Search results
Results from the WOW.Com Content Network
This experiment is an example of a 2 2 (or 2×2) factorial experiment, so named because it considers two levels (the base) for each of two factors (the power or superscript), or #levels #factors, producing 2 2 =4 factorial points. Cube plot for factorial design . Designs can involve many independent variables.
2: 2 3: 6 4: 24 5: 120 6: 720 7: 5 040: 8: 40 320: 9: 362 880: 10: 3 628 800: 11: 39 916 800: 12: 479 001 600: 13: 6 227 020 800: 14: 87 178 291 200: 15: 1 307 674 368 000: 16: 20 922 789 888 000: 17: 355 687 428 096 000: 18: 6 402 373 705 728 000: 19: 121 645 100 408 832 000: 20: 2 432 902 008 176 640 000: 25 1.551 121 004 × 10 25: 50 3.041 ...
2.4 Modified-factorial denominators. 2.5 Binomial coefficients. 2.6 Harmonic numbers. 3 Binomial coefficients. 4 Trigonometric functions. 5 Rational functions.
Stirling permutations, permutations of the multiset of numbers 1, 1, 2, 2, ..., k, k in which each pair of equal numbers is separated only by larger numbers, where k = n + 1 / 2 . The two copies of k must be adjacent; removing them from the permutation leaves a permutation in which the maximum element is k − 1 , with n positions into ...
Before performing a Yates analysis, the data should be arranged in "Yates' order". That is, given k factors, the k th column consists of 2 (k - 1) minus signs (i.e., the low level of the factor) followed by 2 (k - 1) plus signs (i.e., the high level of the factor). For example, for a full factorial design with three factors, the design matrix is
English: The table of signs for a 3-factor, 2-level factorial design used to calculate the effect estimates for each treatment combination. Date: 30 November 2017:
The theorem was first stated by Ibn al-Haytham c. 1000 AD. [2] Edward Waring announced the theorem in 1770 without proving it, crediting his student John Wilson for the discovery. [3] Lagrange gave the first proof in 1771. [4] There is evidence that Leibniz was also aware of the result a century earlier, but never published it. [5]
[24] [25] In the 2 × 3 example above, the degrees of freedom for ,, and the interaction are 1, 2 and 2, respectively. In a fractional factorial experiment, the contrast vectors belonging to a given effect are restricted to the treatment combinations in the fraction. Thus, in the half-fraction {11, 12, 13} in the 2 × 3 example, the three ...