On the validity condition of the chi-squared test in 2×2 tables

Andrés, Antonio Martín; Quevedo, M. J. Sánchez; Tapia, José Miguel Rodríguez; Silva-Mato, A.

doi:10.1007/bf02595399

Cited by 10 publications

(2 citation statements)

References 22 publications

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“…Each cell in the simulation varies from 1 to 99, so that a sufficient range of proportions is explored. The use of continuity corrections, though important [28], are not pertinent to the main issues explored by this paper, and can be examined in future work. Figure 1 shows the plot of LRT (2 × S), χ 2 test and 2 × S var (to convert to approximate to the χ 2 distribution).…”

Section: Comparing the Three Equationsmentioning

confidence: 99%

Likelihood Ratio Test and the Evidential Approach for 2 × 2 Tables

Cahusac

2024

Entropy

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Categorical data analysis of 2 × 2 contingency tables is extremely common, not least because they provide risk difference, risk ratio, odds ratio, and log odds statistics in medical research. A χ2 test analysis is most often used, although some researchers use likelihood ratio test (LRT) analysis. Does it matter which test is used? A review of the literature, examination of the theoretical foundations, and analyses of simulations and empirical data are used by this paper to argue that only the LRT should be used when we are interested in testing whether the binomial proportions are equal. This so-called test of independence is by far the most popular, meaning the χ2 test is widely misused. By contrast, the χ2 test should be reserved for where the data appear to match too closely a particular hypothesis (e.g., the null hypothesis), where the variance is of interest, and is less than expected. Low variance can be of interest in various scenarios, particularly in investigations of data integrity. Finally, it is argued that the evidential approach provides a consistent and coherent method that avoids the difficulties posed by significance testing. The approach facilitates the calculation of appropriate log likelihood ratios to suit our research aims, whether this is to test the proportions or to test the variance. The conclusions from this paper apply to larger contingency tables, including multi-way tables.

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Section: Comparing the Three Equationsmentioning

confidence: 99%

Likelihood Ratio Test and the Evidential Approach for 2 × 2 Tables

Cahusac

2024

Entropy

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“…The calculation results are that the number of samples for r*c chi-squared test sheets of surface weathering condition versus the remaining three variables are all greater than 40, and the theoretical frequencies for r*c chi-squared test sheets of surface weathering condition versus type are all more than 5, with a minimum of 6.77, while partial theoretical frequencies versus decoration and color are less than 5. Therefore, for the correlation analysis between surface weathering condition and type, the chisquared test can be used; while for the correlation analysis between surface weathering condition and decoration or color, then Fisher's exact test can be used [9].…”

Section: Data Preprocessingmentioning

confidence: 99%

Sub-Classification and Type Identification of Weathering Silicate Glasses Based on Spectral Clustering

Xie,

Tang,

et al. 2023

J. Phys.: Conf. Ser.

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Ancient glass products are often weathered to varying degrees after excavation. Detection and analysis of their chemical composition will help to study the ancient glass making process. In this paper, we take a group of ancient glass products as samples, and study the sub-classification and type identification of weathered silicate glasses. Firstly, we identify the main factor of glass weathering through chi-squared test and Fisher’s exact test, then conduct a significance test on the basis of preprocessing various data of glass cultural relics. Secondly, the glass samples are classified into high potassium glass and lead barium glass by spectral clustering method, and further sub-classified into eight classes. The sub-classes are named based on feature extraction, and the clustering quality is tested by contour coefficient. Finally, we analyze the chemical composition affecting the glass types by combining the non-parametric tests to identify the types of glass cultural relics by multiple linear regression with significance testing. In addition, correlation test, spectral clustering and multiple linear regression are used to study the sub-classification and type identification of weathered silicate glasses, which provides a reference for further study of ancient glass making process and weathering process.

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Choice of test for association in small sample unordered r × c tables

Lydersen

Pradhan

Senchaudhuri

et al. 2007

Statistics in Medicine

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Pearson's chi-squared, the likelihood-ratio, and Fisher-Freeman-Halton's test statistics are often used to test the association of unordered r x c tables. Asymptotical, exact conditional, or exact conditional with mid-p adjustment methods are commonly used to compute the p-value. We have compared test power and significance level for these test statistics and p-value calculations in small sample r x c tables, mostly 3 x 2 and some with both r and c are greater than 2. After extensive simulations, in general we recommend using an exact conditional mid-p test with Pearson's chi-squared or Fisher-Freeman-Halton's statistic, which usually is the most powerful test yet preserve the approximate significance level. Moreover, we recommend that the asymptotic Pearson's chi-squared or other asymptotic tests not be used for small sample r x c tables.

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On the validity condition of the chi-squared test in 2×2 tables

Abstract: Asymmetry, Barnard's exact test, chi-squared test, conditional test, continuity correction, Fisher's exact test, minimum expected quantity, unconditional test, validity condition, 2×2 tables, 62F03, 62F04,

Cited by 10 publications

References 22 publications

Likelihood Ratio Test and the Evidential Approach for 2 × 2 Tables

Likelihood Ratio Test and the Evidential Approach for 2 × 2 Tables

Sub-Classification and Type Identification of Weathering Silicate Glasses Based on Spectral Clustering

Choice of test for association in small sample unordered r × c tables

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