Stat-Ease Blog

Here's the latest Publication Roundup! In these monthly posts, we'll feature recent papers that cited Design-Expert® or Stat-Ease® 360 software. Please submit your paper to us if you haven't seen it featured yet!

Featured Article

Orange-Fleshed Sweet Potatoes, Grain Amaranth, Biofortified Beans, and Maize Composite Flour Formulation Optimization and Product Characterization
Food Science and Nutrition, Volume 13, Issue 6. June 2025.
Authors: Julius Byamukama, Robert Mugabi, Dorothy Nakimbugwe, John Muyonga

Mark's comments: "It's good to see response surface methods for optimization of food recipes via mixture design. I appreciate publications that include all the data needed to assess the predictive modeling.  Kudus to EU for funding research like this that alleviates malnutrition in vulnerable populations."

Be sure to check out this important study, and the other research listed below!

More new publications from June

1. Optimization and induction effect evaluation of complex inducer of Aquilaria sinensis based on factorial design
   Scientific Reports, volume 15, Article number: 19656 (2025)
   Authors: Qiuyue Ding, Baoyi Qin, Shimin Deng, Jie Chen, Ziwei Liu, Weiping Zhou, Xiaoying Chen, Weimin Zhang, Xin Zhou, Xiaoxia Gao
2. Adsorption of crystal violet using thiazolium ionic liquid-crosslinked alginate hydrogels: Modelling using Box-Behnken experimental design
   International Journal of Biological Macromolecules, Volume 318, Part 1, July 2025, 144951
   Authors: Merve Ceylan, Jülide Hızal, Elif Nur Özer, Ivaylo Tankov, Rumyana Yankova
3. High-Performance Ultrathin Membrane with Molecular Arrangement Ordered for Proton Exchange Membrane
   ACS Applied Polymer Materials, published June 10, 2025
   Authors: Yuqing Zhang, Ailing Zhang, Kaixiang Zhou, Yongjiang Li
4. Impact of addition of polyvinyl chloride on the properties of clayey soil using experimental approach and optimization for geotechnical engineering applications
   Scientific Reports, volume 15, Article number: 19901 (2025)
   Authors: Ghania Boukhatem, Said Berdoudi, Messaouda Bencheikh, Mohammed Benzerara, Mehmet Serkan Kırgız, N. Nagaprasad, Krishnaraj Ramaswamy
5. Copper Corrosion in Blended Diesel-Biodiesel: Corrosion Rate Evaluation and Characterization
   Chemical Engineering & Technology, e70053, 12 June 2025
   Authors: Lekan Taofeek Popoola, Celestine Chidi Nwogbu, Usman Taura, Yuli Panca Asmara, Alfred Ogbodo Agbo, Paul C. Okonkwo
6. The Effects of Novel Thymoquinone-Loaded Nanovesicles as a Promising Avenue to Modulate Autism Associated Dysregulation by Restoring Oxidative Stress in Autism in Mice
   International Journal of Nanomedicine, 24 June 2025 Volume 2025:20 Pages 8041—8061
   Authors: Nermin Eissa, Jana K Alwattar, Petrilla Jayaprakash, Dana Chkier, Aala Osama Ahmed, Anum Ahmed, Rameen Rizwan, Sulthan Mujeeb, Mohamad Rahal, Bassem Sadek

Here's the latest Publication Roundup! In these monthly posts, we'll feature recent papers that cited Design-Expert® or Stat-Ease® 360 software. Please submit your paper to us if you haven't seen it featured yet!

Featured Article

Enhanced 4-chlorophenol adsorption from aqueous solution using eco-friendly nanocomposite
Ecological Engineering & Environmental Technology, 26(5), pp.174-189
Authors: Fadia A. Sulaiman, Rasha Khalid Sabri Mhemid, Noor A. Mohammed

Mark's comments: It is great to see the application of response surface methods (RSM) to reduce the release of toxic chlorophenols to our environment, particularly via such an eco-friendly process utilizing a natural polymer--xanthan gum.  The 3D graphics are compelling and well supported by the reported statistics.  I also appreciate that all the raw data is including, making it possible for me to reproduce the results.

