Statistical test Student

The Student s (W.S. Gossett) /-lest is useful for comparisons of the means and standard deviations of different analytical test methods. Descriptions of the theory and use of this statistic are readily available in standard statistical texts including those in the references [1-6]. Use of this test will indicate whether the differences between a set of measurement and the true (known) value for those measurements is statistically meaningful. For Table 36-1 a comparison of METHOD B test results for each of the locations is compared to the known spiked analyte value for each sample. This statistical test indicates that METHOD B results are lower than the known analyte values for Sample No. 5 (Lab 1 and Lab 2), and Sample No. 6 (Lab 1). METHOD B reported value is higher for Sample No. 6 (Lab 2). Average results for this test indicate that METHOD B may result in analytical values trending lower than actual values. 

This set of articles presents the computational details and actual values for each of the statistical methods shown for collaborative tests. These methods include the use of precision and estimated accuracy comparisons, ANOVA tests, Student s t-testing, The Rank Test for Method Comparison, and the Efficient Comparison of Methods tests. From using these statistical tests the following conclusions can be derived ... 

Student f-test A statistical test to establish if there is a significant difference between two mean values, taking account of the uncertainties associated with both values. 

This study examines the relationships of a database consisting of soil Pb, blood Pb (BPb) of children 6 years and younger, and scholastic achievement rates of 4th grade students from the Louisiana education assessment program (LEAP 21) in New Orleans. The data was from years 2000-2005 and reflects the pre-Hurricane Katrina conditions of New Orleans. Prior to the flood, schools were organized by attendance districts or neighborhood schools. This arrangement provided the opportunity to conduct a series of statistical tests to evaluate the associations between soil Pb, BPb and... 

The wheat bran used in these studies was milled for us from a single lot of Waldron hard red spring wheat. Other foods and diet ingredients were purchased from local food suppliers. Data from HS-I was analyzed statistically by Student s paired t test, each subject acting as his own control. A three-way analysis of variance (ANOVA) was performed to test for significant differences betwen diet treatments, periods and individuals in HS-II and HS-III. 

Mean + S.E. of the mean, calculated on the total number of mice per group (a non-tumor-beaiing mouse was counted as zero but incorporated into the calculation). The differences in median size of treated and control series were statistically significant (Student s t-test) at P < 0.05 unless for where P < 0.10 only. 

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. 

Equivalency testing. Once the method has been developed, it is compared to similar existing methods. Statistical tests are used to determine if the new and established methods give equivalent results. Typical tests include Student s Most for a comparison of the means and the / -test for a comparison of variances. 

Differences between the means were evaluated statistically by Student s t test. 

Translated into statistics, this implies that for safety pharmacology the risk of Type 2 errors (false negatives) should be decreased as much as possible, even if there is an increase in the risk of Type 1 errors (false positives). In other words, the statistical tests employed in safety pharmacology should err in the direction of oversensitivity rather than the reverse. A test substance found not to have significant safety risks based on preclinical studies, even after the use of oversensitive statistics, is more likely to be truly devoid of risk. As a consequence, the statistical analyses proposed for the CNS safety procedures described below (mainly two-by-two comparisons with control using Student s t tests) have been selected for maximal sensitivity to possible effects per dose at the acknowledged risk of making more Type 1 errors. 

Urine excretion is calculated in ml/kg. Uric acid-, creatinine- and ion-excretions are calculated in mmol/kg and expressed as percent changes versus controls. The changes are evaluated statistically using Student s t-test. 

A common statistical measurement is the Student f test or Student s t test. Student was the pseudonym of W. Gossett, an eminent mathematician. 

A neat reference mixture was prepared that contained 17 pure NHCs plus pyridine and quinoline as retention index markers (Table 1 Fig. 2). Relative amounts were adjusted to give approximately equal peak sizes. Triplicate analyses were performed on the 65 °C headspace above this mixture and above several wastewaters. To minimize any effect of column aging on peak retention times, the reference and wastewater replicates in each test series were alternated. Reproducibilities were excellent with standard deviations averaging 0.12 retention units overall and 0.05 retention units for the reference mixture. Reference-peak to sample-peak correlations were performed by a variety of statistical procedures including z tests. Student-t tests and, later, the procedure described in Section 3.2. 

Since statistical tests determined that the various features were normally distributed, we felt that the findings warranted some cautious claims about how current students were doing or similar students would do on average. To make our case, we drew together the results of both the scoring and the statistical analysis, and made some specific observations. 

