Appendix 5 For a higher order regression curve, a particular PPNLO is:
ENLO = ao + a1xo + a2x2 + .. + ays K For higher order regression curves, the regression coefficients are usually calculated using computer-matrix solutions, since there are many terms.
Defining the vectors: x' = [1 x x* • a row vector Ко = Г 1 1 Хо !
a colum vector and &A-1 : the varience-covarience matrix for the ax values Then the 90 percent confidence interval for a particular noise level, LENo, on a regression curve of EPNL vs. X is;
2 · (AEL) 2 2 Xo A-1 Xo CIo = I t N-K-1 Par 3
Appendix 5 Linear Example 100 8 8 8 5 8 8 82 50 23 (Thousands) regression Quadratic Example 110 105 105 104 102 00 EPNL 21 203 24 Par 3
Appendix 5
CONFIDENCE INTERVAL FOR POOLED DATA SENS The confidence interval for pooled data sets may be calculated as follows. For example, for three data sets (flight test data and two different static tests) - each with its own confidence interval:
let IZ1 = (CI1/t1)2 (square of the confidence interval without the Student's t term for each data set) then for three data sets, the confidence interval for the pooled data 1s:
CIo= +/-+' (221+222 +223) 1/2 241t1 + 222t2 + 2zztz where t'= 2L1 + 272 + 273
5. REFERENCES
(a) Kendall, M G. and Stuart, A, The Advanced Theory of Statistics, Volumes 1 and 2, Hafner, New York, 1973.
(b) Yule, G.U. and Kendall, M. G., An Introduction to the Theory of Statistics, 14th ed, Griffin, New York, 1950.
(c) Walpole, R.E. and Myers, R. H, Probability and Statistics for Engineers and Scientists, MacMillan, New Yoek, 1972.
Cochran, W.G., Approximate Significance Levels of the Behrens-Fisher Test, Biometrics, 20, 191-195, 1964.
(e) Shedecor, G.W. and Cochran, W. G., Statistical Methods, 6th ed, Iowa State University Press, Ames Iowa, 1968, Par 4 5
Appendix 5 Table 5-1 STUDENT'S t DISTRIBUTION FOR 90 PERCENT CONFIDENCE INTERVAL Degree of freedom (V) t
6.314
2.920
2.353 4 2.132 5 2.015
1.943
1.895
1.860
1.833
1.812
1.782
1.761
1.746
1.734
1.725
1.711
1.697
1.671
1.645 6 Par 5 *U.S. GOVERNMENT PRINTING OFFICE: 1992 - 312 - 68 75 5 5 96