adriano Polpo
Keyword(s):  
Contingency Tables ◽  
Small Sample ◽  
Sample Sizes ◽  
Small Sample Sizes

The impact of uneven filling two-way contingency tables on the critical value of the test statistics

2016 ◽  
Vol 61 (4) ◽  
pp. 1-16
Author(s):  
Piotr Sulewski ◽  
Antoni Drapella
Keyword(s):  
Statistical Modeling ◽  
Contingency Tables ◽  
Critical Value ◽  
Small Sample ◽  
Test Statistics ◽  
Chi Square ◽  
Independent Verification ◽  
Power Of The Test ◽  
The Impact ◽  
Measures Of Inequality

The article concerns two-way (2×2) contingency tables. When the H0— hypothesis of independence of features is correct, very often — because of the small sample — the distribution of the test statistics differ from the chi-square. Quantile of the chi-square is therefore not a correct critical value. With the current performance of computers, designation of critical value by statistical modeling of Monte Carlo method is not a problem, but a problem is H0 modeling. The H0 modeling is generating such arrays, which feature value assigned rows are independent of the characteristics of the assigned columns. Suitable for such modeling are tables — uniform of the same probability of belonging to cells and uneven having equal probability in all rows of a given column or in all columns of a given row. Analysis of the results of statistical modeling revealed that even when H0 is right, the distribution of the test statistics significantly depends on the uneven array. The article shows that in order to maximize the power of the test should be set critical value, taking into account measures of inequality array. The final result of the study is offered the reader a ready tool for independent verification of the H0 hypothesis.

STATISTICAL METHODS IN MEDICAL RESEARCH: I. QUALITATIVE STATISTICS (ENUMERATION DATA)

1948 ◽  
Vol 26e (1) ◽  
pp. 1-166 ◽  
Author(s):  
Donald Mainland
Keyword(s):  
Standard Deviation ◽  
Experimental Design ◽  
Random Sampling ◽  
Contingency Tables ◽  
Laboratory Data ◽  
Statistical Treatment ◽  
Small Sample ◽  
Confidence Limits ◽  
Chi Square ◽  
Contingency Test

This article is designed to help investigators in applying to qualitatively classified clinical and laboratory data the appropriate statistical treatment—tests of significance in binomial and multinomial distributions, estimation of confidence limits, analysis of contingency tables, and estimation of sample sizes required for further investigation. Section A is a brief introduction (definitions and principles). Section B comprises 40 examples classified so that the investigator can choose data and problems comparable to his own. Questions that arise in the examples, regarding experimental design (especially random sampling) and the interpretation of the tests, are discussed in Section C (Notes).Because the standard deviation of the binomial and the chi square contingency test are often used without appreciation of the risk entailed, tables, which can be used also in nonmedical investigation, are presented: binomial confidence limits (with graphs) and exact probabilities for small-sample fourfold contingency tables. For samples not covered by the tables, precautions and rules regarding the use of chi square have been derived from more than five hundred comparisons between chi square and the exact method. To help in the exact computation of probabilities where that is necessary, four-decimal logarithms of factorials of numbers up to 1000 are given.

Probing the ultrastructure of the mitotic and meiotic spindle in eggs: An expeditious approach based on semi-thin (0.25 μm) serial sections

1983 ◽  
Vol 41 ◽  
pp. 552-555
Author(s):  
Conly L. Rieder ◽  
S. Bowser ◽  
R. Nowogrodzki ◽  
K. Ross ◽  
G. Sluder
Keyword(s):  
Small Sample Size ◽  
Small Sample ◽  
Meiotic Spindle ◽  
Serial Sections ◽  
Mitotic Apparatus ◽  
Thin Sections ◽  
Cell Cycles ◽  
Ultrastructural Studies

Eggs have long been a favorite material for studying the mechanism of karyokinesis in-vivo and in-vitro. They can be obtained in great numbers and, when fertilized, divide synchronously over many cell cycles. However, they are not considered to be a practical system for ultrastructural studies on the mitotic apparatus (MA) for several reasons, the most obvious of which is that sectioning them is a formidable task: over 1000 ultra-thin sections need to be cut from a single 80-100 μm diameter egg and of these sections only a small percentage will contain the area or structure of interest. Thus it is difficult and time consuming to obtain reliable ultrastructural data concerning the MA of eggs; and when it is obtained it is necessarily based on a small sample size.We have recently developed a procedure which will facilitate many studies concerned with the ultrastructure of the MA in eggs. It is based on the availability of biological HVEM's and on the observation that 0.25 μm thick serial sections can be screened at high resolution for content (after mounting on slot grids and staining with uranyl and lead) by phase contrast light microscopy (LM; Figs 1-2).

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