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Chapter 16: One-Way Analysis of Variance
Figure 16-25:
Normality Plot for the Errors in
Example 16-12
Next we will present the theory behind the test for independence for the
errors.
Validating the Independence Assumption for the Model Errors
Recall we used the
Auto Correlation Function
workbook to compute the
errors for the model when we were testing for normality. We can also use
this
Auto Correlation Function
workbook to help to test for independence
of the errors.
The independence assumption can be tested using the 1-lag autocorrelation
function (ACF). An autocorrelation coefficient, which indicates how the
errors (residuals) are correlated with themselves, is often used to investigate
the independence assumption. To compute this value, denoted by
r
1
, we
correlate the observed residuals (in time series order) with the same errors
moved one position from the originals. Thus, the lag 1 autocorrelation is