Chemical Applications of Statistical Analyses

Measurement is integral to analytical chemistry. Each record comprises a number – denoting the magnitude  – and the unit – a …

An analysis is usually conducted by replicated sampling or repeated measurements on the same sample. This leads to scattered results rather than a single …

Error is the deflection of an obtained result from the expected or true results of an experiment. This happens due to the uncertainty associated with the …

Systematic errors, depending on their source, are of four types – sampling, instrumental, method, and personal errors. Sampling errors occur due to …

Indeterminate or random errors arise from several uncontrollable variables in successive measurements. Since these errors can neither be predicted nor …

A plot of relative deviation from the mean and its frequency of occurrence appears as a Gaussian curve. This probability distribution curve of a …

The uncertainty reflects the possible range of values in which the result of a measurement can exist. However, uncertainty varies from error, which is the …

In an experiment, multiple arithmetic operations are often required. Here, the uncertainty associated with the first measurement propagates to the next in …

The atomic mass of an element obtained from different sources changes slightly due to the variation in relative isotope concentration from one source to …

Standard deviation provides a measure of nearness between the sample mean and the true mean reliably for a large number of measurements. So, when there …

Is the difference between the two values due to an unexplainable random error or a systematic error that can be rationalized by a hypothetical model? The …

The F-test checks if the difference between two variances is too large to be explained by an indeterminate error. It compares the variance of a sample and …

The influence of changing the method, the sample, or the analyst on the analysis results is studied by altering only one in a pair of experiments. The …

Outliers are those data points extremely different from the rest of the data set. Dixon's Q-test is a significance test that helps determine whether …

A calibration curve is a mathematical relationship between the instrument's signal and known analyte concentrations. This curve equation predicts the …

A correlation coefficient is a statistical test to evaluate the degree and the direction of linear correlation between two variables. The Pearson …

Regression and correlation are statistical techniques that examine the relationship between two variables.  While regression is used to understand …

Background noise is intrinsic to any measurement interfering with the detection of the analyte signal. To analyze if the measured signal is from the …

Grubbs' test, like Dixon's Q-test, is a statistical test to identify the outliers in data with a normal distribution. Here, the number of …

The degree of freedom is the number of independent pieces of information or sample values required to perform any calculation. The degrees of freedom vary …

The z score, or standardized score, is the number of standard deviations that a given value is away from the mean. It is one of the commonly used measures …

The analysis of variance—abbreviated as ANOVA —is used when the means of three or more samples need to be tested for equality. For example, …