Chapter 4 Statistics for Quantitative Chemical Analysis

A vocabulary flashcard deck covering statistical methods, confidence intervals, hypothesis tests, standard deviations, and linear regression analysis.

Population Mean

The true average value of an entire population, which is distinct from a sample mean calculated from a subset of experimental measurements.

Gaussian Distribution ($\pm 1\sigma$ Area)

The fraction of measurements expected to lie within plus or minus one standard deviation ($\pm 1\sigma$) of the mean in a normal error curve, equal to $0.6826$ (or $68.26\%$).

Standard Deviation ($s$)

A statistical measure of data precision; a standard deviation close to zero indicates that measurements are clustered near the sample mean, but does not guarantee accuracy relative to the true value.

Relative Standard Deviation ($RSD$)

A measure of relative precision calculated as standard deviation divided by the mean, which remains unchanged when every value in a dataset is divided or multiplied by a constant factor.

$F$ Test

A statistical test used to compare the variances or standard deviations of two datasets; a calculated $F$ exceeding the critical $F$ value at the 95% confidence level indicates a significant difference in precision.

Degrees of Freedom ($df$) for Comparing Two Means

The number of independent data values used when comparing the means of two datasets ($A$ and $B$) with similar variances, calculated as $df = n_A + n_B - 2$.

One-Tailed $t$ Test

A statistical hypothesis test used to determine whether a sample mean lies specifically above a designated threshold or below a designated limit.

Systematic Error

A reproducible error that skews measurements in one direction, indicated when a $t$ test shows a statistically significant difference between two analytical methods.

Potential Outlier

An extreme data value (sample maximum or minimum) that deviates significantly from the rest of the dataset, often caused by a gross error.

Grubbs Test ($G$ Test)

A statistical procedure used to evaluate whether a single questionable data point (potential outlier) can be legitimately rejected at a specified confidence level.

Method of Least Squares

A mathematical technique that calculates the linear equation $y = mx + b$ for the best-fit line through experimental data points by minimizing vertical ($y$) deviations.

Linear Range

The concentration interval over which an analytical instrument's output response is directly proportional (a linear function) to the concentration of the analyte.