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題 名 | Permutation Tests for Difference between Two Multivariate Allometric Patterns=利用置換排列法檢定兩多變量異速成長型式間之差異 |
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作 者 | 曾宗德; 葉顯椏; | 書刊名 | 動物研究學刊 |
卷 期 | 38:1 1999.01[民88.01] |
頁 次 | 頁10-18 |
分類號 | 439.2 |
關鍵詞 | 第一主成份向量; 角度; 異速成長; 重新排列; First eigenvector; Angle; Allometry; Reorder; |
語 文 | 英文(English) |
中文摘要 | 研究不同性別、不同種、同種不同成長階段或不同地理族群間之多變量異速成 長的比較漸漸增加。某些多變量統計方法假設被分析的各群具有相同之異速成長型態。因 此在無檢視或比較各群之異速成長型式是否相同前,不應使用這類之方法。目前已有多個 方法被使用來比較兩異速成長型式間之關係,但這些方法皆缺少一客觀之理論判定兩多變 量異速成長型式是否相同或相異。本研究引用置換排列法以檢定兩多變量異速成長形式間 之差異是否具有統計之顯著性,並引用四個例子加以解釋及測訊本法之能力。多變量異速 成長型式係以變數經對數轉換後之共變方矩陣為資料,再以主成份分析所得之第一特徵向 量估計而得。利用兩第一主成份向量間之角度,當檢定的統計值。每一例子,執行5000次 之隨機排列分析,藉以評估其顯著水準。最後並檢驗兩樣本數目間之差異是否會對此方法 造成影響。結果顯示,第一主成份特徵值皆能解釋絕大部分的變異:第一主成份同量而皆 能充分描述其多變量異速成長型式。四個例子中,不論異速成長型式是相同或有差異皆可 被本法成功測出。因此,重複排列分析法可客觀之判定兩多變量異速成長形式差異之顯著 性,雖然此方法對樣本數目間之差異並不敏感,但我們仍建議當使用這方法時,儘量將兩 樣本數的差異減至最小。 |
英文摘要 | Permutation tests for difference between two multivariate allometric patterns. Zoological Studies 38(l): 10-18. Studies that include comparisons of multivariate allometric patterns between sexes, species, discrete growth stages, or geographic populations have gradually increased. Some statistical methods assume that compared groups share the same multivariate allometric pattern, so comparisons of multivariate allometric patterns also have to be performed before using these methods. Several methods have been used to detect the difference between 2 multivariate allometric patterns, but these methods lack an objective guide to test whether the 2 multivariate allometric patterns are the same or not. In this study, a permutation test was used to determine whether the difference of 2 patterns was significant or not. Four examples were used to explain and verify this test. The muitivariate allometric pattern was estimated by the l st eigenvector of the sample covariance matrix of the logarithmic measurement. The angle between the 2 first eigenvectors was taken as the test statistic. For each example, 5000 permutations were performed to assess the significance level. Finally, the effect of sample size difference on the permutation test was also examined. We found that all 1st eigenvalues explained the largest part of total variance and all 1st eigenvectors can satisfactorily interpret the multivariate allometric patterns. These tests can successfully detect the relationship between 2 multivariate allometric patterns in each example, so they can be a tool to test whether the difference of 2 multivariate allometric patterns is significant or not. Although this method is not sensitive to sample size differences, we still suggest that the sample size difference be as small as possible when using permutation tests to address this question. |
本系統中英文摘要資訊取自各篇刊載內容。