# Stats Tutorial - Aims of Statistics:

Introduction

Basics of Excel™

Basic Statistics

Linear Regression

Data Evaluation & Comparison

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.

© 2006 Dr. David C. Stone & Jon Ellis, Chemistry, University of Toronto
Last updated: September 25th, 2006