One-sided t-test

Analysis of variance appropriate for a crossover design on the pharmacokinetic parameters using the general linear models procedures of SAS or an equivalent program should be performed, with examination of period, sequence and treatment effects. The 90% confidence intervals for the estimates of the difference between the test and reference least squares means for the pharmacokinetic parameters (AUCo-t, AUCo-inf, Cmax should be calculated, using the two one-sided t-test procedure). 

Significant difference (P<0.01) from the corresponding control (II, III or IV). Merc cor 30 in water and in 90% ethanol differs significantly from Merc iod 30c in water and 90% ethanol (P<0.01). Control dilutions made in water (I-IV) differ from those containing alcohol (V and VI). (one-sided t-tests throughout). No significant differences between water controls (I-V) (ANOVA). 

Mean with unknown variance t variable and t distribution Two variances F variable and F distribution Determine the critical region(s) in terms of the test statistic. For example, one-sided t-test t < tay, or two-sided E-test F < F ny y and E> Ei a/2,vi,v2-Calculate the test statistic for the sample data. 

The maximum concentration allowed for nitrate concentration under European Union regulations is 50mgl . To determine whether this regulated value is not exceeded, we perform a one-sided t-test at the upper end. By using the mean of 51.2 and the standard deviation of s = 0.316, we calculate the t-value according to Eq. (2.31) ... 

In Example 2.4, we evaluated the nitrate concentration of drinking water using a one-sided t-test at the upper end and testing the hypothesis that the regulated value of SOmgl" nitrate is not exceeded (Hg-.x < pHp.x > p). The computed f-value corresponds to a significance level (p-level) of 0.002373. This value is lower than the specified level of a = 0.05, so that the null hypothesis is rejected as before. 

Tables 5.23 and 5.24 give the ROC AUC for the univariate models for GIDAS and PCDS. The in-sample and out-of-sample predictive accuracy of the models is high. Regarding the latter one, the models derived from PCDS tend to be more accurate. The optimism is very small (<0.002). One-sided t-tests were used to evaluate the differences between cross-validated multivariate models (as given in Tables 5.15 and 5.20 ) and the corresponding univariate models.

However, if (x is a specified regulatory limit, e.g., a maximum allowed concentration of a compound in a foodstuff, we probably wish to test the null hypothesis [H X2 < x] against the alternative hypothesis [Hj X2 > (x], i.e., Hj proposes that the regulatory hmit has been exceeded. Here, since we are interested only in a one-way deviation, we use a one sided t-test for which the appropriate L = 1.943 (Table 8.1), which is very close to the experimental t-value of 1.918. Nonetheless, by applying the appropriate one sided t-test for this experimental t-value to our chosen null hypothesis [H X2 (x], since the condition for rejection of H is t > t which is not true in this case, we can not reject H , i.e. the regulatory limit was not breached (though it was close ). 

Data were expressed as the mean standard error of the mean (SEM). Differences between means were determined using one-way analysis of variance (ANOVA) followed by the Tukey-Kramer post hoc comparison and two-sided t test. For comparing percentages, nonparametric tests were also applied (Mann-Whitney, Kruskal-Wallis). Differences were considered significant when p < 0.05. 

Next, concentrate on the attractiveness of the odors If equally attractive, the animals would spend a proportion of 0.5 on each side. In a one-sample t test, compare the measured proportion of time against that mean of 0.5. 

The one-sample t test will be used to test the null hypothesis. As there are 10 observations and assuming the change scores (the random variable of interest) are normally distributed, the test statistic will follow a t distribution with 9 df. A table of critical values for the t distribution (Appendix 2) will inform us that the two-sided critical region is defined as t < -2.26 and t > 2.26 - that is, under the null hypothesis, the probability of observing a t value < -2.26 is 0.025 and the probability of observing a t value > 2.26 is 0.025. 

The one-sample t test is being used for a two-sided test of the null hypothesis, Hq. g = 0. For each of the following scenarios, define the rejection region for the test ... 

As with the t-test, other significance levels may be used for the f-test and the critical values can be found from the tables listed in the bibliography at the end of Chapter 1. Care must be taken that the correct table is used depending on whether the test is one- or two-sided for an a% significance level the 2a% points of the F distribution are used for a one-sided test and the a% points are used for a two-sided test. If a computer is used it will be possible to obtain a P-value. Note that Excel carries out only a one-sided E-test and that it is necessary to enter the sample with the larger variance as the first sample. Mlnitab does not give an E-test for comparing the variances of two samples. 

In the second quantitative study of this diesis (part 0) 1 deviated from this practice as the space in the questtonnaire was not as limited as in this study. Here, the ahead of the trend component and the hi er benefits expected component were also signiflcandy correlated (r=0368, p<0,001, two-sided t-test) and formed one single fiictor. 

For the one-sample t-test the null hypothesis is that the mean, p, of X for the population from which the sample was selected is equal to po The test is performed by choosing a significance level, ot, and calculating using the t-distribution the critical values on both tails needed to give a critical region whose volume is equal to a. This is the two-sided test version of the one-sample t-test. The use of slightly different null hypotheses of p > po or p < Po leads to one-sided test versions of the one-sample t-test. 

The most widely used test is that for detecting a deviation of a test object from a standard by comparison of the means, the so-called t-test. Note that before a f-test is decided upon, the confidence level must be declared and a decision made about whether a one- or a two-sided test is to be performed. For details, see shortly. Three levels of complexity, a, b, and c, and subcases are distinguishable. (The necessary equations are assembled in Table 1.10 and are all included in program TTEST.)... 

This amounts to stating the analytical results obtained from HPLC-purity determinations on one batch are not expected to exceed the individual limit AIL more than once in 20 batches. Since a one-sided test is carried out here, the t(a = 0.1,/) for the two-sided case corresponds to the /(a/2 = 0.05,/) value needed. The target level TL is related to the AIL as is the lower end... 

Results The uncertainties associated with the slopes are very different and n = H2, so that the pooled variance is roughly estimated as (V + V2)/2, see case c in Table 1.10 this gives a pooled standard deviation of 0.020 a simple r-test is performed to determine whether the slopes can be distinguished. (0.831 - 0.673)/0.020 = 7.9 is definitely larger than the critical /-value for p - 0.05 and / = 3 (3.182). Only a test for H[ t > tc makes sense, so a one-sided test must be used to estimate the probability of error, most likely of the order p = 0.001 or smaller. 

Table 10.2 Generic output from a one-sided two-sample t-test for higher clearances with urinary acidification...

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