Be sure to check out this important study, and the other research listed below!

More new publications from May

1. Design of Experiments Assisted Formulation Optimization and Evaluation of Efavirenz Solid Dispersion Adsorbate for Improvement in Dissolution and Flow Properties
   Drug Design, Development and Therapy, 2025;19:3715-3734
   Authors: Mujtaba MA, Rashid MA, Alhamhoom Y, Gangane P, Jagtap MJ, Akbar MJ, Wathore SA, Kaleem M, Elhassan GO, Khalid M
   
2. Design of Experiments Approach for the Development of a Validated UPLC-Q-ToF/MS Method to Quantitate Soy-Derived Bioactive Peptide Lunasin in Rabbit Plasma: Application to a Pharmacokinetic Study
   Biomedical Chromatography, 2025, 39: e70098
   Authors: Kowmudi, G., Anoop, K., Varshini, M., Nagappan, K., Konanki, S., Praveen, T
   
3. Development of a Stability-Indicating RP-HPLC Method for Pioglitazone in Cubosomal and Biological Matrices: A Quality by Design-Driven, Lean Six Sigma, and Green Chemistry Approach
   Separation Science Plus, 2025, 8: e70055
   Authors: Vaibhavi D. Torgal, Vinayak Mastiholimath, Rahul Koli
   
4. Optimization process of coffee pulp wines combined with the artificial neural network and response surface methodology
   Scientific Reports, volume 15, Article number: 16684 (2025)
   Authors: Rongsuo Hu, Fei Xu, Liyan Zhao, Wenjiang Dong
   
5. Formulation optimization of furosemide floating-bioadhesive matrix tablets using waste-derived Citrus aurantifolia peel pectin as a polymer
   Scientific Reports, volume 15, Article number: 16704 (2025)
   Authors: Ebrahim Abdela Siraj, Yohannes Mulualem, Fantahun Molla, Ashagrachew Tewabe Yayehrad, Anteneh Belete
   
6. Bio-induced overproduction of heterocycloanthracin-like bacteriocin in Lysinibacillus macroides by Aspergillus austroafricanus: optimization of medium conditions and evaluation of potential applications
   BMC Biotechnology volume 25, Article number: 41 (2025)
   Authors: Philomena Edet, Maurice Ekpenyong, Atim Asitok, David Ubi, Cecilia Echa, Uwamere Edeghor, Sylvester Antai
   
7. Structural characterization, gelling properties, and beef preservation applications of pectin extracted from sweetpotato residue using a hydrothermal method
   International Journal of Biological Macromolecules, Volume 314, 2025, 144348
   Authors: Linchong Hui, Chan Zhang, Junjie Yu, Man Liu, Kunlong Yang, Ling Shen, Bingqian Hu, Jun Tian, Yong-xin Li
   
8. Calibration of soil contact parameters for planting sand shrubs in the desert regions of Inner Mongolia
   Scientific Reports volume 15, Article number: 17231 (2025)
   Authors: Zhang Nannan, Pei Chenghui, Zhang Yantang, Cui Shaoyu, Liang Lingzhi, Liu Zhigang
   
9. Development of a novel tailor-made cocktail from recombinant crude enzymes for efficient saccharification of pretreated elephant grass
   International Journal of Biological Macromolecules, 26 May 2025, 144645
   Authors: Aishwarya Aishwarya, Arun Goyal
   
10. Sustainable discharge printing of marigold-dyed cotton with eucalyptus wood ash extract and its optimisation by response surface methodology
    Coloration Technology, first published: 27 May 2025
    Authors: Harshal Patil, Devansh Chaudhari, Ashok Athalye
    
11. Chitosan-coated nanostructured lipid carriers of amantadine for nose-to-brain delivery: formulation optimization, in vitro-ex vivo characterization, and in vivo anti-parkinsonism assessment
    International Journal of Biological Macromolecules, Volume 316, Part 2, June 2025, 144497
    Authors: Archita Kapoor, Abdul Hafeez, Poonam Kushwaha, Nargis Ara

Ideally all variables other than those included in an experiment are held constant or blocked out in a controlled fashion. However, sometimes a variable that one knows will create an important effect, such as ambient temperature or humidity, cannot be controlled. In such cases it pays to collect measurements run by run. Then the results can be analyzed with and without this ‘covariate.’

