Hypothesis testing analytical chemistry

It is unnecessary to delve into hypothesis testing strategies further to discern the role of values in the choice of decision rules. The following are immediately noteworthy. First, whether one observes analytical chemistry, an old and well established discipline, or chemical oncology, a relatively recent one, the observer is struck by the fact that making odds is an indispensable step of the process of converting data to information. This fact alone establishes beyond reasonable doubt that science is no less subjective than other rational human endeavors. 

There are two main families of statistical tests parametric tests, which are based on the hypothesis that data are distributed according to a normal curve (on which the values in Student s table are based), and non-parametric tests, for more liberally distributed data (robust statistics). In analytical chemistry, large sets of data are often not available. Therefore, statistical tests must be applied with judgement and must not be abused. In chemistry, acceptable margins of precision are 10, 5 or 1%. Greater values than this can only be endorsed depending on the problem concerned. 

The point about this example is that all analytical chemistry should be fit for purpose. When you make a decision based on a statistical test, the choice of the probability level at which the null hypothesis is rejected is made by the user, not by a book or software package. Do not adopt probability levels blindly, but consider the risk of making the different types of error. 

Hartmann, C., Smeyers Verbeke, J., Penninckx, W., VanderHeyden, Y., Venkeerberghen, P., and Massart, D.L. (1995) Reappraisal of hypothesis testing for method validation detection of systematic error by comparing the means of two methods or two laboratories. Analytical Chemistry, 67, 4491 4499. 

Determine whether temperature has a statistical effect on the decomposition of cinnamaldehyde using analysis of variance (ANOVA). (For how to perform ANOVA,. see S. R. Crouch and F. J. Holler. Applications of Microsoft Excel in Analytical Chemistry, Chap. 3, Belmont, CA Brooks/ Cole, 2004.) In the same wtty, determine if time of heating has an effect, (h) Using the data in part (g), assume that decomposition begins at 60°C and test the hypothesis that there is no effect of temperature or time. 

In reviewing the history of detection limits (in Analytical Chemistry) it is helpful to keep these several, often implicit, differences in mind. If it Is agreed that the concept of detection has meaning, then it is essential that the above questions be fully defined and explicitly addressed. In the view of this author a meaningful approach to analyte detection must be consistent with our approach to uncertainty components of measurement processes and experimental results the soundest approach is probably the last [hypothesis testing] tempered with an appropriate measure of the first [scientific intuition]. 

With the hypothesis and confidence level selected, the next step is to apply the chosen test. For outliers, one test used (perhaps even abused) in analytical chemistry is the Q or Dixon test ... 

Before choosing the critical value, one specifies one s tolerance for Type I errors, defined as erroneous rejection of the null hypothesis when it is true. Type I errors are sometimes called/fltoe positives or false rejections. Regardless of the choice of the critical value, there is always the probability of a Type I error. For large enough critical values, this probability is small and generally can be tolerated. The tolerable probability that one specifies is called the significance level of the test and is usually denoted by a. In radioanalytical chemistry, it is common to set a = 0.05. If O = 0.05, then analyte-free samples should produce false positive results at a rate of only about one per twenty measurements. 

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