Evaluation of Analytical Data
ACCURACY and PRECISION
- A description of the reproducibility of results.
- A description of the correctness of results.
High Precision, High Accuracy
Low Precision, High Accuracy
High Precision, Low Accuracy
- 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
- All measurements of an observable. Infinate. (Impossible to get.)
- A subset of all the possible measurements. Finite. (Your results.)
- Sample Mean:
- Sample Standard Deviation:
PROPAGATION OF MEASUREMENT UNCERTAINTIES
*p, q, and r are experimental variables, whose standard deviations are sp, sq, and sr.
x = p + q + r
x = p q / r
x = py
x = ln(p)
- 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
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.