The suggested threshold to reduce data noise for a factorial experiment

Document Type : Research Paper


1 Department of Statistics and Informatics, Mosul University, Iraq

2 Department of Statistics, Baghdad University, Iraq


In this research, a factorial experiment (4*4) was studied, applied in a completely random block design, with a size of $2^5$ observations, where the design of experiments is used to study the effect of transactions on experimental units and thus obtain data representing experiment observations that  The difference in the application of these transactions under different environmental and experimental conditions It causes noise that affects the observation value and thus an increase in the mean square error of the experiment, and to reduce this noise, multiple wavelet reduction was used as a filter for the observations by suggesting an improved threshold that takes into account the different transformation levels based on the logarithm of the base $J$  and obtaining several values for the suggested threshold and applying then Haar wavelet function With the cut-off hard and mid threshold and Comparing the results according to several criteria.


[1] C. Cheng, Theory of Factorial Design Single- and Multi-Stratum Experiments, Taylor & Francis Group, LLC., 2014.
[2] L. Daniels and N. Minot, An Introduction to Statistics and Data Analysis Using Stata, From Research Design to Final Report. Sage Publications, 2019.
[3] B. Dehda and K. Melkemi, Image denoising using new wavelet thresholding function, J. Appl. Math. Comput. Mech. 16(2) (2017) 55–65.
[4] A. Dixit and S. Majumdar, Comparative analysis of conflict and Daubechies wavelets using global threshold for image denoising, Int. J. Adv. Engin. Technol. 6(5) (2013) 2247.
[5] R. Gen¸cay, F. Sel¸cuk and B.J. Whitcher, An Introduction to Wavelets and Other Filtering Methods in Finance and Economics, Elsevier, 2001.
[6] A.S. Hamad, Using Some Thresholding Rules in Wavelet Shrinkage to Denoise Signals for Simple Regression with Application in Rezgary Hospital–Erbil, Doctoral dissertation, PhD. dissertation in statistics, college of Administration and Economic, university of Sulaimania, Iraq, 2010.
[7] C. He, J. C. Xing and Q. L. Yang, Optimal Wavelet Basis Selection for Wavelet Denoising of Structural Vibration Signal, Applied Mechanics and Materials, Vol. 578. Trans Tech Publications Ltd, 2014.
[8] C. He, J. C. Xing, Q. L. Yang and R. Wang, A new wavelet threshold determination method considering interscale correlation in signal denoising, Math. Prob. Engin. 2015 (2015).
[9] R. Hoshmand, Design of experiments for agriculture and the natural sciences, Second Edition, CRC Press, 2006.
[10] H. M. Kaltenbach, Statistical Design and Analysis of Biological Experiments, Springer, 2021.
[11] J. Lawson, Design and Analysis of Experiments with SAS, Chapman and Hall/CRC, 2010.
[12] J. Lawson, Design and Analysis of Experiments with R, CRC Press, 2014.
[13] C.C. Liu, T.Y. Sun, S.J. Tsai, Y.H. Yu and S.T. Hsieh, Heuristic wavelet shrinkage for denoising, Appl. Soft Comput. 1(1) (2011), 256–264.
[14] D.C. Montgomery, Design and Analysis of Experiments, John Wiley & sons, 2017.
[15] P. G. Nason, Wavelet Methods in Statistics with R, New York, Springer, 2008.
[16] J.P. Queen, G.P. Quinn and M.J. Keough, Experimental Design and Aata Analysis for Biologists, Cambridge University Press, 2002.
[17] J. Reid and C. Reading, Developing a framework for reasoning about explained and unexplained variation, Data and context in statistics education: Towards an evidence-based society, 2010
[18] P.R. Tammireddy and R. Tammu, Image Reconstruction Using Wavelet Transform with Extended Fractional Fourier Transform, Msc. Thesis, 2014.
[19] A. Zaeni, T. Kasnalestari and U. Khayam, Application of wavelet transformation symlet type and conflict type for partial discharge signals denoising, 5th Int. Conf. Electric Vehicular Technol. (ICEVT), IEEE, 2018, pp. 78-82.
[20] Y. Zhang, H. Zhou, Y. Dong and L. Wang, Restraining EMI of displacement sensors based on wavelet fuzzy threshold denoising, Signal Inf. Process. Network. Comput. pp. 543-551. Springer, Singapore, 2021.
Volume 13, Issue 1
March 2022
Pages 3861-3872
  • Receive Date: 06 November 2021
  • Revise Date: 22 December 2021
  • Accept Date: 01 February 2022