Kempthorne uses the randomization-distribution and the assumption of * unit treatment additivity* to produce a * derived linear model* , very similar to the textbook model discussed previously. [29] The test statistics of this derived linear model are closely approximated by the test statistics of an appropriate normal linear model, according to approximation theorems and simulation studies. [30] However, there are differences. For example, the randomization-based analysis results in a small but (strictly) negative correlation between the observations. [31] [32] In the randomization-based analysis, there is * no assumption* of a * normal* distribution and certainly * no assumption* of * independence* . On the contrary, * the observations are dependent* !

Beside the professional statistical software Online statistical computation , and the use of a scientific calculator is required for the course. A Scientific Calculator is the one, which has capability to give you, say, the result of square root of 5. Any calculator that goes beyond the 4 operations is fine for this course. These calculators allow you to perform simple calculations you need in this course, for example, enabling you to take square root, to raise e to the power of say, . and so on. These types of calculators are called general Scientific Calculators. There are also more specific and advanced calculators for mathematical computations in other areas such as Finance, Accounting, and even Statistics. The last one, for example, computes mean, variance, skewness, and kurtosis of a sample by simply entering all data one-by-one and then pressing any of the mean, variance, skewness, and kurtosis keys.