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Two Factor Data Analysis with Unequal Cell Frequencies and Interaction

Received: 18 November 2015     Accepted: 5 December 2015     Published: 25 December 2015
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Abstract

This paper proposes a non parametric method for two factor data analysis with unequal cell frequencies and interaction. Chi-square test statistic was developed for testing the null hypothesis of no treatment effect and interaction between factor A and factor B. The proposed methods are illustrated with some data and compared with the usual unweighted mean method. The result showed that the proposed method is more powerful than the method of unweighted mean.

Published in Science Journal of Applied Mathematics and Statistics (Volume 3, Issue 6)
DOI 10.11648/j.sjams.20150306.18
Page(s) 288-292
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Cell Frequency, Interaction, Chi-square, Unweighted Mean, Ranking, Tied Observation

References
[1] Eze, F. C. and Chigbu P. E., (2012), Unbalanced Two-way Random Model with Integer-Valued Degrees of Freedom, Journal of Natural Sciences Research Vol. 2, No 10, pp 100 – 107.
[2] Hogg R. V., Mackean, J. W. and Craig, A. T. (2005), Introduction to Mathematical Statistics, 5th Edition, Prentice Hall New Jersey.
[3] Howell D. C., (2008) The Analysis of Missing Data, in Outhwaite, W and Turner S., Handbook of Social Science Methodology, London, Sage.
[4] Little, R. J. A and Rubin, D. B., (2002), Statistical Analysis with Missing Data, Second Edition, Hoboken, Wiley.
[5] Malwane M. A. and Samaradasa W., (1997) Two-way ANOVA with unequal cell frequencies and Unequal Variances, Statistica Sinica vol. &, 631 – 646.
[6] Montgomery D. C. (2001), Design and Analysis of Experiment, John Wiley and Sons, NewYork, 3rd Edition.
[7] Montgomery, D. C. and Peck, E. A., (1982), Introduction to Linear Regression Analysis, John Wiley New York.
[8] Neter J, Kutner M. A. Nachtshein and Wasserman W. (1996), Applied Linear Statistical Models, Graw Hill, USA.
[9] Oyeka I. C. A (2009), Applied Statistical Methods in Sciences, Norben Avocation Publishers, Enugu, Nigeria.
[10] Oyeka, I. C. A, Uzuke, C. A., obiora-Ilouno, H. O. and Maduakor, C. O., (2012), A Non Parametric Two-way Analysis of Variance with un equal observations per cell, Journal of Nigerian Statistical association, Vol. 24, pp 59 – 66.
Cite This Article
  • APA Style

    Chinwendu Alice Uzuke, Ikewelugo Cyprian Anene Oyeka, Happiness Onyebuchi Obiora-Ilouno. (2015). Two Factor Data Analysis with Unequal Cell Frequencies and Interaction. Science Journal of Applied Mathematics and Statistics, 3(6), 288-292. https://doi.org/10.11648/j.sjams.20150306.18

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    ACS Style

    Chinwendu Alice Uzuke; Ikewelugo Cyprian Anene Oyeka; Happiness Onyebuchi Obiora-Ilouno. Two Factor Data Analysis with Unequal Cell Frequencies and Interaction. Sci. J. Appl. Math. Stat. 2015, 3(6), 288-292. doi: 10.11648/j.sjams.20150306.18

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    AMA Style

    Chinwendu Alice Uzuke, Ikewelugo Cyprian Anene Oyeka, Happiness Onyebuchi Obiora-Ilouno. Two Factor Data Analysis with Unequal Cell Frequencies and Interaction. Sci J Appl Math Stat. 2015;3(6):288-292. doi: 10.11648/j.sjams.20150306.18

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  • @article{10.11648/j.sjams.20150306.18,
      author = {Chinwendu Alice Uzuke and Ikewelugo Cyprian Anene Oyeka and Happiness Onyebuchi Obiora-Ilouno},
      title = {Two Factor Data Analysis with Unequal Cell Frequencies and Interaction},
      journal = {Science Journal of Applied Mathematics and Statistics},
      volume = {3},
      number = {6},
      pages = {288-292},
      doi = {10.11648/j.sjams.20150306.18},
      url = {https://doi.org/10.11648/j.sjams.20150306.18},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20150306.18},
      abstract = {This paper proposes a non parametric method for two factor data analysis with unequal cell frequencies and interaction. Chi-square test statistic was developed for testing the null hypothesis of no treatment effect and interaction between factor A and factor B. The proposed methods are illustrated with some data and compared with the usual unweighted mean method. The result showed that the proposed method is more powerful than the method of unweighted mean.},
     year = {2015}
    }
    

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  • TY  - JOUR
    T1  - Two Factor Data Analysis with Unequal Cell Frequencies and Interaction
    AU  - Chinwendu Alice Uzuke
    AU  - Ikewelugo Cyprian Anene Oyeka
    AU  - Happiness Onyebuchi Obiora-Ilouno
    Y1  - 2015/12/25
    PY  - 2015
    N1  - https://doi.org/10.11648/j.sjams.20150306.18
    DO  - 10.11648/j.sjams.20150306.18
    T2  - Science Journal of Applied Mathematics and Statistics
    JF  - Science Journal of Applied Mathematics and Statistics
    JO  - Science Journal of Applied Mathematics and Statistics
    SP  - 288
    EP  - 292
    PB  - Science Publishing Group
    SN  - 2376-9513
    UR  - https://doi.org/10.11648/j.sjams.20150306.18
    AB  - This paper proposes a non parametric method for two factor data analysis with unequal cell frequencies and interaction. Chi-square test statistic was developed for testing the null hypothesis of no treatment effect and interaction between factor A and factor B. The proposed methods are illustrated with some data and compared with the usual unweighted mean method. The result showed that the proposed method is more powerful than the method of unweighted mean.
    VL  - 3
    IS  - 6
    ER  - 

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Author Information
  • Department of Statistics, Faculty of Physical Sciences, Nnamdi Azikiwe University, Awka, Nigeria

  • Department of Statistics, Faculty of Physical Sciences, Nnamdi Azikiwe University, Awka, Nigeria

  • Department of Statistics, Faculty of Physical Sciences, Nnamdi Azikiwe University, Awka, Nigeria

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