تحليل استوار واريانس بر اساس توزيع جايگشتي ميانگين پيراسته

Robust Analysis of Variance based on Permutation Distribution of Trimmed Mean

ﺳﺎﺧﺘﺎر آزﻣﻮن ﺗﺤﻠﯿﻞ وارﯾﺎﻧﺲ ﺑﻪ ﮔﻮﻧﻪ اي اﺳﺖ ﮐﻪ در ﺻﻮرت ﺣﻀﻮر داده ﻫﺎي دوراﻓﺘﺎده در ﺑﯿﻦ ﻣﺸﺎﻫﺪات، ﻧﺘﺎﯾﺞ آزﻣﻮن ﻣﯽ ﺗﻮاﻧﺪ ﺑﻪ اﺷﺘﺒﺎه ﻣﻨﺠﺮ ﺑﻪ رد ﯾﺎ ﭘﺬﯾﺮش ﻓﺮض ﺻﻔﺮ ﺷﻮد. در اﯾﻦ ﻣﻘﺎﻟﻪ، روش اﺳﺘﻮار ﺗﻮزﯾﻊ ﺟﺎﯾﮕﺸﺘﯽ آﻣﺎرهF ﺑﺮ اﺳﺎس ﻣﯿﺎﻧﮕﯿﻦ ﭘﯿﺮاﺳﺘﻪ ﭘﯿﺸﻨﻬﺎدﺷﺪه اﺳﺖ. اﯾﻦ روش، ﺑﻪ ﮐﻤﮏ ﺗﻮزﯾﻊ ﺟﺎﯾﮕﺸﺘﯽ􀀁 ﺗﺎﺑﻌﯽ از ﻣﯿﺎﻧﮕﯿﻦ ﭘﯿﺮاﺳﺘﻪ، ﺣﺴﺎﺳﯿﺖ ﻧﺴﺒﺖ ﺑﻪ ﻓﺮض ﻫﺎي ﮐﻼﺳﯿﮏ ﻫﻤﭽﻮن ﻧﺮﻣﺎل ﺑﻮدن داده ﻫﺎ و ﺣﻀﻮر داده ﻫﺎي دوراﻓﺘﺎده را ﮐﺎﻫﺶ داده و اﻋﺘﺒﺎر ﻧﺘﺎﯾﺞ ﺣﺎﺻﻞ را ﺗﻀﻤﯿﻦ ﻣﯽ ﮐﻨﺪ. روش ﭘﯿﺸﻨﻬﺎدي ﺑﺎ روش ﺗﺤﻠﯿﻞ اﺳﺘﻮار وارﯾﺎﻧﺲ ﺑﺮ اﺳﺎس رﻫﯿﺎﻓﺖ ﺟﺴﺘﺠﻮي ﭘﯿﺸﺮو ﻣﻘﺎﯾﺴﻪ ﻣﯽ ﺷﻮد. روش اراﺋﻪ ﺷﺪه ﺑﺮﺧﻼف روش ﻣﺒﺘﻨﯽ ﺑﺮ ﺟﺴﺘﺠﻮي ﭘﯿﺸﺮو، ﻣﺎ را از ﻓﺮﺿﯿﺎت ﻣﺤﺪودﮐﻨﻨﺪه ﭘﺎراﻣﺘﺮي ﺑﯽ ﻧﯿﺎز و ازﻧﻈﺮ ﻣﺤﺎﺳﺒﺎﺗﯽ زﻣﺎن ﮐﻤﺘﺮي را ﺻﺮف ﻣﯽ ﮐﻨﺪ. ﻧﺘﺎﯾﺞ ﺑﺮرﺳﯽ ﻫﺎي ﻋﺪدي روي ﺧﻄﺎي ﻧﻮع اول و ﺗﻮان آزﻣﻮن، ﺣﮑﺎﯾﺖ از ﻋﻤﻠﮑﺮد ﺧﻮب اﯾﻦ روش اﺳﺘﻮار در ﻣﻘﺎﯾﺴﻪ ﺑﺎ روش رﻗﯿﺐ دارد.

The presence of outliers in data set may affect structure of analysis of variance test so that test results led to wrong acceptance or rejection of null hypothesis. In this paper the method of robust permutation distribution of F statistic based on trimmed mean is proposed. This method by permutation distribution of a function of trimmed mean, reduces the sensitivity to classical assumptions such as normality and presence of outlier and it guarantees the reliability of result. The proposed method is compared with robust analysis of variance based of forward search approach. The proposed method, unlike the forward search-based approach is free of restricted parametric assumptions and computationally spend less time. Numerically assessment results on type I error and power of test, demonstrate good performance of this robust method in comparison with competitor method.