### Practical statistical tools a lab analyst needs to know

The other day someone in an analytical laboratory asked me what the minimum knowledge was a chemist needed to know before he could handle the routine laboratory data without much problem.

In my opinion, most of the statistical calculations are of high school arithmetic and algebra in nature, although some subjects may be a bit more abstract and complicated. However, it is not really a big deal to get acquainted with. The most challenging part of learning statistics is to understand its principles and reasoning behind these calculations. A very basic point is to appreciate that statistics and probability are not two but one combined subject.

Indeed, statistics cannot be a standalone subject without bringing in the concept of probability. That is because in most cases, we are working only on samples which are subsets of a population but actually we are interested in knowing the bigger picture in the population. We need therefore make inferences and estimation based on the sample data collected through the use of appropriate probability distribution(s) and statistical testing. Indeed probabilities underlie everything in the field of statistics. Having a clear sense of the basic ideas in probability theory will help us more easily digest the more advanced statistical ideas encountered.

An analyst working in a laboratory routinely faces a pool of data that need to be analyzed, from the calculation of simple arithmetic mean and standard deviation to standard calibration curve, precision, accuracy, detection limit, measurement uncertainty, method validation, and so forth. He or she has to be equipped with basic statistical knowledge in order to carry out the duties assigned satisfactorily.

Append below is a list of general statistical subjects which are of value in laboratory data analysis in the first instance:

- Basic probability concepts: outcomes, events, continuous and discrete probability distribution functions, etc.
- Descriptive statistics: error, mean, median, mode, standard deviation, variance, coefficient of variance, relative standard deviation, standard error of mean, linear and non-linear regression, data transformation, etc.
- Inferential statistics: statistical modelling, confidence intervals, Central Limit Theorem, model validation and prediction, outliers’ tests, hypothesis tests, chi-square test, randomization, analysis of variance ANOVA, statistic tests: Fisher’s F-test, Student’s t-test, chi-square test, Anderson Darling test, Shapiro- Wilk test, etc.
- Graphical presentations: histogram, QQ-plots, scatter plots, residual plots, control charts, etc.

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