Section 7.7: Checking for Normality and Normalizing Transformations

Normal Probability Plot – is a scatterplot of the (normal score, observed value) pairs. A substantial linear pattern in a normal probability plot suggests that population normality is plausible. On the other hand, a systematic departure from a straight-line pattern (such as curvature in the plot) casts doubt on the reasonableness of assuming a normal population distribution.

Example The following 10 observations are widths of contact windows in integrated circuit chips: 3.21 2.49 2.94 4.38 4.02 3.62 3.30 2.85 3.34 3.81 10 pairs are: (-1.539, 2.49), (-1.001, 2.85), (-0.656, 2.94), (-0.376, 3.21), (-0.123, 3.30), (0.123, 3.34), (0.376, 3.62), (0.656, 3.81), (1.001, 4.02), (1.539, 4.38)

The normal probability plot

Values to which r can be compared to check for normality* If r < critical r for corresponding n considerable doubt is cast on the assumption of population normality. Values to which r can be compared to check for normality* N 5 10 15 20 25 30 40 50 60 75 Critical R .832 .880 .911 .929 .941 .949 .960 .966 .971 .976