Douglas Montgomery provides a great example of analysis of covariance in section 15.3 of his textbook Design and Analysis of Experiments. It details a simple comparative experiment aimed at assessing the breaking strength in pounds of monofilament-fiber produced by three machines. The process engineer collected five samples at random from each machine, measuring the diameter of each (knowing this could affect the outcome) and testing them out. The results by machine are shown below with the diameters, measured in mils (thousandths of an inch), provided in the parentheses:

1. 36 (20), 41 (25), 39 (24), 42 (25), 49 (32)
2. 40 (22), 48 (28), 39 (22), 45 (30), 44 (28)
3. 35 (21), 37 (23), 42 (26), 34 (21), 32 (15)

The data on diameter can be easily captured via a second response column alongside the strength measures. Montgomery reports that “there is no reason to believe that machines produce fibers of different diameters.” Therefore, creating a new factor column, copying in the diameters and regressing out its impact on strength leads to a clearer view of the differences attributed to the machines.

I will now show you the procedure for handling a covariate with Stat-Ease software. However, before doing so, analyze the experiment as planned and save this work so you can do a before and after comparison.

Figure 1 illustrates how to insert a new factor. As seen in the screenshot, I recommend this be done before the first controlled factor.

The Edit Info dialog box then appears. Type in the name and units of measure for the covariate and the actual range from low to high.

Press “Yes” to confirm the change in actual values when the warning pops up.

After the new factor column appears, the rows will be crossed out. However, when you copy over the covariate data, the software stops being so ‘cross’ (pun intended).

Press ahead to the analysis. Include only the main effect of the covariate in your model. The remainder of the terms involving controlled factors may go beyond linear if estimable. As a start, select the same terms as done before adding the covariate.

In this case, the model must be linear due to there being only one factor (machine) and it being categorical. The p-value on the effect increases from 0.0442 (significant at p<0.05) with only the machine modeled—not the diameter—to 0.1181 (not significant!) with diameter included as a covariate. The story becomes even more interesting by viewing the effects plots.

You can see that the least significant difference (LSD) bars decrease considerably from Figure 4 to Figure 5 without and with the covariate; respectively. That is a good sign—the fitting becomes far more precise by taking diameter (the covariate) into account. However, as Montgomery says, the process engineer reaches “exactly the opposite conclusion”—Machine 3 looking very weak (literally!) without considering the monofilament diameter, but when doing the covariate analysis, it becomes more closely aligned with the other two machines.

In conclusion, this case illustrates the value of recording external variables run-by-run throughout your experiment whenever possible. They then can be studied via covariate analysis for a more precise model of your factors and their effects.

This case is a bit tricky due to the question of whether fiber strength by machine differs due to them producing differing diameters, in which case this should be modeled as the primary response. A far less problematic example would be an experiment investigating the drying time of different types of paint in an uncontrolled environment. Obviously, the type of paint does not affect the temperature or humidity. By recording ambient conditions, the coating researcher could then see if they varied greatly during the experiment and, if so, include the data on these uncontrolled variables in the model via covariate analysis. That would be very wise!

PS: Joe Carriere, a fellow consultant at Stat-Ease, suggested I discuss this topic—very appealing to me as a chemical process engineer. He found the monofilament machine example, which I found very helpful (also good by seeing agreement in statistical results between our software and the one used by Montgomery).

PPS: For more advice on covariates, see this topic Help.

Here's the latest Publication Roundup! In these monthly posts, we'll feature recent papers that cited Design-Expert® or Stat-Ease® 360 software. Please submit your paper to us if you haven't seen it featured yet!

