Downloaded from https://www.everyspec.com AMCP 069 106 and mean u (the distribution need not be j i, j, k, r designates the factor or re- normal). Consider samples of size N, and plication. the means x 1 of those samples. The x, will have variance o0/N and mean p, For ex- 1, !, k a subscripts. I refers to the ample, In Table 2-14, if we take the mean of level of the first factor, / to each sample of 4 (N a 4) in each box, the level of the second, k to those means will have a variance of o0/4. the level of the third. The This fact, in the analysis of variance, usually unused ones are, omitted is used in reverse: if the variance of those when appropriate.
means Is al, then o2 - 4oa, That is, we multiply the "variance of the means" by subscript for replication, (it the "sample size" to get the original is omitted when not used.) variance. It follows the i, /, k, When estimating a population variance from " a mean value of x. A dot a sample variance, the phrase degrees-of- iq used to replace the index freedom often is used. The degree-of- which has been averaged over. freedom for a sample is the number of s- independent measurements in the sample. In I, J, K a number of levels assumed by the usual case of a simple sample of N items, factors i. J, k. respectively. the sample mean is subtracted from each measurement:
the sum of these deviations is R a number of replications, If zero. Thus only N - I are s-independent; r is omitted, it is equivalent once you know those, the last one is uni. to R - I; e.g., I replication quely determined. In the analysis of vari- means I measurement, 3 ance manipulations, calculating the degrees- replications (R - 3) means 3 of-freedom Is more complicated because there measurements. are many subsample means used in the cal- culations. 10 " implies a sum ov k. the index 0 from I to e, The big trick in making estimates of the population variance is to find a set of mea- SS - sum of squares; the subscripts surements that are a-independent.
There are I, J, k, r show what variables many ways to estimate the variance, only a the sum is due to. few of them are useful. After a brief dis- cussion of notation, the uscftil ways of esti- a degrees-of-freedom; the sub- mating the population variance will be shown. scripts I, J, k, r show what variables are being referred to. Use the following notation: - 2 m variance estimate; the sub- X coded experimental value. It scripts i, J, k, r show what has s'abscripts.
All values of variables the estimate is due x are measured from the over- to all mean; i.e., the overall mean of the data has been In Table 2-14, ambient temperatuie is the subtracted from the original first factor (I) and I a 2; supply voltage is experimental value. This the second factor (J) and J a 3; there Is no simplifies the equations, third factor; there are 4 replications and R 2-80