T test values for

Table 3.6 Student s t-test values for the hypothesis that the standard deviations for real and imaginary parts of the impedance, shown in Table 3.5, are equal. See Example 3.4.

Table 3.7 Student s t-test values for Example 3.4 for a test of logjQ — 0.

Table 3.8 t -test values for degree of freedom v and confidence level p. 

Table 10.2 (regression equation Section A) provides the actual h, values, the standard deviation of each h the t-test value for each h and the p-value for each h,. In multiple regression, the i-ratio and p-value have limited use. The standard deviation of the regression equation, Sy xi,x2,x3 = 0.5949, is just more than j log value, and the coefficient of determination, = 86.1%, which means the regression equation... 

For the majority of the 50 experiments = exp(—aCJ turned out to give the best lit. An explanation based on a pore blocking mechanism has been attempted (Beeckman and Froment, to be published). The parameter a was found to be identical for coking from either butene or butadiene and independent of the operating variables, as was concluded from the partial correlation coefficients between a and T, pg, pg, and po, respectir y, and the t-test values for the zero hypothesis for the partial correlation coefficient... 

In a first report [24], the enantioselectivities of various proteases were evaluated by comparing the biocatalyzedhydrolysis of2-chloroethyl esters of N-acetyl-i- and D-amino acids in water and their transesterification with w-propanol in butyl ether. By comparing the ratio of the kc t/Ku values for the l- and D-enantiomers in the two reactions, a remarkable relation of the proteases enantioselectivity was observed apparently, in this case, the organic solvents destroyed the selectivity of the tested enzymes. This finding... 

Sawicki, E., T. W. Stanley, T. R. Hauser, H. Johnson, and W. Elbert. Correlation of piperonal test values for aromatic compounds with the atmospheric concentration of benzo(a)pyrene. Int. J. Air Water Pollut. 7 57-70, 1%3. 

A useful plot for identifying factors that are important is a Pareto chart. The graph in Fig. 1 shows the t-test values in the horizontal axis and also includes a vertical line to indicate the p value (an effect that exceeds the vertical line maybe considered significant). As observed in the Pareto chart, enzyme concentration is the most significant variable influencing monolaurin molar fraction. 

Mean values for aggregation in dosage groups are compared to the vehicle control groups (for rabbits control values before drug administration). Statistical significance is evaluated by means of the Student s t-test (paired for rabbits unpaired for others). 

The longer t 2 values for the laboratory-aged samples reflect the lower average temperature and air movement In the laboratory as compared to the field situation. As expected, the vinyl laminate released the aldehydes much too rapidly but could be suitable for the alcohol component. The acrylic laminate might also be useful for the alcohol. The polymeric PVC and acrylic laminates produced a greater difference In the release of the C] and aldehydes than did the Mylar-coated vinyl dispensers evaluated In the previous test. If the Insect behavior requires that all of the components of the pheromone blend be released in a constant ratio and a rate proportional to their original concentration, then it Is likely that the alcohol would have to be be formulated in one dispenser (e.g. in 3-mll acrylic) and the Cj al and C. al in another (e.g. in Mylar-coated vinyl). Both of the dispensers could then be deployed at each location In the field. 

A second test compared 50 x 12 mm dispensers made of thinner acrylic film (3- instead of 6-mil) with those of 16-mil polymeric PVC each dispenser contained about 10 mg of synthetic racemic pheromone. These were aged in a California greenhouse as in the previous test, and the lure contents were measured weekly for a 6-week period. The analyses showed similar t /2 values for the 2 formulations 16 days for the 16-mil polymeric PVC and 18 days for the 3-mil acrylic dispensers. 

The T test value is a measure of the regression coefficient s significance, i.e., does the coefficient have a real meaning or should it be zero. The larger the absolute value of T the greater the probability that the coefficient is real and should be used for predictions. A T test value 1.7 or higher indicates that there is a high probability that the coefficient is real and the variable has an important effect upon the response. 

The next step is to determine if the obtained t-test value of 8.00 is significant. This is done by using a t-table which can be found in any basic statistics book. To use the t-table, the degrees of freedom are calculated. In this case, the degrees of freedom are 10(12-2= 10). With the t-table, locate the column for a =. 05 and degrees of freedom (d.f.) = 10. The table for a two-tailed test indicates a value of 2.23. Since our obtained t-test value of 8.00 is greater than the table value, we can conclude that there is a significant correlation between the number of traffic accidents and the number of trips to Big City, USA. 

The results obtained for a-tocopherol were compared with an official method (Fabianek et al., 1968) and were in good agreement with no significant difference between these methods observed at 95% confidence level, and gave statistical (F and t tests) values of f,ab = l-Ol < f ai = 6.39, t i = 0.89 < = 2.78 and = 1.02 < f ai = 6.39,... 

FIGURE 116.2 Effective photosynthetic quantum yield of Enteromorpha linza measured after 30 min dark adapta tion, 15 min exposure, and after increasing recovery times in the shade, calculated as (Ent - Ff)/Fm. Gray bars denote the specimens exposed to unfiltered solar radiation. Black bars denote the specimens exposed to UV-A and PAR. White bars represent the specimens exposed to PAR only. The data are mean values of eight measurements and SE. The values for unfiltered solar radiation and under the 320 nm cutoff filter treatments are statistically significantly different from the PAR-only values (395 nm cutoff) in each set with P< 0.001, P< 0.01, or P< 0.1, respectively, as indicated by the student s t-test. Irradiances for the experiment were as follows PAR 349 W m, UV-A 44.15 W m, and UV-B 1.34 W m. (From Hader, D. P., Lebert, M., and Helbling, E.W., /. Photochem. Photohiol. B Biol. 62, 43, 2001. With permission.)... 

The standard deviation of the distribution of means equals cr/N. Since cr is not usually known, its approximation for a finite number of measurements is overcome by the Student t test. It is a measure of error between p and x. The Student t takes into account both the possible variation of the value of x from p on the basis of the expected variance and the reliability of using 5- in... 

An analytical procedure is often tested on materials of known composition. These materials may be pure substances, standard samples, or materials analyzed by some other more accurate method. Repeated determinations on a known material furnish data for both an estimate of the precision and a test for the presence of a constant error in the results. The standard deviation is found from Equation 12 (with the known composition replacing /x). A calculated value for t (Eq. 14) in excess of the appropriate value in Table 2.27 is interpreted as evidence of the presence of a constant error at the indicated level of significance. 

The t test is also used to judge whether a given lot of material conforms to a particular specification. If both plus and minus departures from the known value are to be guarded against, a two-tailed test is involved. If departures in only one direction are undesirable, then the 10% level values for t are appropriate for the 5% level in one direction. Similarly, the 2% level should be used to obtain the 1% level to test the departure from the known value in one direction only these constitute a one-tailed test. More on this subject will be in the next section. 

In the two-sample collaborative test, each analyst performs a single determination on two separate samples. The resulting data are reduced to a set of differences, D, and a set of totals, T, each characterized by a mean value and a standard deviation. Extracting values for random errors affecting precision and systematic differences between analysts is relatively straightforward for this experimental design. 

The t-values in this table are for a two-tailed test. For a one-tailed test, the a values for each column are half of the stated value, column for a one-tailed test is for the 95% confidence level, a = 0.05. For example, the first... 

The effective saturation depth,, represents the depth of water under which the total pressure (hydrostatic plus atmospheric) would produce a saturation concentration equal to for water ia contact with air at 100% relative humidity. This can be calculated usiag the above equation, based on a spatial average value of T, measured by a clean water test. For design purposes,, can be estimated from clean water test results on similar systems, and it can range from 5 to 50% of tank Hquid depth. Effective depth values for coarse bubble diffused air, fine bubble diffused air, and low speed surface aerators are 26 to 34%, 21 to 44%, and 5 to 7%, of the Hquid depth, respectively. 

The Van Krevelen-Hoftyzer relationship was tested experimentally for the second-order system in which CO9 reacts with either NaOH or KOH solutions by Nijsing et al. [Chem. Eng. ScL, 10, 88 (1959)]. Nijsing s results for the NaOH system are shown in Fig. 14-15 and are in excellent agreement with the second-order-reaction theory. Indeed, these experimental results can be described very well by Eqs. (14-80) and (14-81) when values of V = 2 and T)JT = 0.64 are employed in the equations. 

In Fig. 30-25, representation of the fault detection monitoring activity, there appears to be two distinct time periods of unit operation with a transition period between the two. The mean parameter value and corresponding sample standard deviation can be calculated for each time. These means can be tested by setting the null hypothesis that the means are the same and performing the appropriate t-test. Rejecting the null hypothesis indicates that there may have been a shift in operation of the unit. Diagnosis (troubleshooting) is the next step. 

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