01: analytical concepts and statistics

assay

process of determining the amount of an analyte in a sample

analyte

chemical substance being measured

qualitative analysis

concerned with the identification of the elements, ions, or compounds present in an unknown sample

quantitative analysis

concerned with the determination of the quantity of one or more components of the sample

signal

measured quantity that is correlated to the amount of analyte

noise

unwanted variation in a measured quantity

signal-to-noise ratio (S/N)

magnitude of the signal divided by the magnitude of the noise

background

approximately constant signal measured in the absence of analyte

detection limit

amount of analyte that corresponds to a signal just greater than the mean of the background plus three standard deviations of its noise

sample matrix

all the components of a sample except the analyte

blank

a ‘man-made’ sample that lacks the analyte, but otherwise contains the solvent, reagents, etc., used in the analysis

positive control

standard sample that contains a known quantity of the analyte of interest

negative control

standard sample that does not contain any analyte

interference

specific chemical substance in a sample matrix that causes a systematic error in a measured quantity

selectivity

extent to which other substances interfere with the determination of an analyte

masking agent

reagent that prevents one or more components in a sample matrix from interfering with an analysis

accuracy

closeness of a measured value to the “true value”

absolute error

difference between the measured and true value

relative error

error in a measurement, expressed as a percentage

precision

reproducibility between replicate measurements

replicates

samples from the same source, run using the same method, under the same conditions, and expected to give the same result in the absence of error

Gaussian/normal distribution

• used to describe data clustered about a mean value

• continuous and symmetric distribution

• famous “bell curve” shape

• peak position determined by the mean

• width and height determined by the standard deviation

• total area under the curve is 1

population

all possible measurements that are of interest

sample

limited number of measurements that are representative of the population

mean/average

approximates the true value

deviation

difference between a measured value and the mean value of all measurements

standard deviation and relative standard deviation

measure of the uncertainty and precision associated with a measurement

degree of freedom

number of independent measurements

confidence interval

range of values, centered on the sample mean, that have a certain probability of including the true population mean

t statistic

permits use of sample data to test hypotheses about unknown population means without knowledge of the population standard deviation

significance test

determines whether the difference between two or more values is too large to be explained by indeterminate error

null hypothesis

postulates that two observed quantities are the same

significant figures

reflection of a measurement’s magnitude and uncertainty

standard

solution with known concentration

sensitivity

slope (m) of the calibration curve

dynamic range

concentration range over which the calibration curve is analytically useful

selectivity

reflected by the ratio of compound 1’s versus compound 2’s slopes

matrix effect

combined effect of all non-analyte components in a sample on the quantitative measurement of the analyte