Page 174 - Vogel's TEXTBOOK OF QUANTITATIVE CHEMICAL ANALYSIS

4 ERRORS AND STATlSTlCS

Cx, = 1.00; Cy, = 49.5; Cx: = 0.30; Cxly, = 14.73; (CX,)~ 1.000;
=
the number of points (n) = 5
and the values
Cx, 1.00
X=-=--02 -
n 5
and

Cy, 49.5
L"n=5=9.9
By substituting the values in equations (7) and (8), then

and
b = 9.9 - (48.3 x 0.2) = 0.24
So the equation of the straight line is
y = 48.3~ + 0.24
If the fluorescence intensity of the test solution containing quinine was found
to be 16.1, then an estimate of the concentration of quinine (x pg mL-') in this
unknown could be
16.10 = 48.3~ + 0.24

The determination of errors in the slope a and the intercept b of the regression
line together with multiple and curvilinear regression is beyond the scope of
this book but references may be found in the Bibliography, page 156.

4.18 COMPARISON OF MORE THAN TWO MEANS (ANALYSIS OF VARIANCE)
The comparison of more than two means is a situation that often arises in
analytical chemistry. It may be useful, for example, to compare (a) the mean
results obtained from different spectrophotometers al1 using the same analytical
sample; (b) the performance of a number of analysts using the same titration
method. In the latter example assume that three analysts, using the same
solutions, each perform four replicate titrations. In this case there are two
possible sources of error: (a) the random error associated with replicate
measurements; and (b) the variation that may arise between the individual
analysts. These variations may be calculated and their effects estimated by a
statistical method known as the Analysis of Variance (ANOVA), where the
s f
square of the standard deviation, s2, is termed the variance, V. Thus F = 7
S2
"1
where si > s:, and may be written as F = - where VI > V2.
v2