Summation Algebra - Statpower

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2. Summation Algebra In the next 3 chapters, we deal with the very basic results in Summation Algebra , descriptive statistics, and matrix Algebra that are prerequisites for the study of SEM theory. You may be thoroughly familiar with this material, in which case you may merely browse through it. However, it is my experience that many students find a thorough review of these results worthwhile. SINGLE SUBSCRIPT NOTATION. Most of the calculations we perform in statistics are repetitive operations on lists of numbers. For example, we compute the sum of a set of numbers, or the sum of the squares of the numbers, in many statistical formulas. We need an efficient notation for talking about such operations in the abstract. In the simplest situations, we have one or two (or perhaps three) lists, and we wish to refer to particular numbers in those lists.

10 SUMMATION ALGEBRA Student X Y Smith 87 85 Chow 65 66 Benedetti 83 90 Abdul 92 97 Table 2.1 Hypothetical Grades for 4 Students For example, if the X list consists of the numbers 11, 3, 12, 7, 19 the value of x 3 would be 12, because this is the third number (counting from the beginning) in the X list.

  Number, Algebra