Programming Development of Kolmogorov-Smirnov Goodness-of-Fit Testing of Data Normality as a Microsoft Excel® Library Function

Abstract

This paper deliberates on the programming development of the Kolmogorov-Smirnov goodness-of-fit testing of data Normality as a library function in the Microsoft Excel® spreadsheet software, in which researchers normally store data for analysis and processing. The algorithmic program procedure utilised developed implementation of the Normality Kolmogorov-Smirnov D statistics for the one-sided and the two-sided test criteria as a library function in the Microsoft Excel® environment. For these programming developments, the Visual Basic for Applications® was employed for deploying macro embedment in the spreadsheet software. Successful programming development of the Normality K-S D statistics fosters implementation of the Normality K-S p-value estimation procedure also as a library function in the Microsoft Excel® environment. Test-applications of these programming developments in the study portray potency of accurate, speedy and economical procedure for testing compatibility of univariate data of real numbers to the Normal distribution, for datasets of n ≤ 2000 sample size.

Bioremediation: Data on biologically-mediated remediation of crude oil (Escravos Light) polluted soil using Aspergillus niger

“… The Kolmogorov-Smirnov goodness-of-fit analyses validates that the dataset comes from the probability density model of application for probability values (p-values) ≥ 0.05, otherwise the dataset having Kolmogorov-Smirnov goodness-of-fit p-value < 0.05 does not follow the probability density model of application [21,[28][29][30][31][32]. Figure 6, R-T_COP_5% indicates comparison between datasets from raw and treated crude oil polluted soil having 5% w/w Escravos Light pollution, while R-T_COP_8% compares the raw and treated crude oil polluted soil system with 8% w/w pollution.…”

“…Each dataset of absorbance from the tested systems was subjected to the statistical analyses of the Normal, the Gumbel and the Weibull probability density functions [24][25][26][27][28][29]. For each of these distributions, dataset compatibility was tested using the Kolmogorov-Smirnov goodness-of-fit, KS-GoF, test-statistics [30][31][32][33][34][35], also at the p ≥ 0.05 threshold of significance level. For ascertaining whether the duplicated raw data of absorbance measurements from each system of crude oil polluted soil design exhibited significant difference, or otherwise, from one another, the analytical method of the Student's t-test statistics was applied to the data [24,[36][37][38].…”

C6h18n4 Behaviour on Reinforcing-Steel Corrosion in Concrete Immersed in 0.5 M H2so4

“…Apart from the estimations of expected values, via the mean ( expected values, via the standard deviation ( statistical models, the reliability of the obtained expected values followed from their respective cumulative distribution function: 35,37 As per the ASTM G16-13(2019) designation also, Normal and the Weibull pdf was ascertained via application of test-statistics, [42][43][44][45][46][47] using the formula:…”

“…Apart from the estimations of expected values, via the mean (µ distribution ), and variations from such the standard deviation (σ distribution ), from these descriptive Normal and Weibull , the reliability of the obtained expected values followed from their respective 35,[37][38]42 designation also, 36 distribution of each dataset,of corrosion tests, like was ascertained via application of the Kolmogorov-Smirnov goodness : 35,40,[43][44][45] he foregoing analyses, the corrosion-resistance by different C 6 H 18 N 4 concentrations was assessed use of the mean corrosion rate (µ), from the probability distribution of better data, for evaluating the corrosion inhibition efficiency, η (%), according to:…”

Contribuições para a simulação de canais desvanecidos modelados com as distribuições 𝛼-𝜂-𝜇 e 𝛼-𝜅-𝜇

“…Essa vantagem é tanto mais nítida quanto menor for a dimensão da amostra (ABD-ELFATTAH, 2010;FERNANDES, 2013;OLUSEGUN;TOYIN;ADEREMI, 2015;PAPOULIS;PILLAI, 2002;STEPHENS, 1974). O teste de KS, ao contrário do teste do Chi-quadrado, não se aplica a dados qualitativos nem a variáveis discretas, pois os valores críticos para esse teste só são exatos caso a distribuição em teste seja contínua (ABD-ELFATTAH, 2010;FERNANDES, 2013;OLUSEGUN;TOYIN;ADEREMI, 2015;PAPOULIS;PILLAI, 2002;STEPHENS, 1974). Assim, o teste de KS exige distribuições populacionais contínuas e completamente especificadas (o que não sucede com o teste do Chi-quadrado), bem como um maior esforço computacional.…”