They did not recall uniform amounts of information about the five situations, however, and there were distinct differences in how much they remembered. Table 7.3 provides some summary statistics about students recollections. A multivariate test of repeated measures shows that the mean numbers of nodes recalled for the five situations differed significantly, F(4, 22) = 7.96, p <. 01. That this difference is not attributable just to the differing numbers of potential nodes that could be learned can be seen in Table 7.3, where the number of nodes found in instruction is given as well as the proportion of these nodes that were recalled on average by the students. If students had some fixed propensity to remember each detail they encountered in instruction, they should be more likely... 

The choice of the optimal values of the parameter k we can do by means of statistical test of significance for regression coefficients in terms of Student s t-test. 

Statistical treatments. The data were processed with the SAS statistical package version 6.11, 4 edition (SAS Institute, Inc., Cary, NC). ANOVA analyses were performed at level a = 0.05, according to the model attribute = product + subject + product x subject, with subject as a random effect. Means were compared with the Newman - Keuls multiple comparison test (Student t... 

The preciseness of the primary parameters can be estimated from the final fit of the multiexponential function to the data, but they are of doubtful validity if the model is severely nonlinear (35). The preciseness of the secondary parameters (in this case variability) are likely to be even less reliable. Consequently, the results of statistical tests carried out with preciseness estimated from the hnal ht could easily be misleading—thus the need to assess the reliability of model estimates. A possible way of reducing bias in parameter estimates and of calculating realistic variances for them is to subject the data to the jackknife technique (36, 37). The technique requires little by way of assumption or analysis. A naive Student t approximation for the standardized jackknife estimator (34) or the bootstrap (31,38,39) (see Chapter 15 of this text) can be used. 

Unfortunately, not enough time is spent teaching students to think critically about the models they are using. Most mathematics and statistics classes focus on the mechanics of a calculation or the derivation of a statistical test. When a model is used to illustrate the calculation or derivation, little to no time is spent on why that particular model is used. We should not delude ourselves, however, into believing that once we have understood how a model was developed and that this model is the true model. It may be in physics or chemistry that elementary equations may be true, such as Boyle s law, but in biology, the mathematics of the system are so complex and probably nonlinear in nature with multiple feedback loops, that the true model may... 

All data were expressed as means SEM. The Student s t test was used when two groups of data were compared. For multiple comparisons the Newman-Keuls test was used. Other statistical tests, when used, are indicated in the appropriate figure legends. A value of P < 0.05 was considered statistically significant. 

An appropriate sample size, or number of replicates, can be calculated for the type of statistical test by using the a and P error, the minimal detectable difference between two test procedures, and the variability (standard deviation) of data determined from previous neutralization system validations. The statistical test chosen to detect if there was a significant comparative increase or decrease in microorganism populations is the two-tailed, pooled Student s f-test. Both and values have been determined, 0.05 and 0.10, respectively. The minimal detectable difference is the minimal difference between samples from two procedures that the researcher would consider as significant and would want to be assured of detecting. Minimal differences that have been published are 0.15, 0.20, and 0.30 log 10 differences between data from Phase 1 and those from other phases [4,19,20]. The 0.15 logic difference will be used for this validation, because it is the most conservative and is from a validation test that involves multiple samples (replication) and a statistical analysis [4]. The final requirement, variability of the data, will be difficult to establish, especially because many researchers will be performing this validation for the first time. If past data are unavailable, then an option is to use an excessive sample size (at least 10) and use the data from that validation to determine an appropriate sample size for future validation studies. 

Classical statistical tests can be applied mainly to validate regression models that are linear with respect to the model parameters. The most common empirical models used in EXDE are linear models (main effect models), linear plus interactions models, and quadratic models. They all are linear with respect to the p>arameters. The most useful of these (in DOE context) are 1) t-tests for testing the significance of the individual terms of the model, 2) the lack-of-fit test for testing the model adequacy, and 3) outlier tests based on so-called externally studentized residuals, see e.g. (Neter et. al., 1996). 

The two-sample t-test (or Student s t-tesi) is the most widely used parametric statistical test. This test compares the means of two populations that should be normally distributed when a sample size is small. The test statistic is formed as the mean difference divided by its standard error, that is, the difference of measured expressions normalized by the magnitude of noises. If the difference of the measured expressions is very large relative to its noise, it is claimed as being significant. Formally, suppose we want to test null hypotheses, H/. pji = pj2, against alternative hypotheses, Hj pji pp, foij= 1, 2,..., m. The test statistic for each j is... 

Statistical evaluation. Student s t-test (two-tailed) was used for weight of rats and food intake. Differences in plasma lipids, lipoproteins and lipoprotein lipase activities were evaluated with Wilcoxon s test (two-tailed). 

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