Principles of Fluorescence Spectroscopy

136 TIME-DOMAIN LIFETIME MEASUREMENTS
Table 4.4. F Statistic for Calculation of Confidence Intervals a
Probability (P)
Degrees of One parameter (p) b
freedom (ν) 0.32 d 0.25 0.10 0.05 0.025 0.01
10 1.09 1.49 3.29 4.96 6.94 10.0
30 1.02 1.38 2.88 4.17 5.57 7.56
60 1.01 1.35 2.79 4.00 5.29 7.08
120 1.00 1.34 2.75 3.92 5.15 6.85
4 1.00 1.32 2.71c 3.84 5.02 6.63
Two Parametersb 10 1.28 1.60 2.92 4.10 5.46 7.56
30 1.18 1.45 2.49 3.32 4.18 5.39
60 1.16 1.42 2.39 3.15 3.93 4.98
120 1.15 1.40 2.35 3.07 3.80 4.79
4 1.14 1.39 2.30 3.00 3.69 4.61
Three Parameters
10 1.33 1.60 2.73 3.71 4.83 6.55
30 1.22 1.44 2.28 2.92 3.59 4.51
60 1.19 1.41 2.18 2.76 3.34 4.13
120 1.18 1.39 2.13 2.68 3.23 3.95
4 1.17 1.37 2.08 2.60 3.12 3.78
Four Parameters
10 1.34 1.59 2.61 3.48 4.47 5.99
30 1.23 1.42 2.14 2.64 3.25 4.02
60 1.20 1.38 2.04 2.53 3.01 3.65
120 1.19 1.37 1.99 2.45 2.89 3.48
4 1.18 1.35 1.94 2.37 2.79 3.32
Five Parameters
10 1.35 1.59 2.52 3.33 4.24 5.64
30 1.23 1.41 2.05 2.53 3.03 3.70
60 1.20 1.37 1.95 2.37 2.79 3.34
120 1.19 1.35 1.90 2.29 2.67 3.17
4 1.17 1.33 1.85 2.21 2.57 3.02
Eight Parameters
10 1.36 1.56 2.34 3.07 3.85 5.06
30 1.22 1.37 1.88 2.27 2.65 3.17
60 1.19 1.32 1.77 2.10 2.41 2.82
120 1.17 1.30 1.72 2.02 2.30 2.66
4 1.16 1.28 1.67 1.94 2.19 2.51
Ten Parameters
10 1.35 1.55 2.32 2.98 3.72 4.85
30 1.22 1.35 1.82 2.16 2.51 2.98
60 1.18 1.30 1.71 1.99 2.27 2.63
120 1.17 1.28 1.65 1.91 2.16 2.47
4 1.15 1.25 1.59 1.83 2.05 2.32
a From [188]. In the ratio of χR 2 values, the degrees of freedom refer to that for the denominator. The degrees of freedom
in the numerator are one, two, or three, for one, two or three additional parameters.
b These values refer to the degrees of freedom in the numerator (p).
c This value appears to be incorrect in [188], and was taken from [1].
d The values for 0.32 were calculated with a program (F-stat) provided by Dr. M. L. Johnson, University of Virginia.