Use a calibration curve to determine an unknown concentration.
Use a spreadsheet to calculate a 2nd or 3rd order calibration curve.
Understand how to estimate the uncertainty in the unknown concentration.
Complete a propagation of uncertainty for a calibration curve.
Standard Addition
and Internal Standards
Understand the terms standard solution, blank solution, standard addition,
matrix, matrix effect, and internal standard.
Know how to prepare and to use a standard addition calibration curve.
Understand how to prepare a set of solutions for a standard addition experiment.
Know how to graphically depict the standard addition procedure.
Outline the advantages and the situations that would favor the use of standard
addition methods.
Know how to set up and to complete an internal standard calibration procedure.
Know the formula required to determine internal standard response factors.
Understand and outline the advantages and utility of internal standard
procedures.
Propagation of Error
Understand the use of significant figures for addition/subtraction, multiplication/division.
Know what is meant by systematic (determinate) error, random (indeterminate)
error, precision, accuracy, absolute uncertainty, and relative uncertainty.
Know the formulas for propagation of uncertainty for addition/subtraction
and for multiplication/division and demonstrate the ability to determine
the most likely uncertainty in a result after performing arithmetric operations
(addition, subtraction, multiplication, division, or a combination of any
of these) on two or more numbers, each of which has a given random error
associated with them.
Descriptive Statistics
Describe a Gaussian distribution, know the formula for a Gaussian curve,
and describe the major parameters used to describe the distribution.
For a given data set, determine the mean, standard deviation, variance,
relative standard deviation, and the coefficient of variation (CV), both
manually and with a spreadsheet..
For given Gaussian distribution parameters, use a table of areas to determine
the probability of measurements falling within any particular range.
Understand what is specifically mean by a confidence interval. For a given
data set, determine the confidence interval for the true mean at a given
degree of confidence. Understand how changing the number of measurements
affects the size of the confidence interval.
Understand the terms mean, population mean, standard deviation, population
standard deviation, degrees of freedom (DOF), and student's t.
Know the probability of measurements falling within one, two, and three
standard deviations of the mean.
Inferential Statistics
Use a student's t test to compare two sets of measurements to determine
whether they are statistically different at a given level of confidence
for two cases:
Comparing a measurement result with a true value.
Comparing replicate measurements
Conduct a Q test to determine whether one datum is consistent with the
remaining data.
Conduct an F test to determine whether there is a statistically significant
difference in variances between two data sets.
Set up a spreadsheet to perform a given analysis.
Quality of Analytical
Measurements
Understand what is meant by sampling variance and measurement variance.
Demonstrate an understanding of how to set up a sampling plan that structures
a series of measurements to evaluate these. Be able use a spreadsheet
to analyze sampling data to get an estimate of sampling variance and measurement
variance.
Know what is meant by standard reference materials (SRM) and their role
in analytical measurements.
Be able to take a set of quality control data and set up Shewart control
charts for means, ranges, and cumulative sums.
Know and explain what is mean by proficiency testing and collaborative
trials.
Understand the dependence of the relative standard deviation of an analytical
method with the concentration being measured (Horwitz trumpet).
Analysis of Variance
Understand what is meant by the null hypothesis and by rejection of the
null hypothesis.
Given a data set, group the data and perform a single factor analysis of
variance.
Interpret results obtained and determine the fraction of variance accounted
for by a given variable.
Explain the statistical significance of p-values resulting from a given
ANOVA.
Experimental Design
and Optimization
Know how to conduct two factor and two factor with replication ANOVA's;
understand the additional information available with the latter.
Understand how to analyze a data set to evaluate whether factor-factor
interactions are significant
Understand how to design a Latin square for planned experiments.
Understand the importance of and how to randomize uncontrolled factors
Understand and explain the advantage of blocked experiments over those
that are unblocked.
Be able to plan a complete factorial design experiment; demonstrate how
to analyze the results from such a design.
Understand the importance of optimization techniques.
Be familiar with univariate and simplex optimization techniques.