Analysis of variance ANOYA

The first is to normalize the data, making them suitable for analysis by our most common parametric techniques such as analysis of variance ANOYA. A simple test of whether a selected transformation will yield a distribution of data which satisfies the underlying assumptions for ANOYA is to plot the cumulative distribution of samples on probability paper (that is a commercially available paper which has the probability function scale as one axis). One can then alter the scale of the second axis (that is, the axis other than the one which is on a probability scale) from linear to any other (logarithmic, reciprocal, square root, etc.) and see if a previously curved line indicating a skewed distribution becomes linear to indicate normality. The slope of the transformed line gives us an estimate of the standard deviation. If... 

Finally keep in mind that analysis of variance (ANOYA) is the most powerful statistical technique for evaluating the results of factorial designs with replications if the significance of factors is of interest, rather than the models of their relationship. 

A common problem is to compare two or more sets of data. For example, a new analytical method may be assessed by analyzing a test material using the new and an established method. The means of a number of replicate measurement results obtained by each method will not be identical, but within the experimental uncertainty is there a significant difference The preferred method is to use analysis of variance (ANOYA) which can accommodate a number of variables and different numbers of data (see chapter 4). However, a quick test for two means can be performed by calculating a /-statistic and its associated probability. 

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