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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Cronbach's alpha ： ウィキペディア英語版 Cronbach's alpha In statistics (Classical Test Theory), Cronbach's $\backslash alpha$ (alpha) is used as a (lowerbound) estimate of the reliability of a psychometric test. It has been proposed that $\backslash alpha$ can be viewed as the expected correlation of two tests that measure the same construct. By using this definition, it is implicitly assumed that the average correlation of a set of items is an accurate estimate of the average correlation of all items that pertain to a certain construct.〔Nunnally, J. C. (1978). Assessment of Reliability. In: Psychometric Theory (2nd ed.). New York: McGraw-Hill.〕 Cronbach's $\backslash alpha$ is a function of the number of items in a test, the average covariance between item-pairs, and the variance of the total score. It was first named alpha by Lee Cronbach in 1951, as he had intended to continue with further coefficients. The measure can be viewed as an extension of the Kuder–Richardson Formula 20 (KR-20), which is an equivalent measure for dichotomous items. Alpha is not robust against missing data. Several other Greek letters have been used by later researchers to designate other measures used in a similar context. Somewhat related is the average variance extracted (AVE). This article discusses the use of $\backslash alpha$ in psychology, but Cronbach's alpha statistic is widely used in the social sciences, business, nursing, and other disciplines. The term ''item'' is used throughout this article, but items could be anything—questions, raters, indicators—of which one might ask to what extent they "measure the same thing." Items that are manipulated are commonly referred to as ''variables''. ==Definition== Suppose that we measure a quantity which is a sum of $K$ components (''K-items'' or ''testlets''): $X\; =\; Y\_1\; +\; Y\_2\; +\; \backslash cdots\; +\; Y\_K$. Cronbach's $\backslash alpha$ is defined as :$$ \alpha = \left(1 - \over \sigma^2_X}\right) where $\backslash sigma^2\_X$ is the variance of the observed total test scores, and $\backslash sigma^2\_$ the variance of component ''i'' for the current sample of persons. If the items are scored 0 and 1, a shortcut formula is :$$ \alpha = \left(1 - Q_\over \sigma^2_X}\right) where $P\_i$ is the proportion scoring 1 on item ''i'', and $Q\_i\; =\; 1\; -\; P\_i$. This is the same as KR-20. Alternatively, Cronbach's $\backslash alpha$ can be defined as :$\backslash alpha\; =$ where $K$ is as above, $\backslash bar\; v$ the average variance of each component (item), and $\backslash bar\; c$ the average of all covariances between the components across the current sample of persons (that is, without including the variances of each component). The ''standardized Cronbach's alpha'' can be defined as :$\backslash alpha\_\backslash text\; =$ where $K$ is as above and $\backslash bar\; r$ the mean of the $K(K-1)/2$ non-redundant correlation coefficients (i.e., the mean of an upper triangular, or lower triangular, correlation matrix). Cronbach's $\backslash alpha$ is related conceptually to the Spearman–Brown prediction formula. Both arise from the basic classical test theory result that the reliability of test scores can be expressed as the ratio of the true-score and total-score (error plus true score) variances: :$\backslash rho\_=$ The theoretical value of alpha varies from zero to 1, since it is the ratio of two variances. However, depending on the estimation procedure used, estimates of alpha can take on any value less than or equal to 1, including negative values, although only positive values make sense.〔Ritter, N. (2010). "Understanding a widely misunderstood statistic: Cronbach's alpha". Paper presented at ''Southwestern Educational Research Association (SERA) Conference'' 2010: New Orleans, LA (ED526237).〕 Higher values of alpha are more desirable. Some professionals, as a rule of thumb, require a reliability of 0.70 or higher (obtained on a substantial sample) before they will use an instrument. Although Nunnally (1978) is often cited when it comes to this rule, he has actually never stated that 0.7 is a reasonable threshold in advanced research projects. And obviously, this rule should be applied with caution when $\backslash alpha$ has been computed from items that systematically violate its assumptions. Furthermore, the appropriate degree of reliability depends upon the use of the instrument. For example, an instrument designed to be used as part of a battery of tests may be intentionally designed to be as short as possible, and therefore somewhat less reliable. Other situations may require extremely precise measures with very high reliabilities. In the extreme case of a two-item test, the Spearman–Brown prediction formula is more appropriate than Cronbach's alpha. This has resulted in a wide variance of test reliability. In the case of psychometric tests, most fall within the range of 0.75 to 0.83 with at least one claiming a Cronbach's alpha above 0.90 (Nunnally 1978, page 245–246). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Cronbach's alpha」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.