(1) Experimental designs involving factorial combination of multiple independent variables call for some inventiveness when it comes to graphical presentation of data.(2) One possible approach to make this search more systematic is the use of factorial design, which involves a set of experiments intended to identify important effects and interactions.(3) Around 1926, a British statistician, Ronald Fisher, while working in the field of agriculture, developed a new form of experimentation called two-level factorial design.(4) ‘A factorial is the product of consecutive numbers from 1 to that particular digit and is represented by placing a‘!’(5) The experiment was a completely randomized design, with eight treatment combinations, forming a 4 x 2 factorial (four clones and two watering regimes) with five plants in individual pots per treatment combination as replication.(6) They learned of each other's discoveries because each of them communicated his work to James Stirling, whose approximation for the factorial is a special case of the Euler-Maclaurin summation.(7) Our trial was of factorial design in order to compare three types of treatment within a single trial, in order to derive the maximum amount of data from the minimum number of patients.(8) A 2 x 4 x 12 factorial design was used to assess the effects of light, temperature and month, respectively, on the germination of Spergularia marina seeds.(9) The shortened 18-item scale is both more reliable and more factorially pure than the original 25-item measure with which it correlates at a.93 level.(10) These two two-level treatments were combined factorially , leading to the following four combinations.(11) Now Stirling's formula is a classical approximation for the factorial function, and factorials are one way to evaluate binomial coefficients.(12) Three stimulus frequencies were combined factorially with two input channels (left and right ears) and three measurement procedures.(13) In the proof below, we use the fact that e is the sum of the series of inverted factorials .(14) Stirling wrote to De Moivre pointing out some errors that he had made in a table of logarithms of factorials in the book.(15) The gamma function is undefined for zero and negative integers, from which we can conclude that factorials of negative integers do not exist.(16) The investigation of factorially simple tasks, which are not especially cognitively demanding, has prompted hopes of arriving at a definition of intelligence that is both precise and explanatory.
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