聯合國宣布2010年為「國際生物多樣性年」，以彰顯地球上生命的千姿百態，生物學家時常將生物多樣性定義為「基因、物種及一個地區的生態系統之整體」，由此可知生物多樣性的重要。本研究專注於基因相等性來比較兩基因多樣性指標，特別是核苷酸多樣性指標。傳統多樣性估計忽略了沒有找到的基因類型，當這個基因是一種不可忽略的基因序列時會造成低估基因多樣性的結果。
因此，我們合併Horvitz-Thompson方法及採樣覆蓋範圍的觀念來獲取較佳的基因多樣性估計式，接著利用估計式及two one-sided檢定方法來檢定相等性。利用模擬研究來計算型I誤差發生機率及檢定力。此外在小樣本下，也利用拔靴法和two one-sided方法的結果來比較他們之間型I誤差發生機率及檢定力的差異。

The United Nations marked 2010 as the International Year of Biodiversity - the variety of life on Earth 2010. Biologists often define biodiversity as the "totality of genes, species, and ecosystems of a region". It is clear that the importance of biodiversity. This study is concerned with the equivalence for multi-categorical data and focuses on gene comparison by some genetic diversity index, especially in nucleotide diversity index. The traditional estimator of diversity ignores the missing gene types result in to underestimate the gene diversity, when there is a non-negligible number of unseen genetic sequence. Therefore we combine the concept of Horvitz-Thompson and sample coverage to obtain the better genetic diversity estimator. Then we use the estimator and two one-sided test method to test the equivalence. A simulation study was conducted to empirically investigate the size and power of the proposed methods. Besides, a bootstrap-based approach is also proposed in small sample size and compared with the two one-sided test by the size and power.

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