Parallel and strictly parallel

1. To compute the parallel model, recall the Reliability Analysis dialog box.

   

2. Select Parallel as the model.
3. Click OK.

Parallel and strictly parallel are models that allow you to statistically test for equal means and variances ^{1 2}. The strictly parallel model hypothesizes that the true item scores have the same mean and variance, while the parallel model hypothesizes that they have the same variance but not necessarily the same mean. Note that elsewhere the strictly parallel model is simply known as the parallel model, and the parallel model is not often discussed.

If the significance value of the test is greater than 0.05, this indicates that there is no statistically evident reason to reject that hypothesis. The significance value for the parallel model is smaller than 0.0001, which is far less than the cutoff of 0.05; therefore, we must reject the hypothesis of the parallel model. Notice that the reliability estimate for the parallel model is equivalent to Cronbach's alpha (the estimate for the strictly parallel model is also based on Cronbach's alpha but is penalized for differences in the item means). Because the parallel model has been rejected, you know that the strictly parallel model will be rejected because the models are nested; that is, the assumptions of the parallel model are a subset of the assumptions of the strictly parallel model. Few data sets will actually satisfy the requirements of the parallel and strictly parallel models, but these models are still worth considering because they provide variance estimates unavailable in the previous models.

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