Estatistica

Applied Statistics in Chemistry
The latest version of this document is available from www.consol.ca (Teaching link).

The fundamental hypothesis in statistics is the Null Hypothesis. The null hypothesis states that random error is sufficient to explain differences between two values. Statistical tests are designed to test the null hypothesis. Passing a statistical test means that the null hypothesis is retained: there is insufficient evidence to show that there is a difference between the samples.
It is impossible to show that two values are the same; it is only possible to show they are different.

Significant Figures
Some values are known or defined to be exact. For example:
• the ½ and 2 in EK = ½ m v2
• the stoichiometric coefficients and molecular formulae in chemical reactions such as
C3H8 + 5O2
3CO2 + 4H2O
• the speed of light in a vacuum, c, is defined as 2.99792458·108 m/s
There is error in every observation. Error arises due to limitations in the measuring device (ruler, pH meter, balance, etc.) and problems with equipment or methodology. The former are ‘indeterminate’ or
‘random’ errors and cannot be eliminated. Random errors limit the precision with which the final value can be reported. The latter are ‘determinant’ or ‘systematic’ errors and affect the accuracy of the final value. Analytical chemists continuously monitor for systematic errors in procedures.
Significant figures
‘Sig-figs’ are a simple, easy to apply, quick-and-dirty method of getting approximately the correct number of decimal places in a value. The correct, but more difficult, method is to statistically determine the uncertainty and thus the reportable number of decimal places. This approach considers the uncertainty associated with every observation and its importance in the overall uncertainty. It is possible to gain or lose decimal places compared with the sig-figs method.
Instructors may use the term ‘sig-figs’ when they mean ‘statistically calculated