Improving the Quality of Response Surface Analysis of an Experiment for Coffee-Supplemented Milk Beverage: I. Data Screening at the Center Point and Maximum Possible R-Square

Abstract

Response surface methodology (RSM) is a useful set of statistical techniques for modeling and optimizing responses in research studies of food science. As a design for a response surface experiment, a central composite design (CCD) with multiple runs at the center point is frequently used. However, sometimes there exist situations where some among the responses at the center point are outliers and these outliers are overlooked. Since the responses from center runs are those from the same experimental conditions, there should be no outliers at the center point. Outliers at the center point ruin statistical analysis. Thus, the responses at the center point need to be looked at, and if outliers are observed, they have to be examined. If the reasons for the outliers are not errors in measuring or typing, such outliers need to be deleted. If the outliers are due to such errors, they have to be corrected. Through a re-analysis of a dataset published in the Korean Journal for Food Science of Animal Resources, we have shown that outlier elimination resulted in the increase of the maximum possible R-square that the modeling of the data can obtain, which enables us to improve the quality of response surface analysis.

A modeling method for the development of a bioprocess to optimally produce umqombothi (a South African traditional beer)

“…The predicted determination (pred-R 2 ) values for alcohol content and TSS were not as close to the adjusted determination (adj-R 2 ) indicating a slight limitation with the model (Table 5 ). A consideration of outliers, model reduction, and response transformation may improve the empirical model 37 . In contrast, the predicted determination (pred-R 2 ) of 0.89 in the pH optimization model was reasonably close to the adjusted determination (adj-R 2 ) of 0.97, thus confirming the model’s accuracy in correctly predicting responses (Table 5 ).…”

Do Flavonoids from Durum Wheat Contribute to Its Bioactive Properties? A Prospective Study

“…The extraction at the central point (or centroid) represents an equal contribution of all three solvents (0.333, 0.333, 0.333). Runs 7–9, representing the extraction in three replicates, allow estimating the variation in the responses at the central point and provides a basis for the lack-of-fit test [ 78 , 79 ]. The response function was the TPC, which was evaluated in two different advanced breeding lines.…”

Improving the Quality of Response Surface Analysis of an Experiment for Coffee-supplemented Milk Beverage: II. Heterogeneous Third-order Models and Multi-response Optimization

“…The original data to be used for re-analysis is the data described in Ahn et al (2017), in which they tried to optimize manufacturing conditions for improving storage stability of coffee-supplemented milk beverage by using RSM. Through data screening, one outlier was deleted from their data (Rheem and Oh, 2019). The response variables, Y 1 and Y 2 , and the factors in this experiment are described in Table 1A.…”

“…A dataset, which is obtained through the screening of the data in Ahn et al (2017), will be re-analyzed for the illustration of the remedy suggested in this research note. Since Ahn et al (2017) has two responses and a purpose of it is the multi-response optimization of them, this research note, which is a continuation of Rheem and Oh (2019), will model both responses by using heterogeneous third-order models, and optimize them simultaneously by employing the desirability function technique.…”