Residual Errors in a Linear Regression Analysis
The figure here illustrates the basis of a linear regression analysis. The points in blue are the experimental data and the points in red are the predicted values from the regression equation. […]
Illustration
Standard Addition by Serial Spikes
One approach for preparing standard additions is to spike equal volumes of the sample with different volumes of a standard and diluting each to the same final volume. An alternative form of […]
Matrix Effects
Sometimes the solution matrix in which the analyte resides affects the relationship between the signal and the analyte’s concentration, as shown below. We call this a matrix effect. When matrix effects are […]
Determinate Errors in Single-Point Standardizations
When using a single-point standardization, we must assume that there is a linear relationship between the signal and the analyte’s concentration. When this is not true, which often is the case at […]
Detection Limit
The figure below shows the probability of type 1 and type 2 errors for the IUPAC detection limit. (a) The normal distribution curve for the method blank, with a signal for the […]
Dixon’s Q-Test
A data point that is not consistent with the remaining data is called an outlier. Consider, for example, an experiment in which we determine the mass for each penny in a sample […]
t-Test
The figure below shows the relationship between confidence intervals and the result of a t-test. (a) The shaded area under the normal distribution curve shows the confidence interval for the sample based […]
One-Tailed vs. Two-Tailed Significance Tests
Example showing (a) a two-tailed, and (b and c) a one-tailed, significance test of an sample’s experimental mean relative to the population’s true mean. The normal distribution curves are drawn using the sample’s […]
Central Limit Theorem
According to the central limit theorem, when an analysis is subject to a variety of indeterminate errors, the distribution of results for that analysis will approximate a normal distribution. As the number […]
Normal Distribution
A binomial distribution describes a population whose members have only certain, discrete values. This is the case with the number of 13C atoms in cholesterol. A molecule of cholesterol, for example, can […]
Binomial Distribution
A binomial distribution describes a population whose members take on only certain, discrete values. This is the case, for example, with the number of 13C atoms in cholesterol because a molecule of […]
Indeterminate Errors and Noise
Indeterminate errors are random in nature and affect the reproducibility and repeatability of analytical measurements. We can assign indeterminate errors to several sources, including collecting samples, manipulating samples during the analysis, and making […]