tailieunhanh - MEASURE Evaluation_2

Tham khảo tài liệu 'measure evaluation_2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Simpo PDF Merge and Split Unregistered Version - http Tr V ơỉ V Var x It is customary to denote population parameters by Greek letters . X a and sample estimates by Latin letters . X 5 . Another often used convention is to represent sample estimates by Greek letters topped by a caret C thus s and T both denote a sample estimate of a. It is apparent from the above definitions that the variance and the standard deviation are not two independent parameters the former being the square of the latter. In practice the standard deviation is the more useful quantity since it is expressed in the same units as the measured quantities themselves mg dl in our example . The variance on the other hand has certain characteristics that make it theoretically desirable as a measure of spread. Thus the two basic parameters of a population used in laboratory measurement are a its mean and b either its variance or its standard deviation. Sums of squares degrees of freedom and mean squares Equation presents the sample variance as a ratio of the quantities 2 x - x 2 arid N 1 . More generally we have the relation MS Of where MS stands for mean square ss for sum of squares and DF for degrees offreedom. The term sum of squares is short for sum of squares of deviations from the mean which is of course a literal description of the expression 2 x - x 2 but it is also used to describe a more general concept which will not be discussed at this point. Thus Equation is a special case of the more general Equation . The reason for making the divisor N - Ị rather than the more obvious V can be understood by noting that the N quantities Xi X x2 X . . . XN X are not completely independent of each other. Indeed by summing them we obtain ỵ x - x Sx - Sx Sx - - Nx j Substituting for X the value given by its definition Equation we obtain 2 X - - X Xx - N 0 This relation implies that if any N - 1 of the N quantities x - x are given the remaining one can .