GLOSSARY
Glossary of Symbols
A absorbance for computing %reduction in bacte-
rial growth from turbidimetric readings.
b slope of the straight line relating response (y)to
log-dose (x)[Equations 2b,4,5,6].
c constant for computingM¢with Equations 8
and 10.
c¢ constant for computing Lwith Equations 26
and 29.
ci constant for computingM¢when doses are spaced
as in Table 8.
c¢i2 constant for computing Lwhen doses are spaced
as in Table 8.
C term measuring precision of the slope in a
confidence interval [Equations 27,28,35,36].
c2 statistical constant for testing significance of a
discrepancy [Table 9].
cM2 c2testing the disagreement between different
estimates of log-potency [Equations 39,40].
eb eifrom row bin Tables 6to 8.
eb¢i multiple of S(x –bar(x))2[Table 5;Equation 6].
ei sum of squares of the factorial coefficients in each
row of Tables 6to 8.
eq eifrom row qin Tables 6to 8.
f number of responses at each dosage level of a
preparation;number of replicates or sets.
fS number of observations on the Standard.
fU number of observations on the Unknown.
F1to F3 observed variance ratio with 1to 3degrees of
freedom in numerator [Table 9].
G1,G2,and G3 relative gap in test for outlier [Table 1].
h number of Unknowns in a multiple assay.
h¢ number of preparations in a multiple assay,
including the Standard and hUnknowns;i.e.,
h¢=h+1.
i interval in logarithms between successive
log-doses,the same for both Standard
and Unknown.
k number of estimated log-potencies in an average
[Equation 24];number of treatments or doses
[Table 4;Equations 1,13,15,16];number of
ranges or groups in a series [Table 2];number
of rows,columns,and doses in a single Latin
square [Equations 1a,16a].
L length of the confidence interval in logarithms
[Equations 24,26,29,38],or in terms of a
proportion of the relative potency of the
dilutions compared [Equations 31,33].
Lc length of a combined confidence interval
[Equations 42,43].
Lc¢ length of confidence interval for a semi-weighted
mean bar(M)[Equation 48].
LD50 lethal dose killing an expected 50%of the
animals under test [Equation 2c].
M log-potency [Equation 2].
M¢ log-potency of an Unknown,relative to its
assumed potency.
bar(M) mean log-potency.
n degrees of freedom in an estimated variance s2or
in the statistic tor c2.
n¢ number of Latin squares with rows in common
[Equations 1a,16a].
N number;e.g.,of observations in a gap test
[Table 1],or of responses yin an assay
[Equation 16].
P probability of observing a given result,or of the
tabular value of a statistic,usually P=0.05or
0.95for confidence intervals [Tables 1,2,9].
P* potency,P*=antilog Mor computed directly.
R ratio of a given dose of the Standard to the
corresponding dose of the Unknown,or assumed potency
of the Unknown [Equations 2,30,33].
R* ratio of largest of kranges in a series to their sum
[Table 2].
s =Öbar(s)2 standard deviation of a response unit,also of a
single estimated log-potency in a direct assay
[Equation 24].
s2 error variance of a response unit.
Si a log-dose of Standard [Tables 6,7].
S “the sum of.”
t Student's tfor ndegrees of freedom and
probability P=0.05[Table 9].
T total of the responses yin an assay [Equation 16].
T¢ incomplete total for an assay in randomized sets
with one missing observation [Equation 1].
T1 S(y)for the animals injected with the Standard on
the first day [Equations 18,36].
T2 S(y)for the animals injected with the Standard on
the second day [Equations 18,36].
Ta Tifor the difference in the responses to the
Standard and to the Unknown [Tables 6to 8].
Tab Tifor testing the difference in slope between
Standard and Unknown [Tables 6to 8].
Taq Tifor testing opposed curvature in the curves for
Standard and Unknown [Tables 6to 8].
Tb Tifor the combined slope of the dosage-response
curves for Standard and Unknown [Tables 6to
8].
Tb¢ S(x1Tt)or S(x1y)for computing the slope of the
log-dose response curve [Equations 10,23,
28].
Ti sum of products of Ttmultiplied by the
corresponding factorial coefficients in each
row of Tables 6to 8.
Tq Tifor testing similar curvature in the curves for
Standard and Unknown [Tables 6to 8].
Tr row or set total in an assay in randomized sets
[Equation 16].
Tr¢ incomplete total for the randomized set with a
missing observation in Equation 1.
Tt total of fresponses yfor a given dose of a
preparation [Tables 6to 8;Equations 6,13,
14,16].
Tt¢ incomplete total for the treatment with a missing
observation in Equation 1.
Ui a log-dose of Unknown [Tables 6to 8].
v variance for heterogeneity between
assays [Equation 45].
V=1/w variance of an individual M[Equations 44to 47].
w weight assigned to the Mfor an individual assay
[Equation 38],or to a probit for computing an
LD50[Equations 2a,2b].
w¢ semi-weight of each Min a series of assays
[Equations47,48].
x a log-dose of drug in a bioassay [Equation 5];
also the difference between two log-threshold
doses in the same animal [Equation 12].
x* coefficients for computing the lowest and highest
expected responses YLand YHin a log-dose
response curve [Table 4;Equation 3].
x1 a factorial coefficient that is a multiple of (x –bar(x))
for computing the slope of a straight line
[Table 5;Equation 6].
bar(x) mean log-dose [Equation 5].
bar(x)S mean log-dose for Standard [Equation 9].
bar(x)U mean log-dose for Unknown [Equation 9].
X log-potency from a unit response,as interpolated
from a standard curve [Equations 7a,7b,19].
XM confidence limits for an estimated log-potency M
[Equations 25,30].
XP* confidence limits for a directly estimated
potency P*(see Digitalisassay)[Equation 33].
y an observed individual response to a dose of drug
in the units used in computing potency and the
error variance [Equations13to16];a unit
difference between paired responses in 2-dose
assays [Equations17,18].
y1...yN observed responses listed in order of magnitude,
for computing G1,G2,or G3in Table 1.
y¢ replacement for a missing value [Equation 1].
bar(y) mean response in a set or assay [Equation 5].
bar(y)t mean response to a given treatment
[Equations3,6].
Y a response predicted from a dosage-response
relationship,often with qualifying subscripts
[Equations 3to5].
z threshold dose determined directly by titration
(see Digitalisassay)[Equation 11].
bar(z) mean threshold dose in a set (see Digitalisassay)
[Equations 31,32,33].