*3.4. Method Precision*

Method repeatability was tested, making ten analyses on the same sample of each type of vinegar and comparing the results with those obtained with the Community method. The Shapiro-Wilk test showed that the data were linearly distributed (Figure S4). The Huber test excluded the presence of anomalous data (Figures S3–S5). The reproducibility of the three kinds of vinegar were red wine vinegar = 0.55, white wine vinegar = 0.69, and balsamic wine vinegar = 0.66. The limits of method repeatability were: upper limit = 0.548 and lower limit = 1.480, considering the ratio between the

standard deviation (Sr) of the enzymatic method and the repeatability standard deviation of the reference method (σr), satisfied for nine degrees of freedom (Table S6).

#### *3.5. Accuracy Test*

Accuracy was determined, making ten analyses with both methods (Community and enzymatic), and determining significant differences between groups by Student's *t* test (Figures S4–S6). We cannot reject the null hypothesis that there is no difference between means when *p* < 0.05.

#### **4. Discussion**

Automated analyzers are modern instrumentation for routine analytical analysis since they reduce staff errors due to tiredness or a lack of technicality, improve safety, and decrease the amount of reagents, the cost, and the time of analysis. Traditional methods of analysis are struggling to survive in technology. Innovation in technologies brings significant opportunities but also carries risks for society. The validation of new analytical procedures is a developed approach that responds to evolving markets. It is a verification process that checks whether the analytical method achieves predetermined results. The validation of an analytical procedure is used both before its first use and throughout its life, to continually monitor its performance and any critical issues. In food, analysis is indispensable to make available reliable and accurate results with known uncertainty. Therefore, the methods used in analytical laboratories need an accurate validation process to ensure their validity (ISO/IEC, 2005) [16]. Validation is performed to define the linearity, precision, accuracy, and repeatability of the method based on the matrix, the working field, and the uncertainty due to the instrumentation and environmental conditions. Furthermore, it is possible to verify the results by comparing them with those obtained with reference analytical methods. In this work, an enzymatic determination of acetic acid in three different types of vinegar (red wine vinegar, white wine vinegar, and balsamic vinegar) was carried out on automated photometric systems. The method was based on acetate kinase, an enzyme capable of reacting with acetic acid and adenosine-5'-triphosphate, giving acetylphosphate and adenosine-5'-diphosphate (ADP). Acetylphosphate is converted into acetyl-CoA plus phosphate by coenzyme A (CoA) and phosphotransacetylase. ADP reacts with D-glucose through an ADP-dependent exokinase to produce D-glucose-6-phosphate. The latter, in the presence of glucose-6-phosphate dehydrogenase, reacts with NAD+, turning into D-glucono-δ-lactone-6-phosphate and NADH<sup>+</sup> H <sup>+</sup>. The concentration of NADH, proportional to the concentration of acetic acid, is determined spectrophotometrically, according to AOAC instructions (AOAC 2012) [17]. The test uses a kit containing ready-to-use reagents and standards. The analytical problem consisted of adapting the procedures proposed by the industry for the wine matrix to the vinegar matrix and the validation of the analytical procedures. The concentration of the solution influences the spectrophotometric reading. The vinegar samples were diluted 125 times to be able to read the absorbance at the desired wavelength. Any change requires an evaluation of the method's performance. The validation of the method, comparative tests with standard methods, and co-validation between laboratories are the possible strategies to achieve this goal [18]. In this case, the method was validated in terms of the linearity, precision, repeatability, measurement of uncertainty, and accuracy. The linearity of the method was demonstrated by the regression coefficient (1) and a residual diagram (straight line) in the ANOVA test. The ANOVA test describes the difference in the standard deviations of the values obtained from the reference compared to the expected values. The reliability of the test depends on the normal distribution of residues with a 95% confidence level. The sensitivity of the method was defined by deriving the LLOD (0.946 ppm) and LLOQ (2.00 ppm) from the regression curve and determining the measuring range (100 ppm ≤ measuring range ≤ 500 ppm). The precision of the method was determined, confirming its reproducibility and repeatability. Repeatability produces the minimum precision value. It was obtained, making ten analyses of the same sample in short intervals of time, by the same operator, in the same laboratory, with the same method and equipment and comparing the repeatability type difference of the method (sr) with that of the reference method (sr). The Shapiro–Wilk test confirmed the linearity between

the results obtained by the spectrophotometric method and those obtained by the reference method. The null hypothesis (H0) states that two elements or series of elements are normally distributed. This hypothesis is satisfied if the p-value is higher than 0.05, as happens for the types of analysis carried out (Figure S4). Successively, the absence of anomaly data was tested by the Huber test (Tables S3–S5). The Huber test is a robust statistical method to identify outliers, which may invalidate the resulting analysis, by first fitting most of the data and flagging data points. The presence of very few anomalous data was attributed to random errors. Finally, random and systematic uncertainties were detected to establish method accuracy. Random errors are caused by unpredictable changes in the experiment due to environmental conditions and measuring instruments. The errors due to the instrument or its data-handling system, or the instrument being wrongly used by the experimenter cause systematic errors. In this work, the uncertainties due to method repeatability and associated with the standard preparation, the calibration curve, the balances, the flasks (100 mL and 250 mL), and the pipettes (10 mL and 20 mL) were determined to be irrelevant since they were less than 10% of the results. Finally, the accuracy of the enzymatic method was evaluated. The accuracy showed significant differences between the two populations of data. The enzymatic method underestimated the results because of systematic errors. The percentage difference was calculated, and it was observed that the systematic errors were independent of the matrix but were influenced by the measuring range (five samples had waste results around 10). The differences in measurements between the two tests were due to the high selectivity of the enzymatic method, which exclusively measured the concentration of acetic acid and non-specificity of the Community method, which attributed to the concentration of acetic acid all of the acids present in the sample. Consequently, the underestimation of the enzymatic method was expected. Therefore, the method could be considered applicable since the relative percentage deviations compared to the values obtained with the official method are around 10%.
