Evaluation of Analytical Data


ACCURACY and PRECISION

Precision

A description of the reproducibility of results.

Accuracy

A description of the correctness of results.


High Precision, High Accuracy

Low Precision, High Accuracy

High Precision, Low Accuracy



ERROR

Error Types
Random (Indeterminate)
Systematic (Determinate) - Bias, Instrumental, Personal, Method

Absolute Error (Ea)
Ea = X - xt
where xt is the accepted or true value
and X is the measurement or average of several measurements.
Relative Error (Erelative)
Erelative = (X - xt) / xt


POPULATIONS and SAMPLES

POPULATION
All measurements of an observable. Infinate. (Impossible to get.)
SAMPLE
A subset of all the possible measurements. Finite. (Your results.)

Sample Mean:
Sample Standard Deviation:


PROPAGATION OF MEASUREMENT UNCERTAINTIES

Calculation

Example

sx*

Addition
or
Subtraction

x = p + q + r

Multiplication
or
Division

x = p q / r

Exponentiation

x = py

Logarithm

x = ln(p)

*p, q, and r are experimental variables, whose standard deviations are sp, sq, and sr.

Example:

Prepare 10 ml of aqueous 1x10-3 molar NiCl2 using a 10 (+/-0.1) ml volumetric flask and an analytical balance with an uncertainty of +/-0.001g. The formula weight of NiCl2.6H2O is 237.70 (+/-0.01) g/mole.

Define: S = uncertainty, FW = formula weight, g = mass, M = molarity, and L = volume.

Molarity = (g NiCl2.6H2O)/(FW NiCl2.6H2O)/(L H2O)
1x10-3 M = (g NiCl2.6H2O)/(237.70 g/mole)/(0.010 L H2O)
g = 0.002377 g NiCl2.6H2O

What is the uncertainty in the molarity?

What is wrong with this procedure?

How could the uncertainty in the concentration be reduced?


This materil is very important in the laboratory. The linked table has information on uncertainties in laboratory glassware



METHOD OF LEAST SQUARES

Linear Regression in Microsoft Excel.
(If you use a blank and zero your instrument, (0,0) is a data point.)



Copyright © 2004 J.P. Hornak.
All Rights Reserved.