The problem of testing the composite hypothesis of normality is considered for complete samples. Three related test procedures are developed. The testing procedures have their origins in an attempt to formalize the appearance of nonlinearity in probability plots. The fitting of the ordered observations is accomplished by general linear least squares using the expected values of the standard normal order statistics (snos) as plotting positions. The moments of the snos have been approximated where necessary. The test statistics are ratios involving the squares of linear combinations of order statistics and the usual quadratic estimate of the variance. The percentage points ofthe test statistics aregenerally intractable by analytical methods. However percentage points are estimated using simulation techniques. The test procedures are compared to nine other tests of the composite hypothesis of normality in an empirical power study.