史培曼假說新詮

Some New Results on Spearman's Hypothesis

Spearmen（1927）發現智力分測驗在最主要特徵向量上的負載值，和黑白不同人種群體分測驗平均數差距之間呈現正相關：Jensen在後續文章中引述此一發現，並聲稱正相關證實智力中的g因子和黑白人種差異之間存在著密切關聯。然而智力分測驗得分數據只要彼此呈現正相關，且接近多元常態分配就會得到Spearman的結果，和智力g因子或人種差異毫無關聯。此一論點可藉由理論證明、電腦模擬研究、及分析Jensen使用過的數據而得到支持。然而有些文獻依舊質疑此一論點；例如，Steiger（1977）在並充足無證據的情況下宣稱多元常態假設並不適用於Jensen所使用的數據。本文主要證明多元常態分配相對於Steiger所建議的分配模式更適合解釋Jensen的數據。本文最後並重新證明餘弦（cosine）和統計相關之間的關聯，且藉此重新詮釋Spearman假說。

In a number of publications, Jensen has recalled Spearman's (1927) observation that, for Black/White IQ data, the loadings on the dominant eigenvectors (Note 1) in each battery tend to correlate positively with the subtest mean differences ('Spearman's Hypothesis', Level II). According to Jensen, these positive correlations confirm the existence of a general intelligence factor ('g') closely related to Black/White IQ differences. The present author has argued that these positive correlations can be explained as a simple consequence of the multinormality and positivity of IQ data, and thus have nothing to do with race or g. This thesis is supported by algebraic deduction, by geometric argument, by computer simulations, and, indeed, by Jensen's own data. Some authors have challenged this account, most recently Steiger (1997). He contends the needed multinormality assumption is unwarranted for Jensen's data -without, however, providing any evidence to support this claim (Note 9). Here it will be shown that, in fact, Jensen's data fit the multinormality assumption much better than an alternative model ('I') Steiger has proposed. Finally, a new result relating cosines and correlations will be presented, which sheds additional light on the Spearman Hypothesis artefact in the fallible case.