Robust methods or non-parametric tests

A straight line supposes that the errors in y follow the law of Normal distribution. is the determination coefficient that conveys information about how the variations of x overlap variations in y. 

In classic calculations the experimental error is considered to affect the y value exclusively and not the concentration recorded in x. If this is not the case, the data points will not have the same quality for the regression line hence comes the idea of according less value to data more distant from the line. Through iterative calculations the equation of a straight line is reached which takes account of the weighting of each point. 

In order to compare whether two methods of analysis are highly correlated, a series of n standards of different concentrations are analysed by two pathways. Each standard is next represented by a point on a graph where x bears the results of method 1 and y the corresponding results from the second method. The correlation coefficient R is determined and formula 22.26 is applied. If the t value obtained is greater than the value found in the table for — 2 degrees of freedom, there is a strong correlation between the two analytical methods. 

Analysis by multiple linear regression leads to the prediction of a result (the dependent variable) when it depends upon a certain number of factors (the independent variables). Software allows this type of calculation in which the contribution of each factor is determined using standards. The prediction of the result is calculated by a general formula, such as 22.27 and as a composite of three factors in x  

The statistical tests developed above assume that the data follow the Normal distribution. However, there are analytical methods for which the results reveal 

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