克隆巴赫(信度)系数(Cronbach's alpha)

克隆巴赫（信度）系数（Cronbach's alpha），是心理或教育测验中最常用的信度评估信度工具。其依据一定公式估量测验内部的一致性，作为信度的指标。克服部分折半法的缺点，是目前社会研究最常使用的信度指标，它是测量一组同义或平行测“总和”的信度。

克隆巴赫系数公式α﹦（n/ n-1）(1-∑S i2/S t2)

α为信度系数，n为测验题目数，S2i为每题各被试得分的方差，S2t为所有被试所得总分的方差。

一般来说，该系数愈高，即工具的信度愈高。在基础研究中，信度至少应达到0.80 才可接受，在探索性研究中，信度只要达到0.70 就可接受，介于0.70－0.98 均属高信度,而低于0.35 则为低信度，必须予以拒绝。

SPSS FAQ

What does Cronbach's alpha mean?

Cronbach's alpha is a measure of internal consistency, that is, how closely related a set of items are as a group. A "high" value of alpha is often used (along with substantive arguments and possibly other statistical measures) as evidence that the items measure an underlying (or latent) construct. However, a high alpha does not imply that the measure is unidimensional. If, in addition to measuring internal consistency, you wish to provide evidence that the scale in question is unidimensional, additional analyses can be performed. Exploratory factor analysis is one method of checking dimensionality. Technically speaking, Cronbach's alpha is not a statistical test - it is a coefficient of reliability (or consistency).

Cronbach's alpha can be written as a function of the number of test items and the average inter-correlation among the items. Below, for conceptual purposes, we show the formula for the standardized Cronbach's alpha:

Here N is equal to the number of items, c-bar is the average inter-item covariance among the items and v-bar equals the average variance.

One can see from this formula that if you increase the number of items, you increase Cronbach's alpha. Additionally, if the average inter-item correlation

is low, alpha will be low. As the average inter-item correlation increases, Cronbach's alpha increases as well (holding the number of items constant).

An example

Let's work through an example of how to compute Cronbach's alpha

using SPSS, and how to check the dimensionality of the scale using factor analysis. For this example, we will use a dataset that contains four test items - q1, q2, q3 and q4. You can download the dataset by clicking on alpha.sav. To compute Cronbach's alpha for all four items - q1, q2, q3, q4 - use

the reliability command:

RELIABILITY

/VARIABLES=q1 q2 q3 q4.

Here is the resulting output from the above syntax:

The alpha coefficient for the four items is .839, suggesting that the items have relatively high internal consistency. (Note that a reliability coefficient of .70or higher is considered "acceptable" in most social science research situations.)

In addition to computing the alpha coefficient of reliability, we might also want to investigate the dimensionality of the scale. We can use the factor command to do this:

FACTOR

/VARIABLES q1 q2 q3 q4

/FORMAT SORT BLANK(.35).

Here is the resulting output from the above syntax:

Looking at the table labeled Total Variance Explained, we see that the eigen value for the first factor is quite a bit larger than the eigan value for the next factor (2.7 vs. 0.54). Additionally, the first factor accounts for 67% of the total variance. This suggests that the scale items are unidimensional.