Featured Article

Implementation of the QbD Approach to the Analytical Method Development and Validation for the Estimation of the Treprostinil Injection Dosage Form by RP-HPLC
ACS Omega, 2025
Authors: Narasimha Raju Alluri, Mallikharjuna Rao Bandlamudi, Sujatha Kuppusamy, Shabna Roupal Morais

Mark's comments: This one hits the spot for me by deploying a solid central composite design, being succinct in presenting only the most relevant statistics on significance and model fits, showing compelling 3D pictures, and providing the data via a link to supplementary material. It is great to see how response surface methods done with Stat-Ease software led to a “novel, precise, sensitive, stable, and cost-effective” analytical method. Well done!

Be sure to check out this important study, and the other research listed below!

More new publications from April

1. Optimisation of process parameters for lignocellulosic biomass degradation by Pseudomonas sp. using response surface methodology
   International Journal of Biological Macromolecules, Volume 309, Part 1, May 2025, 142792
   Authors: Sunder, Sangita Yadav, Jitender Pal
   
2. Quality by Design Based Chromatography Technique Development and Validation for the Medicine Venetoclax (for Chronic Leukemia), in the Context of Impurities Including Degradation Products
   Biomedical Chromatography, 39: e70072, 02 April 2025
   Authors: Rajeshwari Dandabattina, Karuna Sree Merugu, Lova Gani Raju Bandaru, Haridasyam Sharathbabu, Rambabu Gundla, Naresh Kumar Katari
   
3. Optimization of the Drying Parameters for Plantain Chips using a Locally Made Tray Dryer: A Study on Drying Efficiency and Drying Rate Modeling using RSM
   Journal of Food Technology & Nutrition Sciences, 7(2):1-10, April 2025
   Authors: Arinzechukwu Hipolite Madukasi, Ifeanyichukwu Ugochukwu Onyenanu
   
4. Optimization of low-temperature nitrogen plasma in reducing fungi and aflatoxin human exposure through maize
   Scientific Reports volume 15, Article number: 11707 (2025)
   Authors: Hannah Mugure Kamano, Michael Wandayi Okoth, Wambui Kogi-Makau, Patrick Wafula Kuloba, Joshua Ombaka Owade & Patrick Murigu Kamau Njage
   
5. Smart nanocomposite of carbon quantum dots in double hydrogel (carboxymethyl cellulose/chitosan) for effectively adsorb and remove diquat herbicide: Characterization, thermodynamics, isotherms, kinetics, and optimizing through Box-Behnken Design
   International Journal of Biological Macromolecules Volume 309, Part 1, May 2025, 142806
   Authors: Wesam Abd El-Fattah, Ahlem Guesmi, Naoufel Ben Hamadi, Mohamed G. El-Desouky, Ashraf A. El-Bindary
   
6. Green Analytical Stability Indicating UHPLC Method for the Quantification of Related Impurities in Vonoprazan Formulation Applying Analytical Quality by Design
   Separation Science Plus, Volume 8 Issue 4, April 2025, e70032
   Authors: Ashwinkumar Matta, Raja Sundararajan
   
7. Developing a Model for Reducing Carbon Emissions of Construction Heavy Machinery Through ECO-Hauling and Collaboration
   Proceedings of the International Conference on Smart and Sustainable Built Environment (SASBE 2024), pp 618–628, 20 April 2025
   Authors: Milad Hosseinzadeh Moghaddam, Ehsan Asnaashari, Amrit Sagoo
   
8. Enhanced Antibacterial Effect of pH/Gelatinase-Responsive Florfenicol Nanogels Against Staphylococcus aureus
   International Journal of Nanomedicine, 2025;20:5193-5208
   Authors: Nannan Leng, Jinhuan Liu, Yongtao Jiang, Ning Du, Ali Sobhy Dawood, Samah Attia Algharib, Wanhe Luo
   
9. Amphiphilic mPEG-PLGA copolymer nanoparticles co-delivering colistin and niclosamide to treat colistin-resistant Gram-negative bacteria infections
   Communications Biology volume 8, Article number: 673 (2025)
   Authors: Kaifang Yi, Xilong Wang, Pengliang Li, Yanling Gao, Dandan He, Yushan Pan, Xiaoyuan Ma, Gongzheng Hu, Yajun Zhai

Here's the latest Publication Roundup! In these monthly posts, we'll feature recent papers that cited Design-Expert® or Stat-Ease® 360 software. Please submit your paper to us if you haven't seen it featured yet!

