Graph description: Figure 6. Histograms and Normal plots for the within-group residuals for the raw PSA data and the log transformed PSA data

Four graphs, a histogram of Residual PSA with superimposed Normal distribution curve, a Normal plot for Residual PSA, a histogram of Residual log PSA with superimposed Normal distribution curve, and a Normal plot for Residual log PSA.

The histogram of Residual PSA shows great positive skewness. Most of the area of the histogram is between Residual PSA = -100 and Residual PSA = +100. There are very short bars going out to Residual PSA = -600 and Residual PSA = +500. There is one bar at Residual PSA = +1600 to +1700. The Normal distribution curve is quite different from the histogram.

The Normal plot of Residual PSA has Residual PSA on the vertical axis and Inverse Normal on the horizontal axis. The line of points curves upwards very strongly. The points are above the straight line of perfect Normal distribution for low Residual PSA, and at the low Residual PSA end the line of points is almost horizontal. The line of points goes below the straight line in the middle of the range of Residual PSA, where it bends sharply and then rises steeply above the straight line for high Residual PSA.

The histogram of Residual log PSA shows a very small amount of positive skewness and tails which are slightly longer than the corresponding Normal distribution curve.

The Normal plot of Residual log PSA has Residual log PSA on the vertical axis and Inverse Normal on the horizontal axis. The line of points starts below the straight line and rises rapidly to meet it and rise just above it. The points then fall just below the line in the middle of the range of Residual log PSA, and rise above the line for high Residual log PSA.