Analysis of Variance
LC•GC Europe Online Supplement
statistics and data analysis
9
Analysis of Variance
Shaun Burke, RHM Technology Ltd, High Wycombe, Buckinghamshire, UK. Statistical methods can be powerful tools for unlocking the information contained in analytical data. This second part in our statistics refresher series looks at one of the most frequently used of these tools: Analysis of Variance (ANOVA). In the previous paper we examined the initial steps in describing the structure of the data and explained a number of alternative significance tests (1). In particular, we showed that t-tests can be used to compare the results from two analytical methods or chemical processes. In this article, we will expand on the theme of significance testing by showing how ANOVA can be used to compare the results from more than two sets of data at the same time, and how it is particularly useful in analysing data from designed experiments.
With the advent of built-in spreadsheet functions and affordable dedicated statistical software packages, Analysis of Variance (ANOVA) has become relatively simple to carry out. This article will therefore concentrate on how to select the correct variant of the ANOVA method, the advantages of ANOVA, how to interpret the results and how to avoid some of the pitfalls. For those wanting more detailed theory than is given in the following section, several texts are available (2–5). A bit of ANOVA theory Whenever we make repeated measurements there is always some variation. Sometimes this variation (known as within-group variation) makes it difficult for analysts to see if there have been significant changes between different groups of replicates. For example, in Figure 1 (which shows the results from four replicate analyses by 12 analysts), we can see that the total variation is a combination of the spread of results within groups and the spread between the mean values (betweengroup variation). The statistic that measures the within and between-group
statistics and data analysis
9
Analysis of Variance
Shaun Burke, RHM Technology Ltd, High Wycombe, Buckinghamshire, UK. Statistical methods can be powerful tools for unlocking the information contained in analytical data. This second part in our statistics refresher series looks at one of the most frequently used of these tools: Analysis of Variance (ANOVA). In the previous paper we examined the initial steps in describing the structure of the data and explained a number of alternative significance tests (1). In particular, we showed that t-tests can be used to compare the results from two analytical methods or chemical processes. In this article, we will expand on the theme of significance testing by showing how ANOVA can be used to compare the results from more than two sets of data at the same time, and how it is particularly useful in analysing data from designed experiments.
With the advent of built-in spreadsheet functions and affordable dedicated statistical software packages, Analysis of Variance (ANOVA) has become relatively simple to carry out. This article will therefore concentrate on how to select the correct variant of the ANOVA method, the advantages of ANOVA, how to interpret the results and how to avoid some of the pitfalls. For those wanting more detailed theory than is given in the following section, several texts are available (2–5). A bit of ANOVA theory Whenever we make repeated measurements there is always some variation. Sometimes this variation (known as within-group variation) makes it difficult for analysts to see if there have been significant changes between different groups of replicates. For example, in Figure 1 (which shows the results from four replicate analyses by 12 analysts), we can see that the total variation is a combination of the spread of results within groups and the spread between the mean values (betweengroup variation). The statistic that measures the within and between-group