Using Excel’s worksheet functions for 1-factor ANOVA
Data analysis for one factor analysis of variance ANOVA with an equal number of replicates for each ‘treatment’ is probably quicker and easier by using Excel’s traditional functions in the spreadsheet calculations.
One of the advantages is that the manual calculations return live worksheet functions rather than the static values returned by the Data Analysis Toolpak add-ins, so we can easily edit the underlying data and see immediately whether that makes sense or shows a difference to the outcome. On the other hand, we have to run the Data Analysis tool over again if we want to even change one value of the data.
The following figure shows how simple it can be in analyzing a set of test data obtained from sampling at 6 different targets of a population with the laboratory samples analyzed in four replicates. The manual calculations have been verified by the Single Factor Tool in the Data Analysis add-in, as shown in the lower half of the figure.
With the variance results in the form of MS(between) and MS(within), we can proceed easily to estimate the measurement uncertainty as contributed by the sampling and analytical components.
A simple example of sampling uncertainty evaluation
In analytical chemistry, the test sample is usually only part of the system for which information is required. It is not possible to analyze numerous samples drawn from a population. Hence, one has to ensure a small number of samples taken are representative and assume that the results of the analysis can be taken as the answer for the whole…..
Since the publication of the newly revised ISO/IEC 17025:2017, measurement uncertainty evaluation has expanded its coverage to include sampling uncertainty as well because ISO has recognized that sampling uncertainty can be a serious factor in the final test result obtained from a given sample ……
The concept of measurement uncertainty – a new pespective
Nearly all analysis requires the taking of a sample, a procedure which itself introduces uncertainty into the final test result. Hence a measurement uncertainty should cover both the uncertainties of sampling and analysis….
A worked example to estimate sampling precision and MU
To understand how to go about evaluating sampling uncertainty and quality control of sampling, we must be familiar with the basic analysis of variance ANOVA principles….
An illustration of One-way ANOVA