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Statistics can be used in a variety of ways to present, compute, and critically analyze experimental data. To determine the significance and validity of the experimental data, a variety of statistical tests are used. Using a synthesized CoO/NiO/MnO 2 Nanocomposite, the present study used adsorption to remove the dye Bromophenol Blue (BPB) from a contaminated aqueous solution. In order to (a) determine the optimal pH of the solution, (b) confirm the experiment's success, and (c) investigate the effect of adsorbent dose on BPB dye removal from aqueous solutions. The experimental data were statistically analyzed through hypothesis testing using the t -test, paired t -test, and Chi-square test. The null hypothesis that the optimal pH value is 7 is accepted since t observed (−1.979)

We introduce a heuristic to test the significance of fit of Self-Validated Ensemble Models (SVEM) against the null hypothesis of a constant response. A SVEM model averages predictions from nBoot fits of a model, applied to fractionally weighted bootstraps of the target dataset. It tunes each fit on a validation copy of the training data, utilizing anti-correlated weights for training and validation. The proposed test computes SVEM predictions centered by the response column mean and normalized by the ensemble variability at each of n P o i n t points spaced throughout the factor space. A reference distribution is constructed by refitting the SVEM model to nPerm randomized permutations of the response column and recording the corresponding standardized predictions at the n P o i n t points. A reduced-rank singular value decomposition applied to the centered and scaled n P e r m × n P o i n t reference matrix is used to calculate the Mahalanobis distance for each of the nPerm permutation results as well as the jackknife (holdout) Mahalanobis distance of the original response column. The process is repeated independently for each response in the experiment, producing a joint graphical summary. We present a simulation driven power analysis and discuss limitations of the test relating to model flexibility and design adequacy. The test maintains the nominal Type I error rate even when the base SVEM model contains more parameters than observations. • Supersaturated SVEM predictive models can overfit noise. • Actual-by-predicted plots may show spurious strong correlations due to overfitting. • Test evaluates the significance of SVEM fit with pointwise standardized predictions throughout factor space. • Reference distributions for standardized predictions derived from permutations of the response vector. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive statistical framework in order to rigorously derive the correlation coefficient distribution between two independent chemical data sets. The novel approach not only allows for unequivocal interpretation of distribution parameters and confidence intervals but also the generalization of previous results for fixed size comparisons into the new and experimentally important case of variable dimension data assessments. Original theoretical results include an objective criterion ("number of nines") for the coefficient of multiple determination in mathematical model fitting (e.g. calibration curve acceptance in validation protocols) and the requirement of a minimum correlation coefficient match of approximately 70% in variable size evaluations. Significance tests have been applied to the drug profile linkage of 532 real case cocaine samples seized by the National Police of Peru between the years of 2021 and 2022. • A novel and comprehensive mathematical framework to rigorously derive the correlation coefficient distribution between independent data sets. • Generalization of fixed dimension comparisons into the new and experimentally important case of variable size assessments. • Explicit derivation of critical correlation coefficient values in terms of Excel® statistical functions. • Minimum correlation coefficient value of approximately 70% for variable size data evaluations. • Coefficient of multiple determination criterion for calibration curve acceptance in validation protocols. [ABSTRACT FROM AUTHOR]