مقايسه آزمون هاي همگني واريانس ها در طرح بلوكي كامل تصادفي

Comparison of Variances Homogeneity Tests in Randomized Complete Block Design

آزﻣﻮن ﻫﻤﮕﻨﯽ وارﯾﺎﻧﺲ ﻫﺎ اﻏﻠﺐ ﺑﻪ ﻋﻨﻮان ﯾﮏ آزﻣﻮن ﻣﻘﺪﻣﺎﺗﯽ ﺑﺮاي ﺗﺤﻠﯿﻞ ﻫﺎي دﯾﮕﺮ، ﻣﺜﻞ آزﻣﻮن ﺑﺮاﺑﺮي ﻣﯿﺎﻧﮕﯿﻦ ﻫﺎي ﺟﻮاﻣﻊ ﻣﻮرد اﺳﺘﻔﺎده ﻗﺮار ﻣﯽ ﮔﯿﺮد. ﺗﺎﮐﻨﻮن آزﻣﻮن ﻫﺎي ﻣﺘﻌﺪدي در ﻃﺮح ﺑﻠﻮﮐﯽ ﮐﺎﻣﻞ ﺗﺼﺎدﻓﯽ ﺑﻪ ﻣﻨﻈﻮر ﺑﻬﺒﻮد ﺗﻮان و اراﺋﻪ ي ﯾﮏ آزﻣﻮن اﺳﺘﻮار در ﺑﺮاﺑﺮ ﻓﺮض ﻧﺮﻣﺎل ﺑﻮدن اراﺋﻪ ﺷﺪه اﺳﺖ، ﮐﻪ راﯾﺞ ﺗﺮﯾﻦ آن ﻫﺎ آزﻣﻮن ﺑﺎرﺗﻠﺖ و ﻟﻮن ﺑﻮده و ﺑﻘﯿﻪ ﺗﻌﻤﯿﻤﯽ از اﯾﻦ دو آزﻣﻮن ﻫﺴﺘﻨﺪ. ﺗﻮزﯾﻊ آﻣﺎره ﻫﺎي اﯾﻦ آزﻣﻮن ﻫﺎ ﺑﻪ ﺻﻮرت ﻣﺠﺎﻧﺒﯽ ﻣﺤﺎﺳﺒﻪ ﻣﯽ ﺷﻮد. اﺧﯿﺮا آزﻣﻮﻧﯽ ﺑﺮاﺳﺎس ﺑﺮآورد ﻣﻘﺎدﯾﺮ ﺑﺤﺮاﻧﯽ ﻣﻌﺮﻓﯽ ﺷﺪه اﺳﺖ. در اﯾﻦ ﻣﻘﺎﻟﻪ ﺑﺎ اﺳﺘﻔﺎده از ﺷﺒﯿﻪ ﺳﺎزي روش ﺑﺮآورد ﻣﻘﺎدﯾﺮ ﺑﺤﺮاﻧﯽ را روي ﻧﻪ آزﻣﻮن ﻫﻤﮕﻨﯽ وارﯾﺎﻧﺲ ﻫﺎ اﻋﻤﺎل ﮐﺮده و ﻋﻤﻠﮑﺮد آن ﻫﺎ در ﺗﻮزﯾﻊ ﻫﺎي ﻧﺮﻣﺎل و ﺗﯽ ﺑﺎ ﺗﻌﺪاد ﮔﺮوه ﻫﺎي ﺗﯿﻤﺎري و ﺑﻠﻮﮐﯽ ﻣﺨﺘﻠﻒ ﺳﻨﺠﯿﺪه ﻣﯽ ﺷﻮد. ﻧﺘﺎﯾﺞ ﻧﺸﺎن ﻣﯽ دﻫﻨﺪ ﮐﻪ آزﻣﻮن ﻫﺎ ﺑﺮاﺳﺎس روش ﺑﺮآورد ﻣﻘﺎدﯾﺮ ﺑﺤﺮاﻧﯽ ﻋﻤﻠﮑﺮد ﺑﻬﺘﺮي از ﻟﺤﺎظ ﺣﻔﻆ ﻧﺮخ ﺧﻄﺎي ﻧﻮع اول و ﺗﻮان ﻧﺴﺒﺖ ﺑﻪ ﺣﺎﻟﺖ اﺳﺘﻔﺎده از ﺗﻮزﯾﻊ ﺗﻘﺮﯾﺒﯽ دارﻧﺪ.

Variances homogeneity test are mostly applied as a preliminary test to other analyses like test of equality of means. So far, several tests have been offered in randomized complete block design, that the most prevalent of them are Bartlett and Levene tests, and others are generalized kind of these two tests. The distribution of statistics for these tests are obtained asymptotically. Recently, a test has been introduced base on estimated critical values. In this paper, nine tests are examined based on estimated critical values method and their performance are evaluated with various blocks and treatment groups for normal and t-student distributions by a simulation study. The method of estimated critical values has a good performance in the type I error and a power improvement with respect to using asymptotic distribution.