Gaussian Distribution on Validity Testing to Analyze the Acceptance Tolerance and Significance Level

Rahman, Arif; Oktavianty, Oke; Sari, Ratih Ardia; Azlia, Wifqi; Anggreni, Lavestya Dina

doi:10.13189/ms.2020.080105

Cited by 2 publications

(1 citation statement)

References 27 publications

(28 reference statements)

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“…In general, we see a practical interest in our results since the normal distribution is the basis of parametric methods in applied statistics, widely used in many areas (education, medicine, science, etc.) [59,60,58]. To know whether the normal distribution is applicable or not, is of interest for practitioners in these fields.…”

Section: Discussionmentioning

confidence: 99%

On the Gaussian Approximation to Bayesian Posterior Distributions

Fuhrmann¹,

Harney²,

Harney³

2021

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The present article derives the minimal number N of observations needed to approximate a Bayesian posterior distribution by a Gaussian. The derivation is based on an invariance requirement for the likelihood p(x|ξ). This requirement is defined by a Lie group that leaves the p(x|ξ) unchanged, when applied both to the observation(s) x and to the parameter ξ to be estimated. It leads, in turn, to a class of specific priors. In general, the criterion for the Gaussian approximation is found to depend on (i) the Fisher information related to the likelihood p(x|ξ), and (ii) on the lowest non-vanishing order in the Taylor expansion of the Kullback-Leibler distance between p(x|ξ) and p(x|ξ ML ), where ξ ML is the maximum-likelihood estimator of ξ, given by the observations x. Two examples are presented, widespread in various statistical analyses. In the first one, a chi-squared distribution, both the observations x and the parameter ξ are defined all over the real axis. In the other one, the binomial distribution, the observation is a binary number, while the parameter is defined on a finite interval of the real axis. Analytic expressions for the required minimal N are given in both cases. The necessary N is an order of magnitude larger for the chi-squared model (continuous x) than for the binomial model (binary x). The difference is traced back to symmetry properties of the likelihood function p(x|ξ). We see considerable practical interest in our results since the normal distribution is the basis of parametric methods of applied statistics widely used in diverse areas of research (education, medicine, physics, astronomy etc.). To have an analytical criterion whether the normal distribution is ap-plicable or not, appears relevant for practitioners in these fields.

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Section: Discussionmentioning

confidence: 99%

On the Gaussian Approximation to Bayesian Posterior Distributions

Fuhrmann¹,

Harney²,

Harney³

2021

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Validation of the Cantonese version of the Traditional Chinese Medicine (TCM) Body constitution Questionnaire in elderly people

Wong,

Zhang,

et al. 2023

Chin Med

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Background The Traditional Chinese Medicine (TCM) Body Constitution Questionnaire (For Elderly People) (TCMECQ) is a patient-reported outcome questionnaire developed in Mandarin in 2013 to differentiate the body constitutions of the elderly aged 65 and above. Considering the cultural and linguistic differences between Mainland China and Hong Kong (HK) Special Administrative Region, the TCMECQ was translated into Cantonese following “back translation” policy and validated in proper process. Methods Ten Chinese Medicine Practitioners (CMPs) and 30 senior citizens aged 65 or above were recruited to evaluate the first version of the Traditional Chinese Medicine Body Constitution Questionnaire (For Elderly People) (Cantonese version) (TCMECQ-C). Based on their comments, the second version was developed and discussed in the panel meeting to form the third version, validated the third version on 270 recruited seniors. Based on the validation results, a panel of 5 experts finalized the Questionnaire as the final version. The TCMECQ-C developers finalized the Questionnaire as the validated endorsed third version (i.e. final version). Results The item-level content validity index of most items of the TCMECQ-C (First Version) were ranging from 0.80 to 1.00 in terms of clarity, relevance and appropriateness. Factor loadings of Qi-deficiency Constitution ranging from 0.37 to 0.71, Yang-deficiency Constitution ranging from 0.36 to 0.65, Yin-deficiency Constitution ranging from 0.36 to 0.65, and Stagnant Qi Constitution ranging from 0.68 to 0.82. The chi-squared degree-of-freedom ratio was 2.13 (928.63/436), Goodness-of-Fit Index (0.83), Adjusted Goodness-of-Fit Index (0.79), Normed Fit Index (0.66), Comparative Fit Index (0.78), Incremental Fit Index (0.78), Relative Fit Index (0.61) and Tucker–Lewis Index (0.75), and Root Mean Square Error of Approximation (0.07) and Standardized Root Mean Square Residual (0.07), implied acceptable Confirmatory Factor Analysis model fit of the overall scale. A Pearson correlation coefficient (r) showed the sufficient convergent validity for excessive subscales (Phlegm-dampness Constitution and Dampness-heat Constitution with r = 0.35, p < 0.01). Cronbach’s alpha coefficient ranged from 0.56 to 0.89, including Qi-deficiency Constitution (0.67), Yang-deficiency Constitution (0.84), Yin-deficiency Constitution (0.59), Stagnant Blood Constitution (0.56), Stagnant Qi Constitution (0.89), Inherited Special Constitution (0.76) and Balanced Constitution (0.73), indicating acceptable internal consistency for subscales. The intra-class correlation coefficients of the TCMECQ-C ranged from 0.70 to 0.87 (p < 0.001), indicating moderate to good test–retest reliability. Conclusion TCMECQ-C is a valid and reliable questionnaire for assessing the body constitution in Cantonese elderly.

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Gaussian Distribution on Validity Testing to Analyze the Acceptance Tolerance and Significance Level

Cited by 2 publications

References 27 publications

On the Gaussian Approximation to Bayesian Posterior Distributions

On the Gaussian Approximation to Bayesian Posterior Distributions

Validation of the Cantonese version of the Traditional Chinese Medicine (TCM) Body constitution Questionnaire in elderly people

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