Page 53 - Quality control of pharmaceuticals (07-PA 704)

Statistical Treatment of Analytical Data

1. t-Test:

Comparison of experimental means ̅ 1 and ̅ 2 of data obtained with two methods
or by two persons or by the same person but under different experimental
conditions is often indispensable in analytical chemistry for testing the validity of
an analysis.
For this purpose, the two experimental means ̅ 1 and ̅ 2 are compared using the t-
test. t is computed by the expression:

t = ̅ 1− ̅ ̅ ̅̅2̅ √ 1 2
1−2
1+ 2

Where S1-2 is the standard deviation of any individual value in each of the two sets
of data, which is computed by the expression:

S1-2 = √∑( 1− ̅1)2+∑( 2− ̅2)2
1+ 2−2

Theoretical values are available in statistical tables.

2. F-Test: Comparison of variances, S2

The F-Test is used to compare whether there is a significant different in the
precisions of two series of measurements.
F is defined by:

F = S12 / S22
Where S1 and S2 are the standard deviations of the two sets of data
(S1 > S2). Values of F are available in statistical tables.
When Fexp > Ftheor , it is considered that s1 is statistically different from S2 , whereas
when Fexp ≤ Ftheor , there is no significant different between S1 and S2 .