REPORT FOR A N A L Y T I C A L CHEMISTS
Table III.
NUCLEAR-CHICAGO RESEARCH QUALITY RADIOCHEMICALS
Lengths of Various Confidence Intervals Student's t
Source of uncertainty Replication
Length of confi dence interval
Estimated std. dev.
Degrees of freedom
(95% confi dence)
0.927
33
2.03
3.8
2.98
23
2.07
12.3
23
2.07
12.7
TRITIUM LABELLED STEROIDS A N D STEROID ESTERS
Scatter about calibration line Total, including un certainty of calibra tion line
1.
Obtain the best estimate of X„, denoted b y X„, from the relation Y» - a (9) X» =
(X„ - X ) 2 _ (32.57 - J 2 . 7 1 ) 2 _ S " '" 5476 = 0.0188 K2
2. Use this value in the place of X ' to compute the expression ( X ' — X ) 2 occurring on the right side of Equation 8. T h e n the entire right member of E q u a t i o n 8 is a known numerical value, say K 2
N_+J Ν
K 2 = fc2sr2
+
X)2
(Xu
(2.07) 2 (0.086) 2 ~26 0.0188 25 Κ
= Λ / 0 . 0 3 3 5 5 = 0.1831
Confidence interval for X„: X' -0.4401 -
S
0.03355
(10)
(-1.3802) 0.02886
±0.1831 /38.92 \26.23
Now solve the equation in X ' : (Y u -
X' =
a -
b X ' ) 2 = K2
Yu — a ± Κ
Thus, (H)
B y taking successively both signs for ± K , one obtains two values for X ' , which define the confidence interval. We now illustrate this procedure in terms of Wei's calibra tion curve. I n accordance with E q u a t i o n s 3 and 4 we have a = b = sr =
-1.3802 0.02886 0.086
T h e n u m b e r of points in this calibra tion experiment was X = 2oUsing a 9 5 % confidence interval, we find the value of S t u d e n t ' s t for Ν — 2 = 23 degree's of freedom : t„ = 2.07 Assume t h a t the ratio of the absorbances for the single measure ment on the u n k n o w n sample is 0.363; t h e n we have Y„ = log (0.363) = - 0 . 4 4 0 1 . We now obtain successively : X,
-0.4401 - (-1.3802) = 32.57 0.02886
Ihe confidence interval is 26.2 < X u < 38.9 (12)
I t is important to have a clear con ception of the meaning of this inter val. I t s calculation is based on the observed scatter of points about the calibration line. This scatter is due, in turn, to the dissimilarity among the samples (apart from their differ ent propylene contents). There fore the confidence interval given by E q u a t i o n 12 is valid only if the sample to which it refers belongs to the same general class as the samples used for establishing the calibration line. T h e confidence interval would not be valid, for example, if the new sample were prepared with a catalyst different from the one used in preparing the samples for the calibration curve. No statistical measure of uncertainty can be given for the composition of a sample when it is evaluated by a calibrât ion line obtained on the basis of materials t h a t are of a substantially different n a t u r e from the sample under analysis.
SPECIFIC ACTIVITY (mc/mM)
COMPOUND d(+)Aldosterone-l, 2-T A 4-Androstene-3, 17-dione-7o:-T Cholesterol-T (G) Cholesterol-7a-T Cholesterol-7a-T Cholesteryl-T (G) linoleate Cholesteryl-7«-T linoleate Cholesteryl-T (G) oleate Cholesteryl-7a oleate Cholesteryl oleate(nominally 9, 10-T) Cholesteryl-7«-T palmitate Cholesteryl palmitate(nommally 9, 10-T) Cholesteryl-T (G) stéarate Cholesteryl-7a-T stéarate Cholesteryl stearate(nominally 9, 10-T) Corticosterone-1, 2-T Corticosterone-1, 2-T Cortisol-1, 2-T [Hydrocortisone-1, 2-T] Cortisol-1, 2-T [Hydrocortisone-1, 2-T] Cortisone-T (G) Dehydroep/androsterone-7a-T Dehydroepiandrosterone-7a:-T Dehydroep/androsterone-7o:-T acetate Diethylstilboestrol-T (G) Estradiol-T(G) Estradiol-2, 4-T Estradiol-6, 7-T Estradiol-6, 7-T 17g-acetate Estradiol-6, 7-T 17/3-acetate Estrone-T (G) Estrone-6 f 7-T Hexestrol-T [meso-3. 4-6/s-pHydroxyphenyl-n-hexane(nominally
500-1000 100-300 50-350 100-500 100-500 250-1000 >30.000 1000-2000 >30,000 25-250 250-1000 >5000 500-1800 100-500 50-100 500-1000 100-500 500-1000 >3000 100-200 100-500 100-1000
2 , 3 , 4 , 5-T)]
Ai
-Pregnenolone-16-T ^ -Pregnenolone-7ct-T Progesterone-T (G) Progeste ro ne- 7α-Τ Testosterone-1, 2-T Testosterone-1, 2-T Testosterone- 7α-Τ
1000-1500 100-500 100-500 100-500 500-1000 > 15,000 500-1000
5
Data sheets available on request for every compound. Please write for cur rent schedules containing complete radiochemical listings and information. Or call 312 827-4456 collect. NUC:G-4-24S
©
NUCLEAR-CHICAGO A DIVISION OF NUCLEAR - CHICAGO
{Continued on page 32)
250-2000 500-1000 100-300 100-500 >2000 50-350 100-500 50-350 100-350 100-500
CORPORATION
351 Howard Avenue, Des Plaines, Illinois 60018 Circle No. 164 on Readers' Service Card
VOL. 36, NO. 13, DECEMBER 1904
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29 A
