The Gaussian assumption is easy to apply to economic analyses and many of its properties have been revealed to economists so that the distributional hypothesis has been embraced in economic and financial analyses, despite the fact that empirical evidences show distinct anomalies from the normal distribution. This study shows that the distributions of major U.S. agricultural commodity cash price changes are significantly different from normality. They have fatter tails and hither peaks than the normal distribution. The leptokurtic behaviors of the cash price changes are effectively captured by the stable distribution rather than the normal distribution. At the same time, when real data correspond to the stable distribution, variance may not be an effective scale parameter of the data. This raises a necessity of finding other alternatives to the traditional second moment.