Two-tailed t test

The sorbent materials that performed best in the capacity and desorption efficiency tests were investigated further with respect to the stability of the sorbed analyte. Preliminary tests of analyte stability were conducted by a procedure similar to that in the desorption efficiency tests the procedure differed in that samples were stored 7 d prior to analysis rather than Id. To be acceptable, a sorbent material had to exhibit no statistically significant loss of analyte at the 0.05 significance level by a two-tailed t test. 

The results as summarized in Table V indicated that the stability was satisfactory for all three methods. To be acceptable, the average recovery of each analyte had to be at least 80%, and the difference between the average recovery on the first day and the average recovery after storage (for at least 7 d) had to be statistically insignificant at the 0.05 significance level by a two-tailed t test (9). 

Method two-tailed t test. First determine whether the variations are compatible. 

The critical value of the t test can be abbreviated as fa(2),v, where a(2) refers to the two-tailed probability of a and v = n — 1 (degree of freedom). For the two-tailed t test, compare the calculated t value with the critical value from the t distribution table. In general, if t > ta(2),v, then reject the null hypothesis. When comparing the means of replicate determinations, it is desirable that the number of replicates be the same in each case. 

Results of a two-tailed t test comparing the FDW/IDW obtained from conventional cultures and the gas feed cultures that were run at the same time in-... 

All values are expressed as mean SD. Statistical evaluation is carried out by two-tailed t-test for paired or unpaired observations. 

Zinc and copper values are expressed as mean S.D. Zinc and copper were measured using flame atomic absorption spectrophotometry. A two tailed t-test was used to compare the means for copper (p = 0.8) and for zinc (p = 0.6). 

Data sets were analyzed using a two-population independent two-tailed t-test or an analysis of variance (anova). Figures show means s.e.m. In aU cases, P-values less than 0.05 were considered as significant. 

The initial contraction produced by the submaximal dose A of the chosen contractile agonist is determined. This is then compared to the contraction produced by a second addition of dose A of the same contractile agent, performed after addition to the organ bath of the cannabinoid (or its vehicle). Contractile responses are expressed in g tension (Subheading 3.43.), and comparisons can be made using Student s two-tailed t-test for paired data. 

Continuing with the example about oil well production, the potential buyer was quite perplexed at the result obtained from the two-tailed t test, since it differed from that previously obtained via the original two-tailed Z test. An engineer explained that the difference was probably a resnlt of lack of knowledge concerning the population variance, caused failure to reject the null hypothesis (note that the rejection points were wider). 

A CRM for vitamins in honey does not exist at present and it is unlikely that one could prepare a RM due to the known instability of analytes. Therefore, to evaluate the bias, one must analyse the material by independent methods (Leon-Ruiz et al. 2011) or, more commonly, evaluate the recovery of known amounts of analytes spiked to honey. The first method is based on the fact that there is a negligible statistical probability that two independent methods may provide data affected by same bias, whereas in the spiking/recovery technique, recovery values statistically indistinguishable from 100% e.g. for a two-tailed t-test) indicate the absence of a bias. Table 13.5 shows recovery values of between 85 and 108.7%. Although a number of these recoveries different from 100% probably indicate some bias, it has been previously observed (AOAC 1998) that for low concentration levels recoveries can normally differ from 100%. AOAC guidelines (AOAC 1998) consider recovery levels between 80%... 

The Michaelis-Menten model was fitted to the experimental data using standard nonlinear regression techniques to obtain estimates of and K (Fig. 4.1). Best-fit values of and K of corresponding standard errors of the estimates plus the number of values used in the calculation of the standard error, and of the goodness-of-fit statistic are reported in Table 4.3. These results suggest that succinate is a competitive inhibitor of fumarase. This prediction is based on the observed apparent increase in Ks in the absence of changes in Vmax (see Table 4.1). At this point, however, the experimenter cannot state with any certainty whether the observed apparent increase in Ks is a tme effect of the inhibitor or merely an act of chance. A proper statistical analysis has to be carried out. For the comparison of two values, a two-tailed t-test is appropriate. When more than two values are compared, a one-way analysis of variance (ANOVA),... 

All statistical computations were performed using GraphPad Prism version 4.0a for Mac OS X (GraphPad Software, San Diego, California, USA). Values of experimental groups are shown as mean SEM unless otherwise stated. One-way ANOVA with Tukey s post-test analysis was used to determine statistical significance. Where appropriate, either two-tailed t-tests or Mann Whitney U tests were performed. A probability of P < 0.05 was considered to be statistically significant. 

Both one-tailed and two-tailed t-tests can be used, depending on circumstances, but two-tailed are often preferred Table 3). The application of all three t-test equations is demonstrated by the following examples. 

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