Chemometrics 1: Statistical Evaluation of Data

Errors in an experiment that make the results useless, caused by issues like faulty equipment, contamination, or mislabeling.

Errors that cause a consistent bias in the data, meaning all measurements are either too high or too low.

Errors that cause results to be spread around the average value, impacting precision. These are often uncontrollable.

How close a measurement is to the true value. Low systematic error = high accuracy.

How close multiple measurements are to each other. Low random error = high precision

Measurements made in a single session with the same equipment.

Measurements taken at different times, places, or under different conditions.

The average of a set of values, calculated by summing the values and dividing by the number of values.

A measure of the spread of data; larger variance means lower precision.

The square root of the variance; has the same units as the data.

A measure of error in the final answer, calculated from the standard deviation.

A dimensionless measure of relative error or noise in data, often given as a percentage.

A common probability distribution showing data clusters around a mean.

In a normal distribution, approximately 68% of data falls within 1 standard deviation, 95% within 2, and 99.7% within 3.

The range of values within which we can reasonably expect the true value of a measurement to lie.

The extreme values of the confidence interval, defining the upper and lower bounds of the range.

A statement that there is no difference between the observed and known values, any observed difference being attributed to random variation.

The probability threshold used to reject the null hypothesis. A commonly used level is 0.05 (or 5%), meaning there's a 5% chance of concluding a difference exists when there isn't.

A statistical test used to compare the variances (spread) of two sample sets.

The number of values in a data set that are free to vary. For the F-test, it is calculated as the number of values in the sample minus 1 (n-1).

A threshold value used in the F-test. If the calculated F value is smaller than the critical value, we accept the null hypothesis.

A statistical test used to compare the mean of a sample with a known value or compare the means of two samples. It checks for significant differences between the means.

Using the t-test to check if the average result of a method (sample mean) is significantly different from a known true value (certified value) of a reference material.

Using the t-test to compare the average results of two different samples to determine if there's a significant difference between their means.

A specific t-test for comparing means of two methods using the same samples. It accounts for paired measurements within each sample.

In a paired t-test, this is the average value of the differences between the two methods for each pair of measurements. It represents the overall difference between the methods.

This is a measure of the variability of the differences between the paired measurements. It reflects how much the differences between the methods vary across the pairs.

Analysis of Variance (ANOVA) is a statistical technique used to compare the means of more than two groups or treatments to determine if there is a significant difference between them.

This refers to the variability between the groups or treatments being compared. It measures how different the group means are from each other.

This refers to the variability within each group or treatment. It measures how much the individual measurements within a group vary from each other.

This refers to the variability caused by the different treatments or groups being studied. It's often the primary interest in ANOVA.

This refers to the variability that's not due to the treatments being studied, but to random factors that can influence the results.

A measure of the variation between different groups or treatments, essentially how spread out the group means are.

A measure of the variation within a single group or treatment, reflecting how spread out the individual data points are within that group.

A ratio used in ANOVA to compare the variation between groups to the variation within groups, indicating whether differences between group means are statistically significant.

The probability of observing the obtained results (or more extreme) if the null hypothesis (no difference between groups) were true.

When the analysis indicates the observed differences between group means are unlikely to be due to random error, supporting the idea of a real effect.