Analytical chemistry is concerned with the measurement of the chemical compostion of unknown
substances using exisitng instrumental techniques, and the development or application of new
techniques and instruments. Anytime a measurement is made with an instrument, there is an
error, a deviation from the *true* value, ineherent in that measurement.

Instrumental analysis is very important in all areas of analytical chemistry. Modern analytical chemistry is a quantitative science, meaning that the desired result is almost always numeric. We need to know there is 55 μg of mercury in a sample of water, or 20 mM glucose in a blood sample. Quantitative results for analytical chemistry are obtained using devices or instruments that allow us to determine the concentration of a chemical in a sample from an observable signal.

One of the most important techniques is analytical chemistry is the preparation
of the calibration curve, which is an equation relating a signal measured from
an instrument to the concentration of a substance in the sample that is being
tested. You determine the calibration curve by measuring samples with known
concentrations of the substance, to see how the instrument behaves. Then, you
use a statistical technique called **Linear Regression** to
generate the curve and determine its uncertainty.

Another important part of statistical analysis in chemistry is the comparison
of sets of data, to make conclusions about the validity of our measurements and
the confidence with which we can make these conclusions. These are called
tests of siginificance, and can give tell us the degree of uncertainty of a
measurement. The three tests we cover in this tutorial are the Q-test for
rejecting outliers, the *t*-test for comparing means, and the
*F*-test for comparing precisions.

This section presents concepts in statistics that form the basis for the Linear Regression and
Data Comparison learned in future sections. We begin by covering measures that form the basis
of any statistical analysis mean,
variance and standard deviation, and we talk about
the differences between *population* and
*sample* mean, variance and standard deviations. Then, we discuss
error and residuals, which are other important measures to
describe data. The second half of this section introduces some important statistical concepts,
such as Probability Distributions,
Confidence Levels, and
Degrees of Freedom. These are not essential for this section, but
will become important when we discuss Linear Regression and
Data Comparison.
Finally, we
present a brief introduction to statitsical hypotheses and Type I and Type II errors.