Featured Article

Material-sparing degradation-kinetics model for thermolabile drug stability assessment during twin-screw melt granulation – insights with gabapentin
International Journal of Pharmaceutics, Volume 674, 15 April 2025, 125421
Authors: Adwait Pradhan, Fengyuan Yang, Kapish Karan, Thomas Durig, Quyen Schwing, Brian Haight, Mark Costello, Mark Anderson, Feng Zhang

Mark's comments: "It was a pleasure to help Adwait, et al apply response surface methods (RSM) for process optimization of twin-screw melt granulation to mininimze degradation of life-enhancing drugs such as gabapentin."

Be sure to check out this important study, and the other research listed below!

More new publications from March

1. RSM and AI based machine learning for quality by design development of rivaroxaban push-pull osmotic tablets and its PBPK modeling
   Scientific Reports volume 15, Article number: 7922 (2025)
   Authors: Muhammad Talha Saleem, Muhammad Harris Shoaib, Rabia Ismail Yousuf, Fahad Siddiqui
   
2. A Comprehensive QbD Study on Bioadhesive Ocular Films for Improved Conjunctivitis Management: Insights from Design Expert Software
   Indian Journal of Pharmaceutical Education and Research, 2025; 59(1): 122-133
   Authors: Repollu Maddileti, Haranath Chinthaginjala
   
3. Novel Ketoconazole-Loaded Niosomal Gel with Carbamide for Enhanced Topical Delivery and Skin Hydration in Fungal Infections
   Journal of Pharmaceutical Innovation, Volume 20, article number 46, (2025)
   Authors: Prajitha Biju, Manjunath M. Shenoy, Rouchelle Tellis, Ramesh Bhat, Ranajit Das, Ashwini Prabhu, Mohammed Gulzar Ahmed, Vivek Ghate
   
4. Development of Bread from Different Protein Isolates, Sweet potatoes (Lam Ipomea batata) and Wheat Flour Blends
   Journal of Health, Wellness and Safety Research, Vol. 7 2025
   Authors: Adelakun O. E, Aliyu F
   
5. Optimization of the process of acetylation and carboxymethylation for a polysaccharide from Gastrodia elata and antioxidant and immunomodulatory activities test
   Scientific Reports volume 15, Article number: 8460 (2025)
   Authors: Hao Guan, Wenjie Yin, Xue Zhang, Fangyun Zhao, Tanling Cai, Xi Ling
   
6. Optimization of durability characteristics of engineered cementitious composites combined with titanium dioxide as a nanomaterial applying RSM modelling
   Scientific Reports volume 15, Article number: 9428 (2025)
   Authors: Naraindas Bheel, Imran Mir Chohan, Ahmed Saleh Alraeeini, Mamdooh Alwetaishi, Sahl Abdullah Waheeb, Loai Alkhattabi, Omrane Benjeddou
   
7. Optimizing Foam Properties of Egg White Powder-Based Foam System by Response Surface Methodology
   Black Sea Journal of Agriculture, Year 2025, Volume: 8 Issue: 2, 217 - 224, 15.03.2025
   Authors: Mehmet Güldane
   
8. Leaching Parameters Optimization and Kinetic Studies for Leaching of Copper from Zarara Hill Sulphide Ore in HCl, H₂SO₄ and HNO₃ Solutions
   Journal of Science Innovation and Technology Research, 2025 7(9)
   Authors: Mustapha Mukhtar, K. I. Omoniyi, Faizuan Abdullah