Text, significance, statistical

Thus, SE(ai) = and SE(af) = Now returning to Equation (B.3.1), T is the experimental deviation over the standard error and if this value is larger than the value in a Student s F-distribution table (see any text on statistics for this table) for a given degree of confidence, for example, 95 percent (7 xp = expected deviation/standard error), then the hypothesis is rejected, that is, the y-intercept is significantly different than zero. If < t xp then the hypothesis is accepted and dij can be reported as ... 

The section following shows a statistical test (text for the Comp Meth MathCad Worksheet) for the efficient comparison of two analytical methods. This test requires that replicate measurements be made on two different samples using two different analytical methods. The test will determine whether there is a significant difference in the precision and accuracy for the two methods. It will also determine whether there is significant systematic error between the methods, and calculate the magnitude of that error (as bias). 

The test to determine whether the bias is significant incorporates the Student s /-test. The method for calculating the t-test statistic is shown in equation 38-10 using MathCad symbolic notation. Equations 38-8 and 38-9 are used to calculate the standard deviation of the differences between the sums of X and Y for both analytical methods A and B, whereas equation 38-10 is used to calculate the standard deviation of the mean. The /-table statistic for comparison of the test statistic is given in equations 38-11 and 38-12. The F-statistic and f-statistic tables can be found in standard statistical texts such as references [1-3]. The null hypothesis (H0) states that there is no systematic difference between the two methods, whereas the alternate hypothesis (Hf) states that there is a significant systematic difference between the methods. It can be seen from these results that the bias is significant between these two methods and that METHOD B has results biased by 0.084 above the results obtained by METHOD A. The estimated bias is given by the Mean Difference calculation. 

A comparison of the imprecision of two methods may assist in the choice of one for routine use. Statistical comparison of values for the standard deviation using the F test (Procedure 1.2) may be used to compare not only different methods but also the results from different analysts or laboratories. Some caution has to be exercised in the interpretation of statistical data and particularly in such tests of significance. Although some statistical tests are outlined in this book, anyone intending to use them is strongly recommended to read an appropriate text on the subject. 

Fig. 25. Determination of the confidence interval. Qi(r) is the total quadratic deviation assuming a relaxation rate value r and fitting all other parameters in Eq.(24). Its absolute minimum at r2 defines the most probable relaxation rate R. Q2 is the minimum of Qi(r) and Q i equals Q2 plus the least significant increment determined by statistical methods. This defines the confidence interval C.I. comprised between the two vertical lines. For more details, see the text.

These sections include brief discussions of statistics, data presentation, and terminology. The two major points regarding statistics are that the litter (or mating pair) is the unit of comparison, and that significance tests can be used only as a support for the interpretation of results—the interpretation itself must be based on biological plausibility. That the litter is the unit of comparison is a guiding principle ofvirtually all texts on the subject (e.g., see ref 7). It should be stated that this guideline does not require that statistical analyses be performed on every study. It is implied that statistical analyses should be used as a tool for interpretation. 

Table2 Percentages of colabeling of BrdU with markers for neural progenitors in DG. BrdU+ cells were sampled for colabeling with either Musashil or Nestin as described in the text. Statistically significant differences between percentages were not detected...

Some texts also present tables for a two-tailed F-test, but because we do not employ this in this book, we omit it. However, a two-tailed F statistic at 10% significance is the same as a one-tailed F statistic at 5 % significance, and so on. 

The / distribution is somewhat similar in concept to the F distribution but only one degree of freedom is associated with this statistic. In this text the /-test is used to determine the significance of coefficients obtained from an experiment, but in other contexts it can be widely employed for example, a common application is to determine whether the means of two datasets are significantly different. 

Most tables of / distributions look at the critical value of the / statistics for different degrees of freedom. Table A.4 relates to the two-tailed /-test, which we employ in this text, and asks whether a parameter differs significantly from another. If there are 10 degrees of freedom and the / statistic equals 2.32, then the probability is fairly high, slightly above 95 % (5 % critical value), that it is significant. 

Consult a text book on statistics and set up a triangular test using two different variants of one of the recipes. Carry out the test and analyse the results. Repeat the exercise using two different batches of the same product which are identical except for the random variations that normally occur in cooking. Are they significantly different statistically ... 

If you consult a table of t values in a statistics text (a portion of such a table is shown in Figure 11-15), you will find, for 95% probability and 3 degrees of freedom, that t = 3.18. Since the calculated f-statistic is less than f-critical from the table, the intercept value of 0.0011 does not differ significantly from zero. 

There are many good analytical textbooks now available, however most concentrate on a detailed discussion of analytical techniques (e.g. those based upon the principles of chromatography and spectroscopy), and at the expense of the more fundamental considerations of why the analysis is to be carried out and how the samples are to be taken. Whilst most modern texts will introduce the reader to the importance of sampling, many gloss over the serious errors which may be introduced into the results if the sampling protocol is not undertaken in a logical and statistically significant manner. 

Major depressive disorder is a disorder of mood in which the individual experiences one or more major depressive episodes without a history of manic, mixed, or hypomanic episodes. A major depressive episode is defined by the criteria listed in the Diagnostic and Statistical Manual of Mental Disorders, 4th ed.. Text Revision (DSM-IV-TR), published by the American Psychiatric Association. Depression is associated with significant functional disability, morbidity, and mortality. 

---