Student’s /-test

There are two common methods for comparing results (a) Student s -test and (b) the variance ratio test (F-test). 

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. 

Student s /-test for the difference in the biases between two methods Mean Difference mean(d) = 0.084... 

Homoscedasticity is an important assumption for Student s /-test, analysis of variance, and analysis of covariance. 

The value of / for Student s /-test is calculated using the formula... 

Student s test compares the means of both groups and is restricted to two sets of data, which should come from a normal distribution. The t-test works well if the variances of both groups are not very different and the number of data in each data set is similar. 

Calculate bias and check for its statistical significance. A simple way to perform this is through a Student s /-test [59] ... 

Standard addition, 154, 355 Standard deviation, 387 Stationary phase, 66, 88 Stick diagram, 290 Student s test, 391 Supercritical phase, 96 Support electrolyte, 348... 

Assume that the Student s /-test is applied to test whether or not there is an effect in one variable (for example, x4 = HOLE COUNT) of treatment with 0.05 mg/kg BHT compared with controls. The significance level 5% is then chosen, that is, 5% false positives (type I errors or a-errors) are accepted in the research. When one more measurement (x5 = HOLE TIME) is taken on the same set of data and Student s /-test is applied again to the data, the risk for at least one false positive is no longer 1.0 - 0.95 = 5% but 1.0 - 0.952 = 9.75%. When 10 variables are measured, as in the BHT 920 example, the risk is 1.0 - 0.9510 = 40.13% (a more detailed table has been published elsewhere [10]). This phenomenon is usually referred to as the increased risk of type I errors. 

As a second example of hypothesis testing with PLS, the amphetamine data are used. These data illustrate a control-treatment study. Such data are traditionally handled by univariate Student s /-tests applied to each variable separately. By means of the present methodology, the data are put in a three-way table, which is then unfolded (Figure 6.10) to the usual two-way table, X, which has 10 rows and 4 6 = 24 columns. A one-dimensional Y is... 

The adequacy of the regression equation obtained was tested by the Student s test at five test points, the results being given in Table 3.43. 

Student s /-test Parametric (1) Simple to calculate (2) Easily interpreted (1) Data must be normally distributed (2) Multiple testing requires false positive rate control... 

Note The significance of the differences between the means for experimental groups and control group was tested using Student s /-test. 

In the previous section, Student s /-test was used to compare the statistical significance of mean results obtained by two different methods. When we wish to compare more than two methods or sample treatments, we have to consider two possible sources of variation, those associated with systematic errors and those arising from... 

NS = not significant LSDto.ooi = least significant difference (standard error of difference x Student s test value) at the 0.001 level = significant at the 0.001 level... 

Fig. 3 Pb effect on expression of cytokines IL-6, TGF-P1, and IL-18 in the brain. Cytokine mRNA from the brains of female and male mouse pups at pnd21 was quantified by real-time RT-PCR. Whole-brain RNA was isolated using a Qiagen lipid Tissue kit. Mouse pup brains from each litter were pooled according to gender. AU cytokine RNA quantitation results were normalized to endogenous GAPDH. Each bar represents mean S.D. for an iV of 3 L. Significance, indicated by an asterisk,, was determined by the Student s /-test, p < 0.05. The p value for both female and male lL-6 gene expression Pb is 0.056 and the p value for male TGF-P1 gene expression Pb is 0.20 (Data for lL-6 and TGF-beta has been published in Kasten-JoUy et al., J. Biochem. Molec. Toxicol. 2010)...

The most noticeable difference in test content between a schema-based test and a traditional test is the emphasis in the former on intermediate decisions. A schema-based test will attempt to tease apart the four knowledge components of one or more schemas, and these knowledge components may be utilized at different points in the formulation of a student s test response. It is very difficult to construct a test item in which all four knowledge components for one schema are assessable. Almost certainly some will be invisible. Thus, to evaluate a single schema, one probably will need several items, each devoted to the evaluation of one or perhaps two of the components. The questions that tap into the various knowledge components are unlike those that typically appear on tests because they target the intermediate steps at which these knowledge components are needed. Consider, for example, the nature of the questions asked in the exercises of SPS (see Chapter 5). 

If you can assume that your data are normally distributed, the main test for comparing two means from independent samples is Student s /-test (see Boxes 41.1 and 41.2, and Table 41.2). This assumes that the variances of the data sets are homogeneous. Tests based on the /-distribution are also available for comparing paired data or for comparing a sample mean with a chosen value. 

The recorder used printed out a total activity count every 5 min. The first 4 of these, representing initial exploratory behaviour, were discarded, and a mean activity count was then obtained for the remaining 100 min. Statistical analysis was carried out using the Two-sample rank test (Goldstein, 1964) and Student s /-